Summary: Let $G$ be a group and $\pi_e(G)$ be the set of element orders of $G$. Let $k\in\pi_e(G)$ and $m_k$ be the number of elements of order $k$ in $G$. Set $\operatorname{nse}(G)\coloneq\{m_k|k\in\pi_e(G)\}$. We prove if $G$ is a group such that $\operatorname{nse}(G)=\operatorname{nse}(S_8$), then $G\cong S_8$.