Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
298 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #10611437 | C2 | semidirect |
| 5. #10598256 | C2 | semidirect |
| 6. #10598055 | C2 | semidirect |
| 7. #10598049 | C2 | semidirect |
| 68. C5×Q16 | SD16 | semidirect |
| 183. Q16 | #687 | semidirect |
| 236. C5 | #12353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611437 | 2 |
| C5×#2207 | 2 |
| #10602081 | 2 |
| #10602079 | 2 |
| #10598256 | 2 |
| #10598055 | 2 |
| #10598049 | 2 |
| #12353 | 5 |