Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
366 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10602112 | C2 | semidirect |
| 3. #10601679 | C2 | semidirect |
| 4. #10601667 | C2 | semidirect |
| 5. #10598287 | C2 | semidirect |
| 6. #10598253 | C2 | semidirect |
| 7. #10598252 | C2 | semidirect |
| 18. #64971 | C22 | semidirect |
| 24. C4⋊#672 | C22 | semidirect |
| 25. #64681 | C22 | semidirect |
| 26. #64677 | C22 | semidirect |
| 303. C5 | #12376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3273 | 2 |
| #10602112 | 2 |
| #10601679 | 2 |
| #10601667 | 2 |
| #10598287 | 2 |
| #10598253 | 2 |
| #10598252 | 2 |
| #12376 | 5 |