Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10598132 | C2 | semidirect |
| 5. C2×C5×#117 | C4 | semidirect |
| 6. C2×C5×#117 | C4 | semidirect |
| 8. C5×#390 | C4 | semidirect |
| 77. C2×#117 | Dic5 | semidirect |
| 78. C2×#117 | Dic5 | semidirect |
| 82. #390 | Dic5 | semidirect |
| 243. C5 | #12858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2309 | 2 |
| #10602923 | 2 |
| #10598132 | 2 |
| #12858 | 5 |