Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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. #10611057 | C2 | semidirect |
| 3. #10601628 | C2 | semidirect |
| 4. #10601584 | C2 | semidirect |
| 5. #10601554 | C2 | semidirect |
| 6. C5×#1287 | C2 | semidirect |
| 7. #10598243 | C2 | semidirect |
| 23. #65004 | C4 | semidirect |
| 24. #65002 | C4 | semidirect |
| 25. #65001 | C4 | semidirect |
| 28. #64992 | C4 | semidirect |
| 95. #1287 | D5 | semidirect |
| 381. C5 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611085 | 2 |
| #10611057 | 2 |
| #10601628 | 2 |
| #10601584 | 2 |
| #10601554 | 2 |
| C5×#1287 | 2 |
| #10598243 | 2 |
| #9370 | 5 |