Suppose H is a subgroup of G, and h and h' are elements in H.
How could I show this is true or false:
If h and h' are conjugates in G, then they are conjugates in H.

My attempt:suppose h and h' are conjugates in G then there exists and k$\in$G such that h=kh'$k^{-1}$ but this k may not always belong in H so this seems that it may be false. How could I show this? thanks