# Which subgroups do conjugacy_classes_subgroups() return

Starting with a group G and subgroup H (up to conjugacy), my task is to find all subgroups (up to conjugacy) that contains H.

Do the subgroups returned by conjugacy_classes_subgroups() satisfy the property that if K and L are two of the returned subgroups such that a conjugate of K is a subgroup of L, then K is a subgroup of L (we can construct a lattice from the subgroups returned)

If not, what will be the most optimal way to do this? My current algorithm checks if any conjugate of H is a subgroup of the list returned in conjugacy_classes_subgroups().