Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 122 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. #10604702 | C2 | semidirect |
| 3. C2×#64881 | C2 | semidirect |
| 4. #10598807 | C2 | semidirect |
| 5. #10598799 | C2 | semidirect |
| 27. C5×#135 | C8 | semidirect |
| 77. C5×Q16 | C2×C8 | semidirect |
| 80. C5×D8 | C2×C8 | semidirect |
| 151. #135 | #170 | semidirect |
| 212. Q16 | C2×#170 | semidirect |
| 215. D8 | C2×#170 | semidirect |
| 274. C5 | #11598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic5×#135 | 2 |
| #10604702 | 2 |
| C2×#64881 | 2 |
| #10598807 | 2 |
| #10598799 | 2 |
| #11598 | 5 |