Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 2. #10614864 | C2 | semidirect |
| 3. C5×#1500 | C2 | semidirect |
| 4. #10601558 | C2 | semidirect |
| 5. #10600233 | C2 | semidirect |
| 6. #10598234 | C2 | semidirect |
| 7. #10598106 | C2 | semidirect |
| 12. #65356 | C4 | semidirect |
| 13. #65354 | C4 | semidirect |
| 14. #65347 | C4 | semidirect |
| 15. #65344 | C4 | semidirect |
| 94. #1500 | 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 |
|---|---|
| #10614866 | 2 |
| #10614864 | 2 |
| C5×#1500 | 2 |
| #10601558 | 2 |
| #10600233 | 2 |
| #10598234 | 2 |
| #10598106 | 2 |
| #8997 | 5 |