Order of Group Element/Examples/Possible Orders of x when x^2 = x^12

Examples of Order of Group Element
Let $G$ be a group.

Let $x \in G \setminus \set e$ be such that $x^2 = x^{12}$.

Then the possible orders of $x$ are $2$, $5$ and $10$.

Proof
Hence:
 * $\order x \in \set {2, 5, 10}$

as required.