This is an definition about $p$-solvable. https://groupprops.subwiki.org/wiki/P-solvable_group.
I can't find examples of them in any book, maybe I haven't read enough books. More, I saw that there was writing "a finite group is solvable if and only if it is p-solvable for every prime $p$". I have not yet thought about why it is like that.
Also, is the order of $p$-solvable anything special?