There is my problem:
Let G be a finite group with composition factors $G_1,G_2,...,G_n$, Assume that $G_i$ not isomorphism $G_j$ for all $i \ne j$. Suppose that for any $\sigma \in S_n$, there exists a composition series $1=M_0 \lhd M_1 \lhd ...\lhd M_n=G$ such that $M_k/M_{k-1} \cong G_{\sigma (k)}$ for $k=1,...,n$. Then $G$ has to be the product group $G_1\times ...\times G_n $.
I try to do it by induction, then will have composition series of $M_{n-1}$, and $M_{n-1}$ will equal to product of $n-1$ group in $G_1,...,G_n$, then we can get $G$ has normal subgroup $G^{(k)}=G_1 \times ...\times G_{k-1} \times G_{k+1} \times ...G_{n}$, $k=1,...,n$, and subgroup $G_1,...,G_n$, but then I donnot know if use those infomation can get $G_1\times ...\times G_n. $