Lie--Bianchi theorem

Let $\mathcal{D}\subset TM$ be a regular, involutive distribution of rank $k$, and let $\mathfrak{g}\subset \text{Shuf}(D)$ a transversal algebra of symmetries which is solvable. Then $\mathcal{D}$ can be integrated by quadratures.

Proof: See @lychagin1991 section 1.7.3.