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 |
|---|---|---|
| 1. C5×#3185 | C2 | semidirect |
| 2. #10615079 | C2 | semidirect |
| 5. #10602133 | C2 | semidirect |
| 6. #10602093 | C2 | semidirect |
| 7. #10602018 | C2 | semidirect |
| 8. #10602008 | C2 | semidirect |
| 9. #10600642 | C2 | semidirect |
| 13. C5×#498 | C22 | semidirect |
| 14. C5×#494 | C22 | semidirect |
| 15. C5×#487 | C22 | semidirect |
| 20. #65382 | C22 | semidirect |
| 21. #65381 | C22 | semidirect |
| 26. #65370 | C22 | semidirect |
| 27. #65368 | C22 | semidirect |
| 36. #64675 | C22 | semidirect |
| 37. #64674 | C22 | semidirect |
| 38. C8×#168 | C22 | semidirect |
| 81. #3185 | D5 | semidirect |
| 130. #498 | C2×D5 | semidirect |
| 132. #494 | C2×D5 | semidirect |
| 137. #487 | C2×D5 | 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×#3185 | 2 |
| #10615079 | 2 |
| #10615067 | 2 |
| #10610257 | 2 |
| #10602133 | 2 |
| #10602093 | 2 |
| #10602018 | 2 |
| #10602008 | 2 |
| #10600642 | 2 |
| #19753 | 5 |