Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. #10614685 | C2 | semidirect |
| 3. #10602611 | C2 | semidirect |
| 4. #10602606 | C2 | semidirect |
| 5. #10602511 | C2 | semidirect |
| 6. #10598243 | C2 | semidirect |
| 7. #10598240 | C2 | semidirect |
| 10. C5×#496 | C4 | semidirect |
| 11. C5×#489 | C4 | semidirect |
| 38. C5×C4⋊Q8 | C2×C4 | semidirect |
| 39. C5×#127 | C2×C4 | semidirect |
| 65. C5×#97 | C2×C4 | semidirect |
| 144. #496 | Dic5 | semidirect |
| 145. #489 | Dic5 | semidirect |
| 225. C4⋊Q8 | C2×Dic5 | semidirect |
| 226. #127 | C2×Dic5 | semidirect |
| 257. #97 | C2×Dic5 | semidirect |
| 408. C5 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3213 | 2 |
| #10614685 | 2 |
| #10602611 | 2 |
| #10602606 | 2 |
| #10602511 | 2 |
| #10598243 | 2 |
| #10598240 | 2 |
| #9381 | 5 |