Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3262 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 3262 conjugacy classes of subgroups — too many to draw. Only its 987 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 |
|---|---|---|
| 4. C2×#65381 | C2 | direct (N × H) |
| 18. #65381 | C22 | direct (N × H) |
| 56. C22×C4×C5 | Q16 | semidirect |
| 96. C2×C4×C5 | C2×Q16 | semidirect |
| 129. C22×C5 | #494 | semidirect |
| 135. C4×C5 | C22×Q16 | semidirect |
| 151. C22×C4 | #689 | semidirect |
| 163. C2×C5 | C2×#494 | semidirect |
| 178. C2×C4 | C2×#689 | semidirect |
| 184. C5 | C22×#494 | semidirect |
| 185. C22 | #65381 | direct (N × H) |
| 192. C4 | C22×#689 | semidirect |
| 194. C2 | C2×#65381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C4⋊Q8 | 2 |
| C23×#689 | 2 |
| C22×#4015 | 2 |
| C2×#65381 | 2 |
| C22×C4×#168 | 2 |
| C22×#494 | 5 |