University of Isfahan International Journal of Group Theory 2251-7650 10 2 2021 06 01 Influence of complemented subgroups on the structure of finite groups 65 74 24261 10.22108/ijgt.2019.119105.1570 EN Izabela Agata Malinowska Faculty of Mathematics, University of Bialystok, 15-245 Bialystok, Ciolkowskiego 1M, Poland Journal Article 2019 09 10 P‎. ‎Hall proved that a finite group $G$ is supersoluble with elementary abelian Sylow subgroups if and only if every subgroup of $G$ is complemented in $G$‎. ‎He called such groups complemented‎. ‎A‎. ‎Ballester-Bolinches and X‎. ‎Guo‎ ‎established the structure of minimal non-complemented groups‎. ‎We give the classification of finite non-soluble groups‎ ‎all of whose second maximal subgroups are complemented groups‎. ‎We also prove that every finite group with less than‎ ‎$21$ non-complemented non-minimal $\{2,3,5\}$-subgroups is soluble‎. https://ijgt.ui.ac.ir/article_24261_26abaf2b4bf9f112a26c308aa371615b.pdf