Let $G$ be finite. Suppose that all maximal subgroups of $G$ are conjugate. Then $G$ is cyclic.
I was stuck, then I find one solution. In Jack’s answer, it was mentioned that “one conjugacy class of maximal subgroups in fact implies that there is only one maximal subgroup”.
However, in the beginning of the proof, Lagrange Theorem was applied to the conjugacy class $M$, which is not necessarily a subgroup. I’m really confused about this point. Any help is sincerely appreciated.