Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
560 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10614954 | C2 | semidirect |
| 5. #10602573 | C2 | semidirect |
| 6. #10600661 | C2 | semidirect |
| 7. #10598159 | C2 | semidirect |
| 107. C5×M16 | SD16 | semidirect |
| 286. M16 | #687 | semidirect |
| 358. C5 | #10206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3152 | 2 |
| #10615051 | 2 |
| #10614954 | 2 |
| #10602604 | 2 |
| #10602573 | 2 |
| #10600661 | 2 |
| #10598159 | 2 |
| #10206 | 5 |