Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #66066 | C2 | semidirect |
| 3. C5×#500 | C2 | semidirect |
| 4. #65383 | C2 | semidirect |
| 5. #65376 | C2 | semidirect |
| 6. #65175 | C2 | semidirect |
| 7. #65174 | C2 | semidirect |
| 8. #65173 | C2 | semidirect |
| 9. #65170 | C2 | semidirect |
| 10. C4×#677 | C2 | semidirect |
| 11. #64977 | C2 | semidirect |
| 77. #500 | D5 | semidirect |
| 110. C5×C8 | #41 | semidirect |
| 221. C8 | #713 | semidirect |
| 222. C5 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66066 | 2 |
| #66060 | 2 |
| C5×#500 | 2 |
| #65383 | 2 |
| #65376 | 2 |
| #65175 | 2 |
| #65174 | 2 |
| #65173 | 2 |
| #65170 | 2 |
| C4×#677 | 2 |
| #64977 | 2 |
| #3353 | 5 |