on the order of the schur multiplier of a pair of finite $p$-groups ii

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized the structure of $(g,n)$ when $n$ has a complement in $g$ and‎ ‎$tleq 3$‎. ‎this paper is devoted to classification of pairs‎ ‎$(g,n)$ when $n$ has a normal complement in $g$ and $t=4,5$‎.