Lists of small groups I am looking for lists of small 
-solvable groups
-nilpotents groups
-simple groups.
By this I mean, do there exist lists of all the groups of order smaller than $n$, for $n$ reasonably big, satisfying one of the above properties?
Does anyone know a reference for this?
Thanks in advance.
 A: In http://en.wikipedia.org/wiki/List_of_finite_simple_groups there is a list of simple groups up to 9828. Moreover, the GAP small group library contains all groups of order less than 2000. 
A: This kind of question has a long history (pre-computer), but it's always been difficult to get much intuition about solvable groups just from looking at a big list.  In the case of simple groups the old search by Marshall Hall and others for those of order less than a million was a more sensible fishing expedition: such groups are sparse but interesting, while ruling out certain orders could be suggestive.    Computers (and GAP in particular) have improved numerical searches a lot, but there is only so much to be learned this way.  
For a sense of older times, there is the ambitious book project:
MR0168631 (29 #5889),
Hall, Marshall, Jr.; Senior, James K. ⋆The groups of order 2^n (n ≤ 6).
The Macmillan Co., New York; Collier-Macmillan, Ltd., London 1964 225 pp.
For modern times, there is a 2002 survey with plenty of references:
MR1935567 (2003h:20042), Besche, Hans Ulrich (D-AACH-DM); Eick, Bettina (D-BRNS-G); O’Brien, E. A. (NZ-AUCK), A millennium project: constructing small groups. Internat. J. Algebra Comput. 12 (2002), no. 5, 623–644.
