[GAP Forum] algorithms for subgroups of a permutation group

[dmitrii.pasechnik at cs.ox.ac.uk]

Dear Bill,
On Fri, Sep 20, 2019 at 12:30:22AM +0200, Bill Allombert wrote:
> 
> I have a question about computational group theory:
> 
> Is there an algorithm to compute all the subgroups of a permutation
> group ?
> 
> I know there is an algorithm for solvable groups.
> 
> However I am looking for an algorithm that would work for small
> permutation groups (say degree <=100, order <=1000)
> preferably without having precomputed tables for all perfect groups.
Sure, it's implemented in GAP.
It'd work for much bigger groups, too.
(Naturally, producing representatives of conjugacy classes of subgroups
rather than the full lattice).

Check out ConjugacyClassesSubgroups

and many other related functions (e.g. you might want to first look at
the maximal subroups only, etc).

HTH
Dima