Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
7134 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×#704 | C2 | semidirect |
| 3. C22×#4013 | C2 | direct (N × H) |
| 12. C22×#704 | C22 | semidirect |
| 14. C2×#4013 | C22 | direct (N × H) |
| 36. C2×#704 | C23 | semidirect |
| 38. #4013 | C23 | direct (N × H) |
| 71. #704 | C24 | semidirect |
| 91. C23×C5 | #100 | semidirect |
| 140. C22×C5 | C2×#100 | semidirect |
| 184. C2×C5 | C22×#100 | semidirect |
| 200. C23 | #4013 | direct (N × H) |
| 214. C5 | C23×#100 | semidirect |
| 225. C22 | C2×#4013 | direct (N × H) |
| 235. C2 | C22×#4013 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C22⋊D5 | 2 |
| C23×#704 | 2 |
| C22×#4013 | 2 |
| C23×#100 | 5 |