Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
632 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. #10617368 | C2 | semidirect |
| 3. #10604612 | C2 | semidirect |
| 4. #10604609 | C2 | semidirect |
| 5. #10604596 | C2 | semidirect |
| 6. #10598527 | C2 | semidirect |
| 7. #10598526 | C2 | semidirect |
| 20. C5×#493 | C4 | semidirect |
| 23. #65362 | C4 | semidirect |
| 24. #65359 | C4 | semidirect |
| 25. #64983 | C4 | semidirect |
| 46. C5×#127 | C2×C4 | semidirect |
| 58. #4015 | C2×C4 | semidirect |
| 70. C4×C5×C8 | C2×C4 | semidirect |
| 75. C4×#168 | C2×C4 | semidirect |
| 128. C4×AGL(1,𝔽5) | D8 | semidirect |
| 147. #493 | AGL(1,𝔽5) | semidirect |
| 237. #127 | C2×AGL(1,𝔽5) | semidirect |
| 264. C4×C8 | C2×AGL(1,𝔽5) | semidirect |
| 426. C5 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617368 | 2 |
| #10613516 | 2 |
| #10604612 | 2 |
| #10604609 | 2 |
| #10604596 | 2 |
| #10598527 | 2 |
| #10598526 | 2 |
| #9299 | 5 |