Algebra Question from Mathematics GRE I just started learning algebra, and I came across a question from a practice GRE which I couldn't solve. http://www.wmich.edu/mathclub/files/GR8767.pdf #49  
The finite group $G$ has a subgroup $H$ of order 7 and no element of $G$ other than the identity is its own inverse. What could the order of $G$ be?
Edit: This is a misreading of the problem. The problem intends that no element in G is its own inverse.
a) 27
b) 28
c) 35
d) 37
e) 42
I've already eliminated a) and d) due to LaGrange's theorem.

Hint: You want to make sure there is no element of order $2$.
