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Which of the following are NOT properties of every group $G$ of order $15$?
Notation: We let $e$ be the neutral (identity) element of $G$ and $\circ$ the composition law for $G$.
Select ALL that apply.
$G$ is generated by any $g\in G$ with $g\not=e$.
$G$ is cyclic.
$G$ is abelian.
$G$ is simple.
$G$ is unique up to group isomorphism.