Outline Introduction Study on ν(G) ν(G ) and bound problems p-Groups with same order of non-normal subgroups Study on νc (G) Solvability and Non-Solvability References Effects of non-normal subgroups on the structure of finite groups Hamid Mousavi Department of Mathematics University of Tabriz hmousavi@tabrizu.ac.ir April 6, 2015 Hamid Mousavi Effects of non-normal subgroups on the structure of finite groups