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 |M|=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^(1/2 n(2m+n-1)) and hence it is equal to p^(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 t≥3. This paper is devoted to classification of pairs $(G,N)$ when $N$ has a normal complement in $G$ and $t=4,5$.