  We prove that for a group $\mathrm{SO}_n(\mathrm{R}) \subset G \subset
\mathrm{GL}_n (\mathrm{R})$, any $G$-structure on a smooth manifold can be
endowed with a torsion free connection which is locally the Levi-Civita
connection of a Riemannian metric in a given conformal class. In this process,
we classify the admissible groups.
