### Producing subgroups of Weyl groups

Let W be a Weyl group, e.g.
W = RootSystem('[A, 4]').weight_lattice().weyl_group

Given some elements $S \subset W$, I would like to produce the subgroup generated by $S$. It seems like there are methods in SAGE to do this when W is an abstract group, but I can't see how to do it when $W$ is a Weyl group. Any suggestions?