If are subgroups of a finite group then .

Now since is a subgroup of and it means its order divides and . Therefore, . We cannot have for that would imply . A contradiction.

Therefore, the only possible case is that .

If in the group it means and therefore . But . Therefore, . Since it means the possible values for are .2. Let H be the normal subgroup G, a in G and |H|=10. The element aH of the group G/H has order 3; what are the possibilities for |a|? Explain.