${if\ the\ element\ of\ a\ group\ G\ is\ order\ n,then\ a}^{m}=e\ if\ and\ only\ if\ n\ is\ divisor\ of\ m$
this is a property of subgroup
so in ques have to find number of subgroups
$m\leqslant 960$
factors of m = $2^{6}*3^{1}*5^{1}$
possible value of m = number of divisors of m
$=(6+1)*(1+1)*(1+1)$
$=28$