Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
466 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 144 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. #10598761 | C2 | direct (N × H) |
| 55. C22×Dic5 | C16 | semidirect |
| 111. C2×Dic5 | C2×C16 | semidirect |
| 193. C2×C5 | #1322 | semidirect |
| 229. C5 | C2×#1322 | semidirect |
| 253. C2 | #10598761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3946 | 2 |
| C2×C22⋊#674 | 2 |
| #10598761 | 2 |
| C2×#1322 | 5 |