Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
11422 conjugacy classes of subgroups; only the 5752 normal subgroups are shown.
This group has 11422 conjugacy classes of subgroups — too many to draw. Only its 5752 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×#4133 | C2 | direct (N × H) |
| 3. C23×#700 | C2 | semidirect |
| 4. C23×D5⋊C8 | C2 | semidirect |
| 12. C2×#4133 | C22 | direct (N × H) |
| 13. C22×#700 | C22 | semidirect |
| 14. C22×D5⋊C8 | C22 | semidirect |
| 27. #4133 | C23 | direct (N × H) |
| 28. C2×#700 | C23 | semidirect |
| 29. C2×D5⋊C8 | C23 | semidirect |
| 48. #700 | C24 | semidirect |
| 49. D5⋊C8 | C24 | semidirect |
| 60. C23×C5 | #131 | semidirect |
| 87. C22×C5 | C2×#131 | semidirect |
| 110. C2×C5 | C22×#131 | semidirect |
| 115. C23 | #4133 | direct (N × H) |
| 126. C5 | C23×#131 | semidirect |
| 129. C22 | C2×#4133 | direct (N × H) |
| 135. C2 | C22×#4133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#713 | 2 |
| C22×#4133 | 2 |
| C23×#700 | 2 |
| C23×D5⋊C8 | 2 |
| C23×#131 | 5 |