Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10611073 | C2 | semidirect |
| 3. #10601594 | C2 | semidirect |
| 4. #10600233 | C2 | semidirect |
| 5. #10600224 | C2 | semidirect |
| 6. C5×#1300 | C2 | semidirect |
| 7. #10598160 | C2 | semidirect |
| 23. #65003 | C4 | semidirect |
| 24. #65002 | C4 | semidirect |
| 25. #65001 | C4 | semidirect |
| 27. #64991 | C4 | semidirect |
| 96. #1300 | D5 | semidirect |
| 402. C5 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611073 | 2 |
| #10610263 | 2 |
| #10601594 | 2 |
| #10600233 | 2 |
| #10600224 | 2 |
| C5×#1300 | 2 |
| #10598160 | 2 |
| #8997 | 5 |