ConjugacyClassesSubgroups ordering in GAP for SmallGroups

Question

Does GAP always arrange the conjugacy classes of subgroups by the subgroup order when ConjugacyClassesSubgroups is executed on a group generated by SmallGroup? If not, how can I efficiently get subgroups of a small group by decreasing order (or, equivalently, by increasing index)

Answer 1

The declaration of ConjugacyClassesSubgroups does not guarantee that the list is always ordered, and I can imagine situations (such as special methods for subgroups of a direct product) in which it could produce a list that is not sorted.

The easiest way to get a sorted list is probably

l:=ShallowCopy(ConjugacyClassesSubgroups(group));
SortBy(l,x->Size(Representative(x)));

(replace Size by -Size to get decreasing order).

The cost (both time and memory) for this is probably neglegible.