Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
682 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 155 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. #10613647 | C2 | semidirect |
| 3. C5×#2244 | C2 | semidirect |
| 4. #10602145 | C2 | semidirect |
| 5. #10602082 | C2 | semidirect |
| 6. #10599983 | C2 | semidirect |
| 7. #10599976 | C2 | semidirect |
| 8. #10599873 | C2 | semidirect |
| 9. #10599864 | C2 | semidirect |
| 14. C5×#499 | C22 | semidirect |
| 22. #65163 | C22 | semidirect |
| 27. #64972 | C22 | semidirect |
| 28. C5×#357 | C22 | semidirect |
| 29. C5×#346 | C22 | semidirect |
| 30. #64782 | C22 | semidirect |
| 31. #64729 | C22 | semidirect |
| 32. C16×Dic5 | C22 | semidirect |
| 33. #64711 | C22 | semidirect |
| 34. #64681 | C22 | semidirect |
| 77. #2244 | D5 | semidirect |
| 126. #499 | C2×D5 | semidirect |
| 139. #357 | C2×D5 | semidirect |
| 141. #346 | C2×D5 | semidirect |
| 290. C5 | #33704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613647 | 2 |
| D5×#493 | 2 |
| C5×#2244 | 2 |
| #10602145 | 2 |
| #10602082 | 2 |
| #10599983 | 2 |
| #10599976 | 2 |
| #10599873 | 2 |
| #10599864 | 2 |
| #33704 | 5 |