Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#65144 | C2 | semidirect |
| 5. #10598307 | C2 | semidirect |
| 6. #10598301 | C2 | semidirect |
| 7. #10598211 | C2 | semidirect |
| 30. C2×C5×Q16 | Q8 | semidirect |
| 32. C2×C5×D8 | Q8 | semidirect |
| 158. C2×Q16 | Dic10 | semidirect |
| 160. C2×D8 | Dic10 | semidirect |
| 277. C5 | #13371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65144 | 2 |
| C2×C5×#360 | 2 |
| #10602877 | 2 |
| C2×#64786 | 2 |
| #10598307 | 2 |
| #10598301 | 2 |
| #10598211 | 2 |
| #13371 | 5 |