Ballester-Bolinches, A.Esteban Romero, RamónLu, Jiakuan2020-10-142020-10-1420170003-889Xhttps://riunet.upv.es/handle/10251/151655[EN] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A5 or SL2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A5 or SL2 (5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201 206, 2012).Reserva de todos los derechosFinite groupSupersoluble subgroupSoluble groupMATEMATICA APLICADAArtículo10.1007/s00013-017-1041-4Abierto