On some properties of $X$-semipermutable subgroups

Inspired by the research of Guo, Shum, and Skiba, we investigated the relationship between the classification of the nonabelian composition factor of a group (solvability of a group) and the $X$-semipermutability of a maximal subgroup (a second maximal subgroup). The first theorem answered the question by Li and Yu to some extent.