Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
466 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3993 | C2 | semidirect |
| 4. #10603825 | C2 | semidirect |
| 5. #10598621 | C2 | semidirect |
| 11. C4×C5×Q16 | C4 | semidirect |
| 12. Q16×Dic5 | C4 | semidirect |
| 15. #65161 | C4 | semidirect |
| 18. C4×D40 | C4 | semidirect |
| 20. #64907 | C4 | semidirect |
| 48. #3993 | C2×C4 | semidirect |
| 50. #3990 | C2×C4 | semidirect |
| 83. C5×Q16 | C42 | semidirect |
| 104. D40 | C42 | semidirect |
| 113. C4×Q16 | AGL(1,𝔽5) | semidirect |
| 211. Dic5 | #360 | semidirect |
| 226. Q16 | C4×AGL(1,𝔽5) | semidirect |
| 291. C5 | C4×#360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#4065 | 2 |
| C2×#64907 | 2 |
| C4×#3993 | 2 |
| #10603825 | 2 |
| #10598621 | 2 |
| C4×#360 | 5 |