Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
914 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 115 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. C22×C5×C4⋊C4 | C4 | semidirect |
| 7. C22×C42×C5 | C4 | semidirect |
| 9. C5×#390 | C4 | semidirect |
| 90. C22×C4⋊C4 | Dic5 | semidirect |
| 92. C22×C42 | Dic5 | semidirect |
| 96. #390 | Dic5 | semidirect |
| 303. C5 | #12856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#390 | 2 |
| #10602923 | 2 |
| #10598132 | 2 |
| #12856 | 5 |