Sums of Sylow numbers of finite groups

Let $G$ be a finite group, $n_{p}(G)$ be the number of Sylow $p$-subgroups of $G$, and $pi (G)$ be the set of prime divisors of $|G|$. ##We set $S(G)={pin pi (G)|n_{p}(G) 1}$ and define $delta_{0}(G)=sumlimits_{pin S(G)}n_{p}(G)$. In cite{khalili1}, the authors worked on $delta _{0}(G)$, with small $delta_{0}(G)$. ##Continuing cite{khalili1}, our further investigation show that if $delta_{0}(G) 57$, then $G$ is solvable or $G/Ncong A_{5}$ or $G/Ncong S_{5}$, where $N$ is the largest normal solvable subgroup of $G$.