Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
554 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. #10604848 | C2 | semidirect |
| 4. C2×#64908 | C2 | semidirect |
| 6. #10598664 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽5))⋊C16 | C2 | semidirect |
| 20. C2×C5×SD32 | C4 | semidirect |
| 21. C2×#3960 | C4 | semidirect |
| 22. C2×#3959 | C4 | semidirect |
| 25. C2×#3932 | C4 | semidirect |
| 40. C2×C5×Q16 | C2×C4 | semidirect |
| 52. C2×Dic20 | C2×C4 | semidirect |
| 69. C2×C5×C16 | C2×C4 | semidirect |
| 72. C2×#672 | C2×C4 | semidirect |
| 146. C2×SD32 | AGL(1,𝔽5) | semidirect |
| 180. C2×AGL(1,𝔽5) | SD32 | semidirect |
| 217. C2×Q16 | C2×AGL(1,𝔽5) | semidirect |
| 243. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 394. C5 | #13014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×AGL(1,𝔽5) | 2 |
| C2×D5×SD32 | 2 |
| #10604848 | 2 |
| C2×#64908 | 2 |
| C2×#64904 | 2 |
| #10598664 | 2 |
| (C2×AGL(1,𝔽5))⋊C16 | 2 |
| #13014 | 5 |