Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
528 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 159 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. #10600181 | C2 | semidirect |
| 3. #10598133 | C2 | semidirect |
| 22. C5×#124 | C8 | semidirect |
| 130. #124 | #168 | semidirect |
| 241. C5 | #7567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#124 | 2 |
| #10600181 | 2 |
| #10598133 | 2 |
| #10598130 | 2 |
| #7567 | 5 |