Finite groups with a cyclic maximal subgroup.

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In the book A Course in the Theory of Groups by Derek J.S. Robinson, Finite $p$-groups with a cyclic maximal subgroup are classified.

Now I wish to know whether finite groups with a cyclic maximal subgroup are classified?

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Yes. This paper " V. V. Pylaev, N. F. Kuzennyi, Finite groups with a cyclic maximal subgroup, Ukrainian Mathematical Journal, 28 (5) (1976), 500--506", classify finite groups with a cyclic maximal subgroup.