Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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×#4016 | C2 | semidirect |
| 3. C22×C5×#97 | C2 | semidirect |
| 4. C22×#3953 | C2 | semidirect |
| 5. C2×#65002 | C2 | direct (N × H) |
| 15. C2×#4016 | C22 | semidirect |
| 16. C2×C5×#97 | C22 | semidirect |
| 17. C2×#3953 | C22 | semidirect |
| 18. #65002 | C22 | direct (N × H) |
| 39. #4016 | C23 | semidirect |
| 40. C5×#97 | C23 | semidirect |
| 41. #3953 | C23 | semidirect |
| 46. C22×#97 | D5 | semidirect |
| 83. C2×#97 | C2×D5 | semidirect |
| 124. #97 | C22×D5 | semidirect |
| 125. C22×C5 | #490 | semidirect |
| 160. C2×C5 | C2×#490 | semidirect |
| 183. C5 | C22×#490 | semidirect |
| 187. C22 | #65002 | direct (N × H) |
| 196. C2 | C2×#65002 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4020 | 2 |
| C22×#4016 | 2 |
| C22×C5×#97 | 2 |
| C22×#3953 | 2 |
| C2×#65002 | 2 |
| C22×#490 | 5 |