Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
484 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 82 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. AGL(1,𝔽5)×#135 | C2 | semidirect |
| 3. #10604858 | C2 | semidirect |
| 4. #10604797 | C2 | semidirect |
| 5. #10604784 | C2 | semidirect |
| 6. #10598677 | C2 | semidirect |
| 7. #10598670 | C2 | semidirect |
| 21. C5×#509 | C4 | semidirect |
| 22. #65484 | C4 | semidirect |
| 23. #65436 | C4 | semidirect |
| 28. #65198 | C4 | semidirect |
| 46. C2×C5×D8 | C2×C4 | semidirect |
| 59. C2×Dic20 | C2×C4 | semidirect |
| 78. C5×M32 | C2×C4 | semidirect |
| 83. #3944 | C2×C4 | semidirect |
| 164. #509 | AGL(1,𝔽5) | semidirect |
| 242. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 265. M32 | C2×AGL(1,𝔽5) | semidirect |
| 410. C5 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽5)×#135 | 2 |
| #10613766 | 2 |
| #10604858 | 2 |
| #10604797 | 2 |
| #10604784 | 2 |
| #10598677 | 2 |
| #10598670 | 2 |
| #13027 | 5 |