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We show that given a $G$-structure $P$ on a differentiable manifold $M$, ifthe group $G(M)$ of automorphisms of $P$ is big enough, then there exists thequotient of an stochastic flows $phi_t$ by $G(M)$, in the sense that $\phi_t =\xi_t \circ \rho_t$ where $\xi_t \in G(M)$, the remainder $\rho_t$ hasderivative which is vertical but transversal to the fibre of $P$. Thisgeometrical context generalizes previous results where $M$ is a Riemannianmanifold and $\phi_t$ is decomposed with an isometric component, see Liao\cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds tothe particular case of an SO(n)-structure on $M$.

Decomposition of stochastic flows with automorphism of subbundles component