Dear Forum members,

Azmi Tamid had asked:

Dear GAP-forum,
Is there a way in GAP to compute the number of
non-isomorphic subgroups of a finite group G ?

TIA,Azmi

There are several ways to determine all subgroups of a given group,
and they are described in detail in Chapter 37 (Groups) in the GAP
manual. To get just the number of non-isomorphic subgroups, you should
sort the representatives of the conjugacy classes of subgroups by some
invariants that you should choose according to the situation you are
in (order, some properties such as being abelian, solvable or
nilpotent, number of conjugacy classes of elements of given order,
order of some uniquely determined characteristic subgroups, such as
the commutatorgroup), and then apply isomorphism tests to those that
fall into the same class defined by these invariants.

Please do consult the manual first when you have a question which is
very likely answered using GAP. But next after that rather write to
the address 'gap-trouble' (which will be read by some helpful people)
than asking such a question in 'gap-forum' which will be read by
several hundred users of GAP. The Forum really should be reserved for
more subtle questions for which perhaps only a handful of experts, not
necessarily belonging to the GAP team, may have an answer, as well as
for bug fixes, general announcements and so on.

Kind regards Joachim Neubueser

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Prof. em. J. Neubueser
Lehrstuhl D fuer Mathematik
RWTH Aachen
Germany