GAP:OrderStatistics

Definition
The definition takes one argument, which is a group, and returns a list.

Code
OrderStatistics := function(G) local L,D; L := List(Set(G),Order); D := DivisorsInt(Order(G)); return(List(D,x->Length(Filtered(L,y->x=y)))); end;;

Here is a slight variant, the paired version, that pairs each divisor with the number of elements of that order:

OrderStatisticsPaired := function(G) local L,D; L := List(Set(G),Order); D := DivisorsInt(Order(G)); return(List(D,x->[x,Length(Filtered(L,y->x=y))])); end;;