# D-property for a prime set

Let $G$ be a finite group, and $\pi$ be a set of primes. We say that $G$ satisfies $D_\pi$ if $D$ has a $\pi$-Hall subgroup $H$ (viz, a Hall subgroup whose order contains only primes from $\pi$ and whose index contains no primes from $\pi$) and every $\pi$-subgroup (subgroup whose order contains only primes from $\pi$) is contained in a conjugate of $H$.