Atlas-like websites on specific areas of mathematics In this post, we look for the existing atlas-like websites providing well-presented classifications or database about some specific areas of mathematics. Here are some examples:  


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*GroupNames: https://people.maths.bris.ac.uk/~matyd/GroupNames

Finite groups of order ≤500, group names, extensions, presentations,
  properties and character tables.



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*Atlas of Finite Group Representations: http://brauer.maths.qmul.ac.uk/Atlas/v3/

This ATLAS of Group Representations has been prepared by Robert
  Wilson, Peter Walsh, Jonathan Tripp, Ibrahim Suleiman, Richard Parker,
  Simon Norton, Simon Nickerson, Steve Linton, John Bray, and Rachel
  Abbott (in reverse alphabetical order, because I'm fed up with always
  being last!).   It currently contains information (including 5215
  representations) on about 716 groups [mainly finite simple groups or almost simple].



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*Atlas of subgroup lattice of finite almost simple groups: http://homepages.ulb.ac.be/~dleemans/atlaslat/

This atlas contains all subgroup lattices of almost simple groups $G$
  such that  $S≤G≤Aut(S)$ and $S$ is a simple group of order less than 1
  million appearing in the Atlas of Finite Groups by Conway et al. Some
  simple groups and almost simple groups or order larger than 1 million
  have also been included, but not in a systematic way.



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*The L-functions and Modular Forms Database: https://www.lmfdb.org/

Welcome to the LMFDB, the database of L-functions, modular forms, and
  related objects. These pages are intended to be a modern handbook
  including tables, formulas, links, and references for L-functions and
  their underlying objects [like field extensions and polynomial Galois groups].  



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*The Inverse Symbolic Calculator:  https://isc.carma.newcastle.edu.au/

The Inverse Symbolic Calculator (ISC) uses a combination of lookup
  tables and integer relation algorithms in order to associate a closed
  form representation with a user-defined, truncated decimal expansion
  (written as a floating point expression). The lookup tables include a
  substantial data set compiled by S. Plouffe both before and during his
  period as an employee at CECM.

If you know such a website on any area of mathematics, please put it as an answer (with a short description).
 A: The Database of ring theory records examples of rings and over 100 ring theoretic properties they can have.  There is also some information on important subsets, various dimensions, and meta properties of the properties.
There is also some selected theorems, and some errata. I always welcome suggestions for additions: there is too much work for one person to do.
A: There's the Reverse Math Zoo.
A: Pieter Belmans at the University of Bonn maintains a couple of such websites.
There is Fanography, "a tool to visually study the geography of Fano 3-folds."
And le superficie algebriche, "a tool for studying numerical invariants of minimal algebraic surfaces over the complex numbers". Johan Commelin also contributed to this one.
A: Regina and SnapPy are free program suits for research in low-dimensional topology (particularly in dimension 3), and are accompanied by large census databases of closed 3-manifolds, knots and links. Some highlights:


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*Knot tables up to 19 (!) crossings (Regina)

*Closed, orientable 3-maifolds with at most 11 tetrahedra (Regina)

*Knots and links with up to 14 crossings (SnapPy)

*Various censuses of hyperbolic 3-manifolds (Regina, SnapPy)
A: A classic by Stanisław Radiszowski:
= = = = = = Small Ramsey Numbers = = = = = =
https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS1/pdf
Last update on 2017-03-03. All known Ramsey numbers or their estimates are provided for several different types of graphs and colorings.
A: The Cunningham Project seeks to factor the numbers $b^n \pm 1$ for
$b = 2$, $3$, $5$, $6$, $7$, $10$, $11$, $12$, up to high powers $n$.
A: KnotInfo https://knotinfo.math.indiana.edu/
LinkInfo https://linkinfo.math.indiana.edu/
These are databases of all knots and links up to a certain number of crossings, along with many different computed invariants and properties.
A: There is a database of matroids. For example, it includes a list of all $4,886,380,924$ isomorphism classes of matroids of rank 4 on 10 elements!
A: If you are interested in historical things,
John Jones' number fields database
and 
William Stein's modular forms database (which also includes elliptic curve data, such as the Cremona database) used to be standard such websites.  Now this information is subsumed into the
L-functions and modular forms database (LMFDB)
mentioned by the OP.
A: A database of number fields, by Jürgen Klüners and Gunter Malle. (Note this is not the same as the one mentioned in this answer.)
The site also provides links to similar databases.
A: A classic: The On-Line Encyclopedia of Integer Sequences (OEIS).
A: Another classic, this time about prime numbers, it provides some theoretical results and a lot of data:
= = = = = = https://primes.utm.edu/ = = = = = =
There are many more pages and portals devoted to elementary number theory.
A: Enumerating Order Types for Small Point Sets with Applications


