Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4126 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2232 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 |
|---|---|---|
| 3. C22×#4002 | C2 | direct (N × H) |
| 7. C23×#170 | C4 | semidirect |
| 11. C2×#4002 | C22 | direct (N × H) |
| 21. C22×#170 | C2×C4 | semidirect |
| 25. #4002 | C23 | direct (N × H) |
| 41. C2×#170 | C22×C4 | semidirect |
| 53. C23×C5 | #97 | semidirect |
| 66. #170 | C23×C4 | semidirect |
| 80. C22×C5 | C2×#97 | semidirect |
| 105. C2×C5 | C22×#97 | semidirect |
| 109. C23 | #4002 | direct (N × H) |
| 123. C5 | C23×#97 | semidirect |
| 124. C22 | C2×#4002 | direct (N × H) |
| 133. C2 | C22×#4002 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#170 | 2 |
| C23×C4×Dic5 | 2 |
| C22×#4002 | 2 |
| C23×#97 | 5 |