= Classification of finite groups
As shown in <video Simple Groups - Abstract Algebra by Socratica (2018)>, this can be split up into two steps:
* <classification of finite simple groups>: done
* <group extension problem>
This split is sometimes called the "Jordan-Hölder program" in reference to the authors of the <jordan-Holder Theorem>.
Good lists to start playing with:
History: https://math.stackexchange.com/questions/1587387/historical-notes-on-the-jordan-h%C3%B6lder-program
It is generally believed that no such classification is possible in general beyond the <simple groups>.
Bibliography:
* https://www.quora.com/Is-there-any-classification-result-for-finite-non-simple-groups