Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 131 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. C5×C8×M16 | C2 | semidirect |
| 3. #10601573 | C2 | semidirect |
| 5. #10600672 | C2 | semidirect |
| 7. #10600523 | C2 | semidirect |
| 67. C8×M16 | D5 | semidirect |
| 279. C5 | #9800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64983 | 2 |
| C5×C8×M16 | 2 |
| #10601573 | 2 |
| #10601567 | 2 |
| #10600672 | 2 |
| #10600669 | 2 |
| #10600523 | 2 |
| #9800 | 5 |