Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 500 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. #10604009 | C2 | semidirect |
| 4. C4×#3992 | C2 | semidirect |
| 6. #10598583 | C2 | semidirect |
| 7. #10598531 | C2 | semidirect |
| 9. #65788 | C4 | semidirect |
| 12. #65705 | C4 | semidirect |
| 25. C5×Q8⋊C8 | C4 | semidirect |
| 26. Q8⋊#168 | C4 | semidirect |
| 27. #64703 | C4 | semidirect |
| 28. #64679 | C4 | semidirect |
| 98. #700 | M16 | semidirect |
| 135. Q8⋊C8 | AGL(1,𝔽5) | semidirect |
| 171. #170 | #104 | semidirect |
| 318. C5 | #8196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617196 | 2 |
| C4×#4010 | 2 |
| #10604009 | 2 |
| C4×#3992 | 2 |
| #10599022 | 2 |
| #10598583 | 2 |
| #10598531 | 2 |
| #8196 | 5 |