Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3262 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 3262 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×#64988 | C2 | direct (N × H) |
| 14. #64988 | C22 | direct (N × H) |
| 37. C22×C4×C5 | Q16 | semidirect |
| 68. C2×C4×C5 | C2×Q16 | semidirect |
| 94. C22×C5 | #494 | semidirect |
| 99. C4×C5 | C22×Q16 | semidirect |
| 109. C22×C4 | Dic20 | semidirect |
| 120. C2×C5 | C2×#494 | semidirect |
| 131. C2×C4 | C2×Dic20 | semidirect |
| 137. C5 | C22×#494 | semidirect |
| 138. C22 | #64988 | direct (N × H) |
| 144. C4 | C22×Dic20 | semidirect |
| 146. C2 | C2×#64988 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic20 | 2 |
| C22×#4015 | 2 |
| C22×C4×C5×C8 | 2 |
| C2×#64988 | 2 |
| C22×#494 | 5 |