Chad Scherrer writes in his e-mail messages of 1993/04/29
Is there a way in GAP to find all the subgroups of a given group,
and if so, what about finding all normal subgroups of a given group?
The function 'ConjugacyClassesSubgroups' will return the conjugacy
classes of subgroups of a given group (whose largest perfect subgroup
must have size <= 10000). With
List( ConjugacyClassesSubgroups(G), Representative );
you get a list of representatives of the conjugacy classes, i.e.,
one subgroups from each conjugacy class. With
Concatenation( List( ConjugacyClassesSubgroups(G), Elements ) );
you get all the subgroups.
Note that 'ConjugacyClassesSubgroups' is somewhat slow for large solvable
groups. I have rewritten this function so that it is now faster. This
new implementation will be made available in the third upgrade (sorry I
don't know when we will release this upgrade).
The function 'NormalSubgroups' will return a list of normal subgroups of
a given group.
-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany