Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2337 | C2 | semidirect |
| 3. #10602511 | C2 | semidirect |
| 4. #10600357 | C2 | semidirect |
| 5. #10600285 | C2 | semidirect |
| 6. #10598124 | C2 | semidirect |
| 7. #10598112 | C2 | semidirect |
| 20. #65347 | C4 | semidirect |
| 22. #65344 | C4 | semidirect |
| 57. #4020 | C2×C4 | semidirect |
| 60. #4015 | C2×C4 | semidirect |
| 78. #3935 | C2×C4 | semidirect |
| 81. #2337 | D5 | semidirect |
| 408. C5 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2337 | 2 |
| #10614678 | 2 |
| #10602511 | 2 |
| #10600357 | 2 |
| #10600285 | 2 |
| #10598124 | 2 |
| #10598112 | 2 |
| #9381 | 5 |