Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10602254 | C2 | semidirect |
| 3. #10600151 | C2 | semidirect |
| 4. C5×#1419 | C2 | semidirect |
| 5. #10598097 | C2 | semidirect |
| 6. #10598091 | C2 | semidirect |
| 7. #10598073 | C2 | semidirect |
| 15. #64740 | C4 | semidirect |
| 16. #64739 | C4 | semidirect |
| 35. Dic40 | C2×C4 | semidirect |
| 37. D80 | C2×C4 | semidirect |
| 39. #3926 | C2×C4 | semidirect |
| 44. #1419 | D5 | semidirect |
| 160. C5 | #13658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602254 | 2 |
| #10602251 | 2 |
| #10600151 | 2 |
| C5×#1419 | 2 |
| #10598097 | 2 |
| #10598091 | 2 |
| #10598073 | 2 |
| #13658 | 5 |