Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1502 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1502 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×#64693 | C2 | direct (N × H) |
| 6. C23×Dic10 | C4 | semidirect |
| 13. C2×#4082 | C4 | semidirect |
| 15. C22×C4×Dic5 | C4 | semidirect |
| 20. #64693 | C22 | direct (N × H) |
| 38. C22×Dic10 | C2×C4 | semidirect |
| 50. #4082 | C2×C4 | semidirect |
| 53. C2×C4×Dic5 | C2×C4 | semidirect |
| 104. C2×Dic10 | C22×C4 | semidirect |
| 114. C4×Dic5 | C22×C4 | semidirect |
| 231. C22×C5 | #354 | semidirect |
| 300. C2×C5 | C2×#354 | semidirect |
| 348. C5 | C22×#354 | semidirect |
| 367. C22 | #64693 | direct (N × H) |
| 383. C2 | C2×#64693 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4082 | 2 |
| C22×C5×#99 | 2 |
| C22×#3966 | 2 |
| C2×#64693 | 2 |
| C22×#354 | 5 |