Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
530 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10614685 | C2 | semidirect |
| 3. C5×#1527 | C2 | semidirect |
| 4. #10601628 | C2 | semidirect |
| 5. #10600660 | C2 | semidirect |
| 6. #10598241 | C2 | semidirect |
| 7. #10598157 | C2 | semidirect |
| 18. #65347 | C4 | semidirect |
| 20. #65344 | C4 | semidirect |
| 57. #4020 | C2×C4 | semidirect |
| 60. #4015 | C2×C4 | semidirect |
| 79. #3935 | C2×C4 | semidirect |
| 83. #1527 | 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 |
|---|---|
| #10614685 | 2 |
| #10614678 | 2 |
| C5×#1527 | 2 |
| #10601628 | 2 |
| #10600660 | 2 |
| #10598241 | 2 |
| #10598157 | 2 |
| #9381 | 5 |