Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C5×Q8 | C2 | semidirect |
| 3. #65516 | C2 | semidirect |
| 4. #65316 | C2 | semidirect |
| 5. #65315 | C2 | semidirect |
| 6. #65310 | C2 | semidirect |
| 7. #65256 | C2 | semidirect |
| 8. #65215 | C2 | semidirect |
| 66. C2×C4×Q8 | D5 | semidirect |
| 77. C5×Q8 | #41 | semidirect |
| 180. Q8 | #709 | semidirect |
| 201. C5 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×Q8 | 2 |
| #65811 | 2 |
| #65516 | 2 |
| #65316 | 2 |
| #65315 | 2 |
| #65310 | 2 |
| #65256 | 2 |
| #65215 | 2 |
| #3112 | 5 |