Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1486 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 291 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×#64696 | C2 | direct (N × H) |
| 6. C24×Dic5 | C4 | semidirect |
| 10. C22×C22⋊Dic5 | C4 | semidirect |
| 13. C2×#4081 | C4 | semidirect |
| 20. #64696 | C22 | direct (N × H) |
| 37. C23×Dic5 | C2×C4 | semidirect |
| 46. C2×C22⋊Dic5 | C2×C4 | semidirect |
| 50. #4081 | C2×C4 | semidirect |
| 102. C22×Dic5 | C22×C4 | semidirect |
| 111. C22⋊Dic5 | C22×C4 | semidirect |
| 229. C22×C5 | #352 | semidirect |
| 296. C2×C5 | C2×#352 | semidirect |
| 343. C5 | C22×#352 | semidirect |
| 362. C22 | #64696 | direct (N × H) |
| 377. C2 | C2×#64696 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4081 | 2 |
| C22×C5×#100 | 2 |
| C22×#3966 | 2 |
| C2×#64696 | 2 |
| C22×#352 | 5 |