From Rotman "Introduction to the Theory of Groups", ex. 2:54:
Let $ G $ be a finite group, and let $H$ be a normal subgroup with $(H,[G:H])=1$. Prove that $H$ is the unique such subgroup in G.
That exercise was introduced here before: link
It's easy that $HK$ is a subgroup of $G$, thus $|K| / |H\cap K|$ divides $|G|/|H|$. But I don't see what to do in next step anyway, in spite of reading link above.