Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
632 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10614903 | C2 | semidirect |
| 3. C5×#1545 | C2 | semidirect |
| 4. #10601583 | C2 | semidirect |
| 5. #10601306 | C2 | semidirect |
| 6. #10598228 | C2 | semidirect |
| 7. #10598204 | C2 | semidirect |
| 19. #65362 | C4 | semidirect |
| 21. #65359 | C4 | semidirect |
| 51. #4020 | C2×C4 | semidirect |
| 54. #4015 | C2×C4 | semidirect |
| 69. C4×#168 | C2×C4 | semidirect |
| 73. #1545 | D5 | semidirect |
| 130. C4×Dic5 | D8 | semidirect |
| 388. C5 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614903 | 2 |
| #10614897 | 2 |
| C5×#1545 | 2 |
| #10601583 | 2 |
| #10601306 | 2 |
| #10598228 | 2 |
| #10598204 | 2 |
| #9299 | 5 |