The following should work and be instant (this possibly requires the optional databases_gap package).

sage: G = SymmetricGroup(5)
sage: G.conjugacy_classes_subgroups()

RuntimeError:
Gap produced error output
Variable: 'Sym' must have a value


   executing $sage85:=Sym( [ 1 .. 5 ] );;

I really wanted this to find out which representative subgroups
are transitive, but can't do that either since G.is_transitive()
isn't wrapped -- since Gap has IsTransitive, this would be trivial to wrap.

Component: group theory

Issue created by migration from https://trac.sagemath.org/ticket/1187