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 |
|---|---|---|
| 2. #10611073 | C2 | semidirect |
| 3. C5×#1496 | C2 | semidirect |
| 4. #10602609 | C2 | semidirect |
| 5. #10601581 | C2 | semidirect |
| 6. #10598239 | C2 | semidirect |
| 7. #10598234 | C2 | semidirect |
| 14. #65378 | C4 | semidirect |
| 15. #65369 | C4 | semidirect |
| 16. #65363 | C4 | semidirect |
| 17. #65360 | C4 | semidirect |
| 95. #1496 | 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 |
|---|---|
| #10615023 | 2 |
| #10611073 | 2 |
| C5×#1496 | 2 |
| #10602609 | 2 |
| #10601581 | 2 |
| #10598239 | 2 |
| #10598234 | 2 |
| #8997 | 5 |