1. The problem statement, all variables and given/known data How would I go about proving that if K = gHg-1, for some g [itex]\in[/itex]G, where K and H are both subgroups of G with a prime number of elements, then K = H? 2. Relevant equations I've tried to prove it by saying that if K = gHg-1 then Kg = gH, and since H = gHg-1, then Hg = gH also, so Hg = Kg, and hence H = K. I don't think that this proof is valid, unfortunately. And I've just realised that H does not necessarily equal gHg-1 unless g is in the normaliser of H. :( 3. The attempt at a solution This is actually something which I am attempting to prove in order to prove something else, so I'm not even sure if what I'm trying to prove holds at all. I just need K = H for my proof to work.