Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
7646 conjugacy classes of subgroups; only the 1976 normal subgroups are shown.
This group has 7646 conjugacy classes of subgroups — too many to draw. Only its 1976 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. C24×#170 | C2 | semidirect |
| 3. C22×#4003 | C2 | direct (N × H) |
| 11. C23×#170 | C22 | semidirect |
| 12. C2×#4003 | C22 | direct (N × H) |
| 17. C24×D5 | C8 | semidirect |
| 29. C22×#170 | C23 | semidirect |
| 30. #4003 | C23 | direct (N × H) |
| 41. C23×D5 | C2×C8 | semidirect |
| 54. C2×#170 | C24 | semidirect |
| 64. C23×C5 | C22⋊C8 | semidirect |
| 72. C22×D5 | C22×C8 | semidirect |
| 100. C22×C5 | C2×C22⋊C8 | semidirect |
| 108. C2×D5 | C23×C8 | semidirect |
| 133. C2×C5 | C22×C22⋊C8 | semidirect |
| 143. C23 | #4003 | direct (N × H) |
| 157. C5 | C23×C22⋊C8 | semidirect |
| 162. C22 | C2×#4003 | direct (N × H) |
| 171. C2 | C22×#4003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×D5 | 2 |
| C24×#170 | 2 |
| C22×#4003 | 2 |
| C23×C22⋊C8 | 5 |