Here are some inclusions between graph classes that I suspect to hold.
In order to include them in ISGCI, they need a (reference to a) nice proof.

[outerplanar][1] << [EPT][2]

[P_4-comparability][3] << [co-C_6-free][4]

[unipolar][5] << [biclique separable][6]

[unipolar][5] << [interval filament][7]

[perfectly orderable][8] << [co-sun-free][9]

[bip*][10] << [(anti-hole,odd-hole)-free][11]

And a question:
Is the [book thickness][12] of [2-subdivision][13] unbounded?


  [1]: https://www.graphclasses.org/classes/gc_110.html
  [2]: https://www.graphclasses.org/classes/gc_128.html
  [3]: https://www.graphclasses.org/classes/gc_6.html
  [4]: https://www.graphclasses.org/classes/AUTO_92.html
  [5]: https://www.graphclasses.org/classes/gc_1273.html
  [6]: https://www.graphclasses.org/classes/gc_754.html
  [7]: https://www.graphclasses.org/classes/gc_390.html
  [8]: https://www.graphclasses.org/classes/gc_4.html
  [9]: https://www.graphclasses.org/classes/AUTO_2075.html
  [10]: https://www.graphclasses.org/classes/gc_57.html
  [11]: https://www.graphclasses.org/classes/gc_977.html
  [12]: https://www.graphclasses.org/classes/par_32.html
  [13]: https://www.graphclasses.org/classes/gc_472.html