Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3678 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C2×#65226 | C2 | direct (N × H) |
| 6. C22×C42×C5 | C4 | semidirect |
| 9. #65226 | C22 | direct (N × H) |
| 17. C2×C42×C5 | C2×C4 | semidirect |
| 33. C42×C5 | C22×C4 | semidirect |
| 36. C22×C42 | Dic5 | semidirect |
| 56. C2×C42 | C2×Dic5 | semidirect |
| 59. C22×C5 | #383 | semidirect |
| 76. C42 | C22×Dic5 | semidirect |
| 77. C2×C5 | C2×#383 | semidirect |
| 90. C5 | C22×#383 | semidirect |
| 91. C22 | #65226 | direct (N × H) |
| 98. C2 | C2×#65226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C5 | 2 |
| C22×#3963 | 2 |
| C2×#65226 | 2 |
| C22×#383 | 5 |