I have to prove this exercise for my math study:
With a rotation I mean {$\rho_{x}| x \in \mathbb{R^{2}}$} and $x$ is the angle of rotation.
Let $H$ be the group of all rotations around the origin, and $E(\mathbb{R^{2}})$ the group of all isometries in $\mathbb{R^{2}}$. Then $H$ $\subset$ $E(\mathbb{R^{2}})$. Prove that $H$ is not a normal subgroup of $E(\mathbb{R^{2}})$.
I think I should start the prove by taking an element of $H$, i.e. $\rho$, and an element of $E(\mathbb{R^{2}})$, let's say, a reflection $\sigma$, and prove that $\sigma\rho\sigma^{-1} \notin H$
I have really no idea about how I have to complete the proof. Could you please explain it to me? thanks in advance!