Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
826 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 235 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. C22×Dic40 | C2 | semidirect |
| 3. C2×#64988 | C2 | semidirect |
| 5. C2×C5×#346 | C2 | semidirect |
| 6. #10599877 | C2 | direct (N × H) |
| 17. C2×Dic40 | C22 | semidirect |
| 21. #64988 | C22 | semidirect |
| 24. C5×#346 | C22 | semidirect |
| 63. C2×#346 | D5 | semidirect |
| 117. #346 | C2×D5 | semidirect |
| 224. C2×C5 | #2251 | semidirect |
| 254. C5 | C2×#2251 | semidirect |
| 268. C2 | #10599877 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic40 | 2 |
| C22×#3932 | 2 |
| C2×#64988 | 2 |
| C2×#64985 | 2 |
| C2×C5×#346 | 2 |
| #10599877 | 2 |
| C2×#2251 | 5 |