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In his message, Chad Scherrer asked:

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?

GAP provides routines for both tasks. Subgroups are computed using the

'Lattice' command, which computes the whole lattice of subgroups (and

stores conjugated subgroups is a somehow shortened form). In case you

really want to have a list of all subgroups for looping over them, you

might use

l:=Lattice(g); # supposing g is your group

s:=Flat(List(l.classes,Elements));;

Then the variable 's' will contain a list of all subgroups. If you

replace 'Elements' by 'Representative', you will obtain a list of

representatives of each conjugacy class of subgroups.

For computing all normal subgroups, GAP provides the command

'NormalSubgroups'.

Yours,

Alexander Hulpke

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