Is the dihedral group $D_n$ nilpotent? solvable? Is the dihedral group $D_n$ nilpotent? solvable?
I'm trying to solve this problem but I've been trying to apply a couple of theorems but have been unsuccessful so far. Can anyone help me?

A general proof that $D_n$ is solvable for all $n \geq 1$.
Here is the normal series with abelian quotients:
$$\{e\} \trianglelefteq \langle \sigma \rangle \trianglelefteq D_n$$
$$\langle \sigma \rangle/\{e\} \cong \mathbb{Z}_n,   D_n/\langle \sigma \rangle \cong \mathbb{Z}_2$$ both obviously abelian, therefore $D_n$ is solvable.
