Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
364 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10601542 | C2 | semidirect |
| 5. #10600184 | C2 | semidirect |
| 6. C5×#1276 | C2 | semidirect |
| 7. #10598236 | C2 | semidirect |
| 19. #64706 | C4 | semidirect |
| 20. #64705 | C4 | semidirect |
| 61. #1276 | D5 | semidirect |
| 285. C5 | #9582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10601565 | 2 |
| #10601551 | 2 |
| #10601542 | 2 |
| #10600188 | 2 |
| #10600184 | 2 |
| C5×#1276 | 2 |
| #10598236 | 2 |
| #9582 | 5 |