Let \(G\ne 1\) be a finite group. A subgroup chain \(1=M_0< M_1< \ldots< M_{n-1}< M_n=G\) , in which \(M_i\) is a maximal subgroup of \(M_{i+1}\) for every i, is called a maximal chain, and n is its length. Every chain is associated with a sequence of positive integers \(j_1\) , \(j_2\) , ..., \(j_n\) , where \(j_i=|M_i:M_{i-1}|\) . If \(j_1\le j_2\le \ldots \le j_n\) ( \(j_1\ge j_2\ge \ldots \ge j_n\) ), then we say that a chain is a <-chain (respectively, >-chain). We prove that a group G is supersolvable if G has two chains of the same length, one of which is a \({<}\) -chain and the other is a >-chain. We classify finite groups in which every maximal chain in every proper subgroup is a <-chain or a >-chain.
