Function: galoissubgroups
Section: number_fields
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 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 is the product of the
 relative orders. Such subgroup can be used instead of a Galois group in the
 following command: \kbd{galoisisabelian}, \kbd{galoissubgroups},
 \kbd{galoisexport} and \kbd{galoisidentify}.

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