Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 2. #10615079 | C2 | semidirect |
| 4. #10610271 | C2 | semidirect |
| 5. #10601986 | C2 | semidirect |
| 6. #10601985 | C2 | semidirect |
| 7. #10601984 | C2 | semidirect |
| 8. #10601976 | C2 | semidirect |
| 9. #10600642 | C2 | semidirect |
| 20. #65382 | C22 | semidirect |
| 21. #65381 | C22 | semidirect |
| 22. #65370 | C22 | semidirect |
| 23. #65368 | C22 | semidirect |
| 33. #64988 | C22 | semidirect |
| 34. #64970 | C22 | semidirect |
| 35. #64969 | C22 | semidirect |
| 36. #64675 | C22 | semidirect |
| 37. #64674 | C22 | semidirect |
| 38. C8×#168 | C22 | semidirect |
| 300. C5 | #19753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3138 | 2 |
| #10615079 | 2 |
| #10614890 | 2 |
| #10610271 | 2 |
| #10601986 | 2 |
| #10601985 | 2 |
| #10601984 | 2 |
| #10601976 | 2 |
| #10600642 | 2 |
| #19753 | 5 |