Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 2. C22×#3959 | C2 | semidirect |
| 3. C2×#65198 | C2 | semidirect |
| 4. #10610900 | C2 | semidirect |
| 5. C5×#2140 | C2 | semidirect |
| 6. #10602214 | C2 | semidirect |
| 7. #10601444 | C2 | semidirect |
| 8. #10599998 | C2 | semidirect |
| 9. #10599997 | C2 | semidirect |
| 27. C2×Dic40 | C22 | semidirect |
| 28. C2×#3932 | C22 | semidirect |
| 29. #65162 | C22 | semidirect |
| 32. #64721 | C22 | semidirect |
| 33. #64712 | C22 | semidirect |
| 34. #64711 | C22 | semidirect |
| 56. C2×Dic20 | D4 | semidirect |
| 85. #2140 | D5 | semidirect |
| 332. C5 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615561 | 2 |
| C22×#3959 | 2 |
| C2×#65198 | 2 |
| #10610900 | 2 |
| C5×#2140 | 2 |
| #10602214 | 2 |
| #10601444 | 2 |
| #10599998 | 2 |
| #10599997 | 2 |
| #33587 | 5 |