Is there any classification of finite non-solvable non-simple groups? (I mean finite groups which are neither solvable nor simple.)
2026-04-09 07:14:39.1775718879
Non-solvable non-simple groups
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No, and there is zero hope there will ever be one. Take for example a group of type $G=P \times S$, where $P$ is a $p$-group and $S$ is a non-abelian simple group. To find every $G$ of this type you would first need to find (or classify) all $p$-groups.