Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
614 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 614 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. #10603913 | C2 | semidirect |
| 5. #10598559 | C2 | semidirect |
| 6. C23×#170 | C4 | semidirect |
| 9. C2×C22⋊#170 | C4 | semidirect |
| 12. C2×#4004 | C4 | semidirect |
| 14. C2×C4×#170 | C4 | semidirect |
| 21. C5×#323 | C4 | semidirect |
| 22. #64745 | C4 | semidirect |
| 23. #64689 | C4 | semidirect |
| 48. #4011 | C8 | semidirect |
| 83. C22⋊AGL(1,𝔽5) | C2×C8 | semidirect |
| 125. #323 | AGL(1,𝔽5) | semidirect |
| 130. C23×C5 | C4×C8 | semidirect |
| 154. C2×Dic5 | C4×C8 | semidirect |
| 164. #170 | #99 | semidirect |
| 284. C23 | C8×AGL(1,𝔽5) | semidirect |
| 316. C5 | C8×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65692 | 2 |
| #10604216 | 2 |
| #10603913 | 2 |
| #10598912 | 2 |
| #10598559 | 2 |
| C8×#99 | 5 |