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