A solution of Wielandt's problem for the sporadic groups

Let $\pi$ be a set of primes. A finite group $G$ is a $D_\pi$-group if all maximal $\pi$-subgroups of $G$ are conjugate. In 1979 H. Wielandt posed the following problem: in which finite simple groups every subgroup is a $D_\pi$-group? We solve this problem for the sporadic groups.