Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 134 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. C4×#3994 | C2 | semidirect |
| 4. C4×D5⋊C16 | C2 | semidirect |
| 5. #10598619 | C2 | semidirect |
| 11. C4×C5×D8 | C4 | semidirect |
| 12. D8×Dic5 | C4 | semidirect |
| 15. #65161 | C4 | semidirect |
| 18. C4×D40 | C4 | semidirect |
| 20. #64904 | C4 | direct (N × H) |
| 48. #3994 | C2×C4 | semidirect |
| 50. D5⋊C16 | C2×C4 | semidirect |
| 88. C5×D8 | C42 | semidirect |
| 106. D40 | C42 | semidirect |
| 119. C4×D8 | AGL(1,𝔽5) | semidirect |
| 221. C4×C5 | #357 | semidirect |
| 226. Dic5 | #357 | semidirect |
| 249. D8 | C4×AGL(1,𝔽5) | semidirect |
| 318. C5 | C4×#357 | semidirect |
| 339. C4 | #64904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×D8 | 2 |
| C2×#64904 | 2 |
| C4×#3994 | 2 |
| C4×D5⋊C16 | 2 |
| #10598619 | 2 |
| C4×#357 | 5 |