  Let $G$ be a finite group and $\sigma_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$.
In this note, we prove that if $\sigma_1(G)<\frac{117}{20}$, then $G$ is
solvable. Moreover, we have $\sigma_1(G)=\frac{117}{20}$ if and only if $G\cong
A_5$. This solves an open problem posed in \cite{8}.
