I need your help in following question. I apologies for asking similar type questions. I would appreciate any help. I am sorry for the inconvenience.
I wish to classify $p$ group $G$ ($p$ prime) of order $p^4$ and $p^5$ such that whenever $H$ is a non normal subgroup of order $p$, $G$ is the semidirect product of $H$ and a subgroup $K$ with $K$ isomorphic to the quotient $G/L$ where $L$ is any normal subgroup of order $p$.
Can we classify finite $p$ group with this property.
Thanks in advance.