Groups of order 1280

Statistics at a glance
The number 80 has prime factorization $$1280 = 2^8 \cdot 5$$. There are only two prime factors, and order has only two prime factors implies solvable, so all groups of order 1280 are solvable groups (specifically, finite solvable groups).

GAP implementation
The order 1280 is part of GAP's SmallGroup library. Hence, all groups of order 1280 can be constructed using the SmallGroup function and have group IDs. Also, IdGroup is available, so the group ID of any group of this order can be queried.

Here is GAP's summary information about how it stores groups of this order:

gap> SmallGroupsInformation(1280);

There are 1116461 groups of order 1280. They are sorted by normal Sylow subgroups. 1 - 56092 are the nilpotent groups. 56093 - 1083472 have a normal Sylow 5-subgroup with centralizer of index 2. 1083473 - 1116308 have a normal Sylow 5-subgroup with centralizer of index 4. 1116309 - 1116357 have a normal Sylow 2-subgroup. 1116358 - 1116461 have no normal Sylow subgroup.

This size belongs to layer 3 of the SmallGroups library. IdSmallGroup is available for this size.