Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3870 conjugacy classes of subgroups; only the 1976 normal subgroups are shown.
This group has 3870 conjugacy classes of subgroups — too many to draw. Only its 1976 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 |
|---|---|---|
| 3. C22×#4004 | C2 | direct (N × H) |
| 11. C2×#4004 | C22 | direct (N × H) |
| 16. C23×Dic5 | C8 | semidirect |
| 26. #4004 | C23 | direct (N × H) |
| 37. C22×Dic5 | C2×C8 | semidirect |
| 55. C23×C5 | C4⋊C8 | semidirect |
| 63. C2×Dic5 | C22×C8 | semidirect |
| 84. C22×C5 | C2×C4⋊C8 | semidirect |
| 91. Dic5 | C23×C8 | semidirect |
| 111. C2×C5 | C22×C4⋊C8 | semidirect |
| 115. C23 | #4004 | direct (N × H) |
| 130. C5 | C23×C4⋊C8 | semidirect |
| 131. C22 | C2×#4004 | direct (N × H) |
| 141. C2 | C22×#4004 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#170 | 2 |
| C23×C4×Dic5 | 2 |
| C22×#4004 | 2 |
| C23×C4⋊C8 | 5 |