Producing subgroups of Weyl groups

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There is no general answer to be good enough for special choices of $S$. Using the general group methods the following is working:

# W = RootSystem('[A, 4]').weight_lattice().weyl_group    # does not work 

W = RootSystem( [ 'A', 4 ] ).weight_lattice().weyl_group()
some_elements = [ W.random_element() for _ in range( 3 ) ]
G = W.subgroup( some_elements )
G . order()
# G.list()[:10]

We simply want, ask for and get the W.subgroup generated by the specified elements.