Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
726 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 120 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. #10598703 | C2 | direct (N × H) |
| 23. C23×Dic5 | C8 | semidirect |
| 73. C22×Dic5 | C2×C8 | semidirect |
| 232. C2×C5 | #1317 | semidirect |
| 277. C5 | C2×#1317 | semidirect |
| 312. C2 | #10598703 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65232 | 2 |
| C2×#64933 | 2 |
| #10598703 | 2 |
| C2×#1317 | 5 |