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*Database (maintained by Oswin Aichholzer, TU Graz)

*Background paper (by O. Aichholzer, F. Auerhammer, H. Krasser (2002))
A: Many Internet pages provide (or used to) lotto design tables. In particular, the following paper seems solid:
= = = Lotto Design Tables (by P. C. Li and G. H. J. van Rees),
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.5.4298&rep=rep1&type=pdf
A: The Atlas of Small Regular Polytopes (Michael Hartley) "contains information about all regular polytopes with $n$ flags where $n$ is at most 2000, and not equal to 1024 or 1536".
The website of Dimitri Leemans has


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*An Atlas of Abstract Regular Polytopes for Small Almost Simple Groups

*An Atlas of Chiral Polytopes for Small Almost Simple Groups

*An atlas of subgroup lattices of finite almost simple groups
The website of Marston Conder has many catalogs of information related to maps, hypermaps, polytopes, symmetric graphs, and surface actions.
Combinatorial Data (Brendan McKay) has complete collections of various classes of graph, up to some number of vertices, in graph6 format.
Combinatorial Catalogues (Gordon Royle) has class 2 graphs up to 9 vertices, trees up to 16, bipartite up to 14, 3-regular up to 22, and more.
Regular Graphs (M. Meringer) has information and shortcode files for "simple connected $k$-regular graphs on $n$ vertices and girth at least $g$ with given parameters $n,k,g$."
The House of Graphs is a searchable "Database of interesting graphs".
A: Table of absolutely maximally entangled states. 
Abbreviated as AME(n,D), the table lists quantum states of n parties with D levels each that show maximal entanglement across every bipartition. These states are equivalent to pure $((n,1,n/2+1))_D$ quantum error correcting codes, and are in the case of n even also known as perfect tensors or multi-unitary matrices. They can be seen as a type of self-dual quantum codes.
A: *

*Atlas of Lie Groups and Representations: info on lie groups, there is a nice article on the history of this atlas


*Atlas of Finite Group Representations: info on finite groups actually the succesor of a book (already mentioned by OP but added it anyway to keep it symmetric with the first point)


*Complexity zoo:list of complexity classes and what is know about them


*Quantum algorithm zoo: list of quantum algorithms


*Knot Atlas: list of knots


*Encyclopedia of triangles center: list of triangle centers


*Bilbao chrystallographic server: list of space groups and info although more physics oriented


*Cantor's Attic: A wiki about large cardinal axioms, large countable ordinals, and infinity in general


*Googology wiki: Info on googology


*Digital Library of Mathematical Functions: a spiritual successor to a book too and there is also a nice article on the history
A: This catalogue of mathematical datasets could be of some interest to you - at least some of the entries are atlas-like websites. It includes several of the websites mentioned above, and I'm slowly adding more to it.
A: Here's another one.


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*The Manifold Atlas Project: http://www.map.mpim-bonn.mpg.de/Main_Page
A: Forking and dividing is a map of the model theory universe, visually classifying some 63 first-order theories.
A: http://www.polychora.de/wiki/images/ has renders of cross-sections, vertex figures and their duals, and cellets for many (possibly all) of the 1849 uniform polychora known at the time it was created.
A: PolyDB is a database of polytopes. It can either be accessed through the website or directly from polymake.
A: The Information System on Graph Classes and their Inclusions:
http://www.graphclasses.org/
This is a database of graph classes with a java application that helps you to research what's known about particular graph classes. 
A: I am trying to keep up with the area of symmetric functions, and various generalizations:
The symmetric functions catalog
A: Another one is the Catalogue of Lattices.

This data-base of lattices is a joint project of Gabriele Nebe, RWTH Aachen university (nebe(AT)math.rwth-aachen.de) and Neil Sloane. (njasloane(AT)gmail.com).
Our aim is to give information about all the interesting lattices in "low" dimensions (and to provide them with a "home page"!). The data-base now contains about 160,000 lattices!

A: The graded rings database
http://www.grdb.co.uk
A database of varieties (toric varieties, Fano varieties, Calabi-Yaus).
A: $\pi$-base has examples of topological spaces and their properties.
A: Here is a database of Vertex Operator Algebras and Modular Categories, though it is still in an early version.
A: The Blocks of Finite Groups wiki, which aims to classify the Morita equivalence classes of blocks with a given defect group. This is in part to understand Donovan's Conjecture better. 
A: Maybe not exactly an "atlas", but there is a classification of some certain types of PDEs studied in analysis at


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*The Dispersive PDE Wiki: https://kvm16.pims.math.ca/DispersiveWiki/index.php?title=Main_Page

*WikiWaves: https://wikiwaves.org/
A: You can look at HandWiki https://handwiki.org/ too. It is a dedicated resource for mathematics
