Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
566 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. C2×#64906 | C2 | semidirect |
| 3. C4×#3995 | C2 | semidirect |
| 4. #10603827 | C2 | semidirect |
| 47. #3995 | D4 | semidirect |
| 188. C4×C5 | #361 | semidirect |
| 192. Dic5 | #361 | semidirect |
| 272. C5 | #13257 | semidirect |
| 288. C4 | #64906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#493 | 2 |
| C2×#64906 | 2 |
| C4×#3995 | 2 |
| #10603827 | 2 |
| #13257 | 5 |