In the paper the following proposition is proved. Let $(Q,A)$ be an n-group, $|Q|\in N\setminus\{1\}$, and let $n\geq 3$. Further on, let $\Theta$ be an arbitrary congruence of the $n$-group $(Q, A)$ and let $C_{t}$ be an arbitrary class from the set $Q/\Theta$. Then there is a $k\in N$ such that the pair $(C_{t},\overset{k}{A})$ is a $(k(n-1)+l)$-subgroup of the $(k(n-1)+l)$-group $(A,\overset{k}{A})$.