Let $\mathbb{P}$ is a set primes numbers, $\pi \subseteq P$ and $\pi ^{\prime }=P-\pi $
Let $O_{\pi }\left( G\right) =\left\langle N~;~N\trianglelefteq G\text{ and }% N\text{ is }\pi \text{-subgroup}\right\rangle $
Is it true that $O_{\pi }\left( G\right) =1\Longrightarrow G$ is $\pi ^{\prime }-$group?
if it is true, could not it have other $H$ $\pi $-subgroup (not normal) in $G$?