Unique Normal Subgroups

brownnrl

Our professor posed this question, and I'm having a very difficult time with it.

If you have a unique subgroup H of G such that H is of order 10 or 20, then H is a normal subgroup. How can you generalize this?

If you have the time to give some hints or suggestions, I'd appreciate it.

-Nelson

brownnrl

Quick note: By stating that theorem, he meant prove it for orders of 10 or 20, then generalize the findings.