Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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×#4082 | C2 | semidirect |
| 2. #65934 | C2 | semidirect |
| 4. #65507 | C2 | semidirect |
| 5. #65444 | C2 | semidirect |
| 6. #65442 | C2 | semidirect |
| 7. #65329 | C2 | semidirect |
| 8. #65057 | C2 | semidirect |
| 9. #65056 | C2 | semidirect |
| 10. #65028 | C2 | semidirect |
| 11. #65007 | C2 | semidirect |
| 22. #4082 | C22 | semidirect |
| 25. D4×Dic5 | C22 | semidirect |
| 27. C2×#687 | C22 | semidirect |
| 30. C2×Dic20 | C22 | semidirect |
| 31. #4036 | C22 | semidirect |
| 32. #4033 | C22 | semidirect |
| 39. #3948 | C22 | semidirect |
| 40. #3946 | C22 | semidirect |
| 41. C8×Dic5 | C22 | semidirect |
| 42. #3942 | C22 | semidirect |
| 259. C5 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4082 | 2 |
| #65934 | 2 |
| C5×#447 | 2 |
| #65507 | 2 |
| #65444 | 2 |
| #65442 | 2 |
| #65329 | 2 |
| #65057 | 2 |
| #65056 | 2 |
| #65028 | 2 |
| #65007 | 2 |
| #3211 | 5 |