Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×#3959 | C2 | semidirect |
| 3. C22×#3932 | C2 | semidirect |
| 4. C2×C5×#357 | C2 | semidirect |
| 5. #10601420 | C2 | semidirect |
| 6. C2×#64711 | C2 | semidirect |
| 7. #10598295 | C2 | semidirect |
| 54. C2×Dic20 | D4 | semidirect |
| 63. C2×C5×C16 | D4 | semidirect |
| 72. C2×#672 | D4 | semidirect |
| 79. C2×#357 | D5 | semidirect |
| 187. C2×Dic5 | SD32 | semidirect |
| 239. C2×C16 | C22⋊D5 | semidirect |
| 373. C5 | #13328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65440 | 2 |
| C22×#3959 | 2 |
| C22×#3932 | 2 |
| C2×C5×#357 | 2 |
| #10601420 | 2 |
| C2×#64711 | 2 |
| #10598295 | 2 |
| #13328 | 5 |