Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
276 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #10601441 | C2 | semidirect |
| 5. C5×#1384 | C2 | semidirect |
| 6. #10598313 | C2 | semidirect |
| 7. #10598215 | C2 | semidirect |
| 59. #1384 | D5 | semidirect |
| 251. C5 | #13500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64735 | 2 |
| #10601458 | 2 |
| #10601457 | 2 |
| #10601441 | 2 |
| C5×#1384 | 2 |
| #10598313 | 2 |
| #10598215 | 2 |
| #13500 | 5 |