Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1174 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1174 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×#3996 | C2 | semidirect |
| 3. C22×D5⋊C16 | C2 | semidirect |
| 4. C2×#64909 | C2 | direct (N × H) |
| 17. C2×#3996 | C22 | semidirect |
| 19. C2×D5⋊C16 | C22 | semidirect |
| 20. #64909 | C22 | direct (N × H) |
| 53. #3996 | C23 | semidirect |
| 55. D5⋊C16 | C23 | semidirect |
| 180. C22×C5 | #359 | semidirect |
| 234. C2×C5 | C2×#359 | semidirect |
| 268. C5 | C22×#359 | semidirect |
| 275. C22 | #64909 | direct (N × H) |
| 285. C2 | C2×#64909 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4065 | 2 |
| C22×#3996 | 2 |
| C22×D5⋊C16 | 2 |
| C2×#64909 | 2 |
| C22×#359 | 5 |