I know that if $\zeta$ is a $n^{th}$ primitive root of the unity, we have :$$Gal(\mathbb{Q}[\zeta ]|\mathbb{Q})\cong U(n)$$
Where $U(n)$ is the group of units.
I was wondering, if there were some results on the solvability of these groups. I know that if $n=pq$ or $n=pqr$ or $n=p^2q$ where $p,q,r$ are distincts primes, then $U(n)$ is solvable.
Is there a generalisation of these results ?