Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 442 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. C5×#535 | C2 | semidirect |
| 2. #66164 | C2 | semidirect |
| 3. #65523 | C2 | semidirect |
| 4. #65506 | C2 | semidirect |
| 5. #65328 | C2 | semidirect |
| 6. #65327 | C2 | semidirect |
| 7. #65325 | C2 | semidirect |
| 8. #65324 | C2 | semidirect |
| 9. #65292 | C2 | semidirect |
| 11. C22×C5×D4 | C22 | semidirect |
| 12. C22×D20 | C22 | semidirect |
| 16. C5×#121 | C22 | semidirect |
| 19. C5×#117 | C22 | semidirect |
| 27. #4076 | C22 | semidirect |
| 28. #4072 | C22 | semidirect |
| 29. C2×#681 | C22 | semidirect |
| 30. C22×#168 | C22 | semidirect |
| 31. #3964 | C22 | semidirect |
| 32. #3964 | C22 | semidirect |
| 33. C22⋊#168 | C22 | semidirect |
| 34. C22⋊#168 | C22 | semidirect |
| 35. #3941 | C22 | semidirect |
| 36. #3941 | C22 | semidirect |
| 37. #3940 | C22 | semidirect |
| 38. #3939 | C22 | semidirect |
| 80. #535 | D5 | semidirect |
| 127. C22×D4 | C2×D5 | semidirect |
| 139. #121 | C2×D5 | semidirect |
| 145. #117 | C2×D5 | semidirect |
| 259. C5 | #3199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#535 | 2 |
| #66164 | 2 |
| #65523 | 2 |
| #65506 | 2 |
| #65328 | 2 |
| #65327 | 2 |
| #65325 | 2 |
| #65324 | 2 |
| #65292 | 2 |
| #3199 | 5 |