My question is: If |G|=15, show that G must have an element of order 3.
We're currently learning about Lagrange's Theorem, so I know that I need to use it somehow, and I can't use Sylow's or Cauchy's Theorems yet. It makes sense that elements of order 3 and 5 (and 1 and 15) would be in G but I don't know how to use Lagrange to show that.
Thanks! Any help would be greatly appreciated!