Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
670 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 267 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. #10602289 | C2 | direct (N × H) |
| 9. C2×C5×Q32 | C4 | semidirect |
| 35. C5×Q32 | C2×C4 | semidirect |
| 78. C2×Q32 | Dic5 | semidirect |
| 121. Q32 | C2×Dic5 | semidirect |
| 165. C2×C5 | #2176 | semidirect |
| 186. C5 | C2×#2176 | semidirect |
| 196. C2 | #10602289 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Q32 | 2 |
| C2×Q16×Dic5 | 2 |
| C2×#64784 | 2 |
| #10602289 | 2 |
| C2×#64725 | 2 |
| C2×#64722 | 2 |
| C2×#2176 | 5 |