Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
474 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10604852 | C2 | semidirect |
| 5. C2×#64908 | C2 | semidirect |
| 6. #10598674 | C2 | semidirect |
| 7. #10598673 | C2 | semidirect |
| 21. C5×#510 | C4 | semidirect |
| 22. #65484 | C4 | semidirect |
| 23. #65468 | C4 | semidirect |
| 28. #65198 | C4 | semidirect |
| 46. C2×C5×Q16 | C2×C4 | semidirect |
| 59. C2×Dic20 | C2×C4 | semidirect |
| 78. C5×M32 | C2×C4 | semidirect |
| 83. #3944 | C2×C4 | semidirect |
| 164. #510 | AGL(1,𝔽5) | semidirect |
| 240. C2×Q16 | C2×AGL(1,𝔽5) | semidirect |
| 263. M32 | C2×AGL(1,𝔽5) | semidirect |
| 411. C5 | #13023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617440 | 2 |
| D5×#510 | 2 |
| D5⋊#359 | 2 |
| #10604852 | 2 |
| C2×#64908 | 2 |
| #10598674 | 2 |
| #10598673 | 2 |
| #13023 | 5 |