Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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. #10615637 | C2 | semidirect |
| 2. C2×#65482 | C2 | semidirect |
| 3. C22×D80 | C2 | semidirect |
| 4. #10610898 | C2 | semidirect |
| 5. C5×#2138 | C2 | semidirect |
| 6. #10602194 | C2 | semidirect |
| 7. #10601445 | C2 | semidirect |
| 8. #10600028 | C2 | semidirect |
| 9. #10599995 | C2 | semidirect |
| 19. #65480 | C22 | semidirect |
| 20. C2×#3960 | C22 | semidirect |
| 22. #65440 | C22 | semidirect |
| 23. C2×#3958 | C22 | semidirect |
| 29. #65161 | C22 | semidirect |
| 31. C5×#358 | C22 | semidirect |
| 32. C5×#357 | C22 | semidirect |
| 33. #64721 | C22 | semidirect |
| 34. #64711 | C22 | semidirect |
| 60. C2×D40 | D4 | semidirect |
| 86. #2138 | D5 | semidirect |
| 157. #358 | C2×D5 | semidirect |
| 159. #357 | C2×D5 | semidirect |
| 339. C5 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615637 | 2 |
| C2×#65482 | 2 |
| C22×D80 | 2 |
| #10610898 | 2 |
| C5×#2138 | 2 |
| #10602194 | 2 |
| #10601445 | 2 |
| #10600028 | 2 |
| #10599995 | 2 |
| #33585 | 5 |