Characterization of the simple groups $PSL(2,2^n)$ and $Sz(q)$ by biprimary subgroups

A property of the groups $PSL(2,2^n)$ and $Sz(q)$ is derived which no other finite simple group possesses. This property restricts the structure of biprimary subgroups of the group. A description is given of all finite nonsolvable groups with this property.