Subgroup of order $n-1$ of a group of order $n$ Here is question 2.1.5 from Dummit and Foote : Prove that $G$ cannot have a subgroup $H$ with $|H| = n-1$, where $n = |G| > 2$.
How can one show this without using Lagrange's theorem (which is in chapter 3 of Dummit).
Thank you

Let $g$ be an element of $G$ that is not in $H$.  Let $h$ be any nonidentity element of $H$.  Now show that $gh$ is not in $H$.  
