Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
616 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 138 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. C4×#4002 | C2 | semidirect |
| 4. #10598722 | C2 | semidirect |
| 17. #64921 | C4 | direct (N × H) |
| 41. #4002 | C2×C4 | semidirect |
| 170. C4×C5 | #329 | semidirect |
| 249. C5 | C4×#329 | semidirect |
| 268. C4 | #64921 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#4082 | 2 |
| C2×#64921 | 2 |
| C4×#4002 | 2 |
| #10598722 | 2 |
| C4×#329 | 5 |