With reference to the preceding exercise, let M also be a normal subgroup of G. Show that NM is again a normal subgroup of G.

Data from Exercise 40 

Let N be a normal subgroup of G and let H be any subgroup of G. Let HN = { hn | h∈ H, n ∈ N}. Show that H N is a subgroup of G, and is the smallest subgroup containing both N and H.