Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
498 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 498 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. #10617422 | C2 | semidirect |
| 3. #10604847 | C2 | semidirect |
| 4. #10604830 | C2 | semidirect |
| 5. #10604786 | C2 | semidirect |
| 6. #10598666 | C2 | semidirect |
| 7. #10598661 | C2 | semidirect |
| 20. C2×C5×SD32 | C4 | semidirect |
| 21. C2×#3960 | C4 | semidirect |
| 22. C2×#3958 | C4 | semidirect |
| 25. C2×D80 | C4 | semidirect |
| 39. C2×C5×Q16 | C2×C4 | semidirect |
| 52. C2×D40 | C2×C4 | semidirect |
| 67. C2×C5×C16 | C2×C4 | semidirect |
| 70. C2×#672 | C2×C4 | semidirect |
| 139. C2×SD32 | AGL(1,𝔽5) | semidirect |
| 197. C2×Q16 | C2×AGL(1,𝔽5) | semidirect |
| 225. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 351. C5 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617422 | 2 |
| C2×#65203 | 2 |
| #10604847 | 2 |
| #10604830 | 2 |
| #10604786 | 2 |
| #10598666 | 2 |
| #10598661 | 2 |
| #13033 | 5 |