Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
316 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #10602222 | C2 | semidirect |
| 5. C4×#3951 | C2 | semidirect |
| 6. C5×#1376 | C2 | semidirect |
| 7. #10598312 | C2 | semidirect |
| 19. #64737 | C4 | semidirect |
| 20. #64736 | C4 | semidirect |
| 63. #1376 | D5 | semidirect |
| 264. C5 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602241 | 2 |
| #10602235 | 2 |
| #10602222 | 2 |
| #10600588 | 2 |
| C4×#3951 | 2 |
| C5×#1376 | 2 |
| #10598312 | 2 |
| #13137 | 5 |