Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1390 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1390 conjugacy classes of subgroups — too many to draw. Only its 280 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×#3995 | C2 | semidirect |
| 3. C22×#3990 | C2 | semidirect |
| 4. C2×#64906 | C2 | direct (N × H) |
| 17. C2×#3995 | C22 | semidirect |
| 19. C2×#3990 | C22 | semidirect |
| 20. #64906 | C22 | direct (N × H) |
| 53. #3995 | C23 | semidirect |
| 55. #3990 | C23 | semidirect |
| 186. C22×C5 | #361 | semidirect |
| 243. C2×C5 | C2×#361 | semidirect |
| 280. C5 | C22×#361 | semidirect |
| 291. C22 | #64906 | direct (N × H) |
| 301. C2 | C2×#64906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×D8 | 2 |
| C22×#3995 | 2 |
| C22×#3990 | 2 |
| C2×#64906 | 2 |
| C22×#361 | 5 |