Simple groups with only odd-order branch elements have only a single rotational/translational subgroup of order 2, which is also the commutator subgroup, examples [3,3], [3,5], [3,3,3], [3,3,5]. For other Coxeter groups with even-order branches, the commutator subgroup has index 2, where c is the number of disconnected subgraphs when all the even-order branches are removed.