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. #10604843 | C2 | semidirect |
| 5. #10604830 | C2 | semidirect |
| 6. #10598677 | C2 | semidirect |
| 7. #10598670 | C2 | semidirect |
| 21. C5×#510 | C4 | semidirect |
| 22. #65482 | C4 | semidirect |
| 23. #65468 | C4 | semidirect |
| 28. #65197 | C4 | semidirect |
| 46. C2×C5×Q16 | C2×C4 | semidirect |
| 60. C2×D40 | C2×C4 | semidirect |
| 78. C5×M32 | C2×C4 | semidirect |
| 83. #3944 | C2×C4 | semidirect |
| 161. #510 | AGL(1,𝔽5) | semidirect |
| 238. C2×Q16 | 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 |
| #10613770 | 2 |
| #10604858 | 2 |
| #10604843 | 2 |
| #10604830 | 2 |
| #10598677 | 2 |
| #10598670 | 2 |
| #13027 | 5 |