Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
230 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10602105 | C2 | semidirect |
| 5. C5×#1362 | C2 | semidirect |
| 6. #10598052 | C2 | semidirect |
| 7. #10597961 | C2 | semidirect |
| 53. #1362 | D5 | semidirect |
| 204. C5 | #12434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602105 | 2 |
| #10602098 | 2 |
| #10600072 | 2 |
| #10599370 | 2 |
| C5×#1362 | 2 |
| #10598052 | 2 |
| #10597961 | 2 |
| #12434 | 5 |