Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 3. C5×#1515 | C2 | semidirect |
| 4. #10602616 | C2 | semidirect |
| 6. #10598245 | C2 | semidirect |
| 7. #10598124 | C2 | semidirect |
| 12. #65377 | C4 | semidirect |
| 13. #65374 | C4 | semidirect |
| 14. #65370 | C4 | semidirect |
| 15. #65367 | C4 | semidirect |
| 71. #1515 | D5 | semidirect |
| 296. C5 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615078 | 2 |
| #10611068 | 2 |
| C5×#1515 | 2 |
| #10602616 | 2 |
| #10600357 | 2 |
| #10598245 | 2 |
| #10598124 | 2 |
| #9415 | 5 |