The $D_\pi$-property in finite simple groups

Let $\pi$ be some set of primes. A finite group is said to possess the $D_\pi$-property if all of its maximal $\pi$-subgroups are conjugate. It is not hard to show that this property is equivalent to satisfaction of the complete analog of Sylow's theorem for Hall $\pi$-subgroups of a group. In the paper, we bring to a close an arithmetic description of finite simple groups with the $D_\pi$-property, for any set $\pi$ of primes. Previously, it was proved that a finite group possesses the $D_\pi$-property iff each composition factor of the group has this property. Therefore, the results obtained mean in fact that the question of whether a given group enjoys the $D_\pi$-property becomes purely arithmetic.