Function: galoissubgroups
Section: number_fields_galois
C-Name: galoissubgroups
Prototype: G
Help: galoissubgroups(G): output all the subgroups of G.
Doc: outputs all the subgroups of the Galois group \kbd{gal}. A subgroup is either a
 list of group elements or a vector [\var{gen}, \var{orders}], with the same meaning
 as for $\var{gal}.gen$ and $\var{gal}.orders$. Hence \var{gen} is a vector of
 permutations generating the subgroup, and \var{orders} is the relatives
 orders of the generators. The cardinality of a subgroup can be obtained by
 calling \kbd{galoisorder}.
 Such subgroup can be used instead of a Galois group in the
 following command: \kbd{galoischardet}, \kbd{galoisexport}, \kbd{galoisisnormal},
 \kbd{galoischarpoly}, \kbd{galoisidentify}, \kbd{galoisorder},
 \kbd{galoissubfields}, \kbd{galoischartable}, \kbd{galoissubgroups},
 \kbd{galoisconjclasses}, \kbd{galoisisabelian}.

 To get the subfield fixed by a subgroup \var{sub} of \var{gal}, use
 \bprog
 galoisfixedfield(gal,sub[1])
 @eprog
