Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
642 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 642 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. C22×C5×C4⋊C4 | C4 | semidirect |
| 7. C5×#391 | C4 | semidirect |
| 75. C2×#117 | Dic5 | semidirect |
| 76. C22×C4⋊C4 | Dic5 | semidirect |
| 79. #391 | Dic5 | semidirect |
| 236. C5 | #12859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2311 | 2 |
| #10602932 | 2 |
| #10598132 | 2 |
| #12859 | 5 |