Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×D20 | C2 | semidirect |
| 2. C5×#2206 | C2 | semidirect |
| 3. #10602083 | C2 | semidirect |
| 4. #10602075 | C2 | semidirect |
| 5. #10598254 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10598047 | C2 | semidirect |
| 11. C5×#493 | C22 | semidirect |
| 20. C5×C4⋊C16 | C22 | semidirect |
| 23. C4×#672 | C22 | semidirect |
| 24. #64678 | C22 | semidirect |
| 59. #2206 | D5 | semidirect |
| 85. C5×D8 | D8 | semidirect |
| 110. #493 | C2×D5 | semidirect |
| 117. C4⋊C16 | C2×D5 | semidirect |
| 151. D20 | D16 | semidirect |
| 237. D8 | #686 | semidirect |
| 296. C5 | #12316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D20 | 2 |
| C5×#2206 | 2 |
| #10602083 | 2 |
| #10602075 | 2 |
| #10598254 | 2 |
| #10598051 | 2 |
| #10598047 | 2 |
| #12316 | 5 |