Finite nilpotent groups having exactly four conjugacy classes of non-normal subgroups. (Q2862494)

The authors investigate finite nilpotent groups which have exactly four conjugacy classes of non-normal subgroups. They give a complete classification theorem, too long to be stated here, by means of a list of fifteen distinct nilpotent groups.NEWLINENEWLINE The problem of classifying those groups \(G\) with a small number of conjugacy classes of non-normal subgroups, \(\nu(G)\), and how this number may have implications on the solvability of \(G\) has been treated by several authors, such as R. Brandl, S. Chen or H. Mousavi. For instance, \textit{R. Brandl} gave a complete classification of finite groups whose non-normal subgroups are conjugate and more recently has classified non-solvable groups with \(\nu(G)<14\) [Beitr. Algebra Geom. 54, No. 2, 493-501 (2013; Zbl 1284.20022)].