So I'm working through Hall's Theorem for Solvable groups and there is one part of it which I cannot seem to prove. I am following through Isaac's book on Finite group Theory for reference.
Currently I can prove Hall-E (existence of a Hall-$\pi$-subgroup), Hall-C (any two such are conjugate) however the proof of Hall-D eludes me.
For those without the book it is stated as; Let $U \subseteq G$ be a $\pi$ subgroup, where $\pi$ is a set of primes and $G$ is a finite solvable group. Then $U$ is contained in some Hall-$\pi$-subgroup of $G$.