Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4638 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 1067 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 |
|---|---|---|
| 1. C23×D40 | C2 | semidirect |
| 2. C22×#4020 | C2 | semidirect |
| 3. C22×C4×C5×C8 | C2 | semidirect |
| 4. C2×#64984 | C2 | direct (N × H) |
| 10. C22×D40 | C22 | semidirect |
| 12. C2×#4020 | C22 | semidirect |
| 13. C2×C4×C5×C8 | C22 | semidirect |
| 14. #64984 | C22 | direct (N × H) |
| 24. C22×C5×C8 | D4 | semidirect |
| 29. C2×D40 | C23 | semidirect |
| 31. #4020 | C23 | semidirect |
| 32. C4×C5×C8 | C23 | semidirect |
| 36. C22×C4×C8 | D5 | semidirect |
| 41. C22×C4×C5 | D8 | semidirect |
| 52. C2×C5×C8 | C2×D4 | semidirect |
| 66. C2×C4×C8 | C2×D5 | semidirect |
| 75. C2×C4×C5 | C2×D8 | semidirect |
| 83. C5×C8 | C22×D4 | semidirect |
| 94. C22×C8 | D20 | semidirect |
| 100. C4×C8 | C22×D5 | semidirect |
| 101. C22×C5 | #493 | semidirect |
| 109. C4×C5 | C22×D8 | semidirect |
| 121. C22×C4 | D40 | semidirect |
| 127. C2×C8 | C2×D20 | semidirect |
| 131. C2×C5 | C2×#493 | semidirect |
| 146. C2×C4 | C2×D40 | semidirect |
| 151. C8 | C22×D20 | semidirect |
| 152. C5 | C22×#493 | semidirect |
| 156. C22 | #64984 | direct (N × H) |
| 161. C4 | C22×D40 | semidirect |
| 164. C2 | C2×#64984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D40 | 2 |
| C22×#4020 | 2 |
| C22×C4×C5×C8 | 2 |
| C2×#64984 | 2 |
| C22×#493 | 5 |