Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
662 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. C22×#3960 | C2 | semidirect |
| 3. C5×#1969 | C2 | semidirect |
| 4. C2×#64711 | C2 | semidirect |
| 5. #10598148 | C2 | semidirect |
| 27. C2×C5×Q16 | D4 | semidirect |
| 50. C2×#672 | D4 | semidirect |
| 54. #1969 | D5 | semidirect |
| 126. C2×C4×C5 | SD32 | semidirect |
| 147. C2×Q16 | D20 | semidirect |
| 255. C2×C4 | #3960 | semidirect |
| 265. C5 | #13328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3960 | 2 |
| C2×#64984 | 2 |
| C5×#1969 | 2 |
| C2×#64711 | 2 |
| #10598148 | 2 |
| #13328 | 5 |