Let $H \leq S_n$ be an intransitive group with orbits $\Omega_1, \Omega_2, \ldots ,\Omega_k$. Then certainly $H$ is a subdirect product of the direct its projections on each orbit, $H|_{\Omega_1} \times H|_{\Omega_2} H|_{\Omega_k}$. Here we provide polynomial time algorithm for computing finest partition $P$ $H$-orbits such that = \prod_{c \in P} H|_c$ and demonstrate usefulness in some applica...
