Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 12. C5×C82 | C4 | semidirect |
| 13. C8×#168 | C4 | semidirect |
| 14. C8×#168 | C4 | semidirect |
| 15. C8×#168 | C4 | semidirect |
| 70. C82 | AGL(1,𝔽5) | semidirect |
| 86. C5×C8 | #106 | semidirect |
| 87. C5×C8 | #107 | semidirect |
| 89. #168 | #106 | semidirect |
| 90. #168 | #107 | semidirect |
| 165. C8 | #3993 | semidirect |
| 166. C8 | #3994 | semidirect |
| 167. C5 | #8814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603848 | 2 |
| #10603847 | 2 |
| #10603845 | 2 |
| C82×D5 | 2 |
| #8814 | 5 |