This is of my final study guide, and Im confused by the question please help....

For $\displaystyle H,K \leq G$ Set $\displaystyle H$~$\displaystyle K $ when for some $\displaystyle g \in G, K = g^{-1} Hg$

Finish the Statement: "|[$\displaystyle H$]_~| = 1 $\displaystyle \iff $$\displaystyle H$ is...." and justify your answer

Thanks in advance...