Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1606 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 216 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 |
|---|---|---|
| 2. #10617506 | C2 | semidirect |
| 3. #10604943 | C2 | semidirect |
| 4. #10604942 | C2 | semidirect |
| 5. #10604168 | C2 | semidirect |
| 9. C2×C5×#127 | C4 | semidirect |
| 10. C2×#4086 | C4 | semidirect |
| 11. C2×#4085 | C4 | semidirect |
| 13. C2×#4082 | C4 | semidirect |
| 15. C2×#4021 | C4 | semidirect |
| 26. C22×C5×D4 | C2×C4 | semidirect |
| 27. C22×C5×D4 | C2×C4 | semidirect |
| 29. C22×C22⋊D5 | C2×C4 | semidirect |
| 31. C23×Dic5 | C2×C4 | semidirect |
| 38. C22×Dic10 | C2×C4 | semidirect |
| 44. C2×C42×C5 | C2×C4 | semidirect |
| 45. C2×C22⋊Dic5 | C2×C4 | semidirect |
| 51. C2×#685 | C2×C4 | semidirect |
| 53. C2×#683 | C2×C4 | semidirect |
| 54. C2×C4×Dic5 | C2×C4 | semidirect |
| 116. C2×#127 | AGL(1,𝔽5) | semidirect |
| 181. C22×D4 | C2×AGL(1,𝔽5) | semidirect |
| 182. C22×D4 | C2×AGL(1,𝔽5) | semidirect |
| 203. C2×C42 | C2×AGL(1,𝔽5) | semidirect |
| 327. C5 | #21750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66049 | 2 |
| #10617506 | 2 |
| #10604943 | 2 |
| #10604942 | 2 |
| #10604168 | 2 |
| #21750 | 5 |