Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1566 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 280 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. #10604168 | C2 | direct (N × H) |
| 7. C22×C42×C5 | C4 | semidirect |
| 9. C22×#683 | C4 | semidirect |
| 10. C22×C4×Dic5 | C4 | semidirect |
| 13. C2×#4018 | C4 | semidirect |
| 36. C2×C42×C5 | C2×C4 | semidirect |
| 43. C2×#683 | C2×C4 | semidirect |
| 46. C2×C4×Dic5 | C2×C4 | semidirect |
| 102. C22×C42 | AGL(1,𝔽5) | semidirect |
| 172. C2×C42 | C2×AGL(1,𝔽5) | semidirect |
| 236. C2×C5 | #1820 | semidirect |
| 278. C5 | C2×#1820 | semidirect |
| 304. C2 | #10604168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4018 | 2 |
| C2×#65764 | 2 |
| C2×#64917 | 2 |
| #10604168 | 2 |
| C2×#1820 | 5 |