Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
514 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 124 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. #10604011 | C2 | semidirect |
| 4. C4×#3992 | C2 | semidirect |
| 6. #10598583 | C2 | semidirect |
| 7. #10598531 | C2 | semidirect |
| 9. Q8×#170 | C4 | semidirect |
| 13. #65702 | C4 | semidirect |
| 25. C5×Q8⋊C8 | C4 | semidirect |
| 26. Q8⋊#168 | C4 | semidirect |
| 27. #64703 | C4 | semidirect |
| 28. #64679 | C4 | semidirect |
| 135. Q8⋊C8 | AGL(1,𝔽5) | semidirect |
| 146. C5×Q8 | #97 | semidirect |
| 158. D20 | #97 | semidirect |
| 171. #170 | #104 | semidirect |
| 285. Q8 | #3992 | semidirect |
| 318. C5 | #8192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617195 | 2 |
| C4×#4010 | 2 |
| #10604011 | 2 |
| C4×#3992 | 2 |
| #10599022 | 2 |
| #10598583 | 2 |
| #10598531 | 2 |
| #8192 | 5 |