Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
590 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 159 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. C5×#1846 | C2 | semidirect |
| 3. C2×#64711 | C2 | semidirect |
| 4. C2×#64681 | C2 | semidirect |
| 14. #64984 | C4 | semidirect |
| 40. C2×#672 | D4 | semidirect |
| 44. #1846 | D5 | semidirect |
| 199. C5 | #13206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64984 | 2 |
| C5×#1846 | 2 |
| C2×#64711 | 2 |
| C2×#64681 | 2 |
| #13206 | 5 |