Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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. #10600558 | C2 | semidirect |
| 4. C5×#1374 | C2 | semidirect |
| 5. #10598297 | C2 | semidirect |
| 44. #1374 | D5 | semidirect |
| 238. C5 | #13480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64729 | 2 |
| #10600569 | 2 |
| #10600558 | 2 |
| C5×#1374 | 2 |
| #10598297 | 2 |
| #13480 | 5 |