Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3950 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 3950 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 |
|---|---|---|
| 2. C23×#687 | C2 | semidirect |
| 3. C22×#4015 | C2 | semidirect |
| 4. C2×#65365 | C2 | direct (N × H) |
| 5. C22×C4×#168 | C2 | semidirect |
| 13. C22×#687 | C22 | semidirect |
| 17. C2×#4015 | C22 | semidirect |
| 18. #65365 | C22 | direct (N × H) |
| 19. C2×C4×#168 | C22 | semidirect |
| 38. C2×#687 | C23 | semidirect |
| 40. C22×#168 | D4 | semidirect |
| 43. #4015 | C23 | semidirect |
| 44. C4×#168 | C23 | semidirect |
| 60. C22×C4×C5 | SD16 | semidirect |
| 75. C2×#168 | C2×D4 | semidirect |
| 102. C2×C4×C5 | C2×SD16 | semidirect |
| 111. #168 | C22×D4 | semidirect |
| 139. C22×C5 | #492 | semidirect |
| 144. C4×C5 | C22×SD16 | semidirect |
| 163. C22×C4 | #687 | semidirect |
| 175. C2×C5 | C2×#492 | semidirect |
| 192. C2×C4 | C2×#687 | semidirect |
| 199. C5 | C22×#492 | semidirect |
| 203. C22 | #65365 | direct (N × H) |
| 208. C4 | C22×#687 | semidirect |
| 212. C2 | C2×#65365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#127 | 2 |
| C23×#687 | 2 |
| C22×#4015 | 2 |
| C2×#65365 | 2 |
| C22×C4×#168 | 2 |
| C22×#492 | 5 |