Subgroups and cyclic groups

Question

Suppose a group $G$ has no proper subgroups (that is, the only subgroup of $G$ is $G$ itself and the trivial subgroup $\{e\}$. Show that $G$ is cyclic.

Answer 1

Hint: For any $g\in G$, we have $\langle g\rangle\subseteq G$, where $\langle g \rangle$ is the cyclic group generated by $g$.