doi:10.3390/math10071153engBallester-Bolinches, A.Esteban-Romero, R.Jiménez Seral, P.Bounds on the number of maximal subgroups of finite groups: applicationsART-2022-129198The determination of bounds for the number of maximal subgroups of a given index in a finite group is relevant to estimate the number of random elements needed to generate a group with a given probability. In this paper, we obtain new bounds for the number of maximal subgroups of a given index in a finite group and we pin-point the universal constants that appear in some results in the literature related to the number of maximal subgroups of a finite group with a given index. This allows us to compare properly our bounds with some of the known bounds.2022http://zaguan.unizar.es/record/11798110.3390/math10071153http://zaguan.unizar.es/record/117981oai:zaguan.unizar.es:117981info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-095140-B-I00Mathematics 10, 7 (2022), 1153 [25 pp.]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess