Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
582 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 244 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 |
|---|---|---|
| 13. #170⋊C8 | C4 | semidirect |
| 14. C8×#170 | C4 | semidirect |
| 15. C5×#322 | C4 | semidirect |
| 16. #64675 | C4 | semidirect |
| 17. #64674 | C4 | semidirect |
| 70. #322 | AGL(1,𝔽5) | semidirect |
| 82. #170 | #97 | semidirect |
| 84. C5×C8 | #97 | semidirect |
| 86. #168 | #97 | semidirect |
| 148. C8 | #3992 | semidirect |
| 149. C5 | #7846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3992 | 2 |
| #10603806 | 2 |
| C8×D5⋊C8 | 2 |
| D5×#322 | 2 |
| #7846 | 5 |