Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 2. #10604188 | C2 | semidirect |
| 3. #10604173 | C2 | semidirect |
| 5. #10598713 | C2 | semidirect |
| 29. C4×C5×D4 | C8 | semidirect |
| 168. C4×D4 | #170 | semidirect |
| 313. C5 | #7580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614050 | 2 |
| #10604188 | 2 |
| #10604173 | 2 |
| #10598824 | 2 |
| #10598713 | 2 |
| #7580 | 5 |