Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
524 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 121 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. #10612580 | C2 | semidirect |
| 2. #10610988 | C2 | semidirect |
| 3. C5×#2238 | C2 | semidirect |
| 5. #10601517 | C2 | semidirect |
| 6. #10600108 | C2 | semidirect |
| 7. #10600102 | C2 | semidirect |
| 8. #10600055 | C2 | semidirect |
| 9. #10600047 | C2 | semidirect |
| 10. #10599914 | C2 | semidirect |
| 11. #10599908 | C2 | semidirect |
| 17. #65444 | C22 | semidirect |
| 18. #65441 | C22 | semidirect |
| 29. #65144 | C22 | semidirect |
| 30. #65142 | C22 | semidirect |
| 33. C5×#365 | C22 | semidirect |
| 34. C5×#361 | C22 | semidirect |
| 38. #64732 | C22 | semidirect |
| 39. #64731 | C22 | semidirect |
| 40. #64716 | C22 | semidirect |
| 41. #64714 | C22 | semidirect |
| 96. #2238 | D5 | semidirect |
| 181. #365 | C2×D5 | semidirect |
| 184. #361 | C2×D5 | semidirect |
| 384. C5 | #33691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10612580 | 2 |
| #10610988 | 2 |
| C5×#2238 | 2 |
| #10601882 | 2 |
| #10601517 | 2 |
| #10600108 | 2 |
| #10600102 | 2 |
| #10600055 | 2 |
| #10600047 | 2 |
| #10599914 | 2 |
| #10599908 | 2 |
| #33691 | 5 |