Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
458 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. D4×D40 | C2 | semidirect |
| 2. C5×#1667 | C2 | semidirect |
| 3. #10602086 | C2 | semidirect |
| 4. #10602083 | C2 | semidirect |
| 5. D4⋊#672 | C2 | semidirect |
| 6. #10597964 | C2 | semidirect |
| 7. #10597962 | C2 | semidirect |
| 10. C5×#493 | C22 | semidirect |
| 20. C5×#335 | C22 | semidirect |
| 23. C4⋊#672 | C22 | semidirect |
| 24. C4×#672 | C22 | semidirect |
| 60. #1667 | D5 | semidirect |
| 102. D40 | D8 | semidirect |
| 110. #493 | C2×D5 | semidirect |
| 120. #335 | C2×D5 | semidirect |
| 135. C5×D4 | D16 | semidirect |
| 281. D4 | #3958 | semidirect |
| 296. C5 | #12316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D40 | 2 |
| C5×#1667 | 2 |
| #10602086 | 2 |
| #10602083 | 2 |
| D4⋊#672 | 2 |
| #10597964 | 2 |
| #10597962 | 2 |
| #12316 | 5 |