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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

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