According to a result of Higman and Sims (which I learned about in [this paper](http://arxiv.org/abs/math/0608491) of Poonen's) the typical p-group is 3-step nilpotent of a particular form. In particular the typical group is a 3-step nilpotent 2-group of a particular form. By typical here I mean that eventually the number of these groups dominate.


Is anything known about what the typical non-solvable group looks like? Probably some sort of modification of PSL\_2(F\_p)?



What does the typical non-solvable group look like?
It seems like, if solvable groups dominate everything else, then groups with a single $A\_5$ factor and all other factors cyclic should likewise dominate every other type of nonsolvable group.


