Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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. C5×#1518 | C2 | semidirect |
| 4. #10602633 | C2 | semidirect |
| 6. #10598228 | C2 | semidirect |
| 7. #10598122 | C2 | semidirect |
| 13. #65377 | C4 | semidirect |
| 14. #65374 | C4 | semidirect |
| 32. C5×C4⋊Q8 | C2×C4 | semidirect |
| 33. C5×C4⋊Q8 | C2×C4 | semidirect |
| 67. C4×#168 | C2×C4 | semidirect |
| 72. #1518 | D5 | semidirect |
| 121. C4×Dic5 | SD16 | semidirect |
| 196. C4⋊Q8 | C4×D5 | semidirect |
| 197. C4⋊Q8 | C4×D5 | semidirect |
| 357. C5 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615086 | 2 |
| #10605884 | 2 |
| C5×#1518 | 2 |
| #10602633 | 2 |
| #10601567 | 2 |
| #10598228 | 2 |
| #10598122 | 2 |
| #9295 | 5 |