Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2398 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 2398 conjugacy classes of subgroups — too many to draw. Only its 1067 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 |
|---|---|---|
| 4. C2×#64969 | C2 | direct (N × H) |
| 14. #64969 | C22 | direct (N × H) |
| 21. C22×C5×C8 | Q8 | semidirect |
| 46. C2×C5×C8 | C2×Q8 | semidirect |
| 75. C5×C8 | C22×Q8 | semidirect |
| 81. C22×C8 | Dic10 | semidirect |
| 92. C22×C5 | #498 | semidirect |
| 110. C2×C8 | C2×Dic10 | semidirect |
| 117. C2×C5 | C2×#498 | semidirect |
| 132. C8 | C22×Dic10 | semidirect |
| 133. C5 | C22×#498 | semidirect |
| 134. C22 | #64969 | direct (N × H) |
| 142. C2 | C2×#64969 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4015 | 2 |
| C22×C4×C5×C8 | 2 |
| C22×#3949 | 2 |
| C2×#64969 | 2 |
| C22×#498 | 5 |