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.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,  +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany