Element structure of groups of order 8

Full listing
Because of the small order, it turns out that the nilpotency class completely determines the number of conjugacy classes of each size.

Action of automorphisms and endomorphisms
The automorphism group acts on the group, permuting conjugacy classes, and the inner automorphism group sends every element to within its conjugacy class. We thus get an action of the outer automorphism group on the set of conjugacy classes.

In the table below, the column "Sizes of orbits of size 2 conjugacy classes" gives the sizes of the orbits under the action on size 2 conjugacy classes. Each orbit on elements is twice the size, and the row underneath gives that data.

1-isomorphism
There are no 1-isomorphisms between non-isomorphic groups of order 8. In fact, no two non-isomorphic groups of order 8 are order statistics-equivalent.

Order statistics
Here are the statistics for a particular order.

Here are the number of $$n^{th}$$ root statistics. The number of $$n^{th}$$ roots equals the number of elements whose order divides $$n$$.