The homomorphism conjecture for $d52f$-submaximal subgroups

Let $d52f$ be a class of finite groups, let $A$ be an $d52f$-separable normal subgroup of a finite group $G$, and let $G\rightarrow G/A$ be the canonical epimorphism. The homomorphism conjecture. This epimorphism always maps every $d52f$-submaximal subgroup of $G$ to an $d52f$-submaximal subgroup of $G/A$; conversely, every $d52f$-submaximal subgroup of $G/A$ is the image of an $d52f$-submaximal subgroup of $G$. The conjecture asks for a reduction theorem for $d52f$-submaximal subgroups analogous to Wielandt's theorem for $d52f$-maximal subgroups, and is presented as central to the paper's investigation of inductiveness under homomorphisms.