Minimal non-abelian groups with an average condition on subgroups

For a finite group $G$, the average order $o(G)$ is defined to be the average of all order elements in $G$. We say that $G$ satisfies the average condition if $o(H)\leq o(G)$ for all subgroups $H$ of $G$. In [On a question of Jaikin-Zapirain about the average order elements of finite groups, Int. J. Group Theory, To appear] we proved that every abelian group satisfies the average condition. In this paper, we classify minimal non-abelian groups which satisfy the average condition.