Groups of order 640

Statistics at a glance
The number 640 has prime factorization $$640 = 2^7 \cdot 5$$. There are only two prime factors, and order has only two prime factors implies solvable, so all groups of order 640 are solvable groups (specifically, finite solvable groups).

GAP implementation
gap> SmallGroupsInformation(640);

There are 21541 groups of order 640. They are sorted by their Frattini factors. 1 has Frattini factor [ 10, 1 ]. 2 has Frattini factor [ 10, 2 ]. 3 has Frattini factor [ 20, 3 ]. 4 - 402 have Frattini factor [ 20, 4 ]. 403 - 564 have Frattini factor [ 20, 5 ]. 565 - 919 have Frattini factor [ 40, 12 ]. 920 - 5021 have Frattini factor [ 40, 13 ]. 5022 - 5854 have Frattini factor [ 40, 14 ]. 5855 - 7108 have Frattini factor [ 80, 50 ]. 7109 - 17941 have Frattini factor [ 80, 51 ]. 17942 - 19094 have Frattini factor [ 80, 52 ]. 19095 - 19099 have Frattini factor [ 160, 234 ]. 19100 - 19104 have Frattini factor [ 160, 235 ]. 19105 - 19649 have Frattini factor [ 160, 236 ]. 19650 - 21284 have Frattini factor [ 160, 237 ]. 21285 - 21453 have Frattini factor [ 160, 238 ]. 21454 - 21456 have Frattini factor [ 320, 1635 ]. 21457 - 21467 have Frattini factor [ 320, 1636 ]. 21468 - 21474 have Frattini factor [ 320, 1637 ]. 21475 - 21501 have Frattini factor [ 320, 1638 ]. 21502 - 21526 have Frattini factor [ 320, 1639 ]. 21527 - 21535 have Frattini factor [ 320, 1640 ]. 21536 - 21541 have trivial Frattini subgroup.

For the selection functions the values of the following attributes are precomputed and stored: IsAbelian, IsNilpotentGroup, IsSupersolvableGroup, IsSolvableGroup, LGLength, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 2 of the SmallGroups library. IdSmallGroup is available for this size.