Given a covering space action of a group G on a path-connected, locally path-connected space X, then each subgroup H⊂G determines a composition of covering spaces X→X/H→X/G. Show:
((a)) Every path-connected covering space between X and X/G is isomorphic to X/H for some subgroup H⊂G.
((b)) Two such covering spaces X/H1 and X/H2 of X/G are isomorphic iff H1 and H2 are conjugate subgroups of G.
((c)) The covering space X/H→X/G is normal iff H is a normal subgroup of G, in which case the group of deck transformations of this cover is G/H.