Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
716 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 716 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. #10615612 | C2 | semidirect |
| 2. C22×#3960 | C2 | semidirect |
| 4. #10610898 | C2 | semidirect |
| 5. C5×#2141 | C2 | semidirect |
| 6. #10602214 | C2 | semidirect |
| 7. #10601444 | C2 | semidirect |
| 8. #10600028 | C2 | semidirect |
| 9. #10600027 | C2 | semidirect |
| 18. #65480 | C22 | semidirect |
| 20. #65470 | C22 | semidirect |
| 31. C5×#358 | C22 | semidirect |
| 32. #64721 | C22 | semidirect |
| 33. #64712 | C22 | semidirect |
| 34. #64711 | C22 | semidirect |
| 85. #2141 | D5 | semidirect |
| 158. #358 | C2×D5 | semidirect |
| 332. C5 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615612 | 2 |
| C22×#3960 | 2 |
| C2×#65197 | 2 |
| #10610898 | 2 |
| C5×#2141 | 2 |
| #10602214 | 2 |
| #10601444 | 2 |
| #10600028 | 2 |
| #10600027 | 2 |
| #33586 | 5 |