Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 2. C5×#2208 | C2 | semidirect |
| 3. #10602106 | C2 | semidirect |
| 4. #10602098 | C2 | semidirect |
| 5. #10598254 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10598047 | C2 | semidirect |
| 11. C5×#494 | C22 | semidirect |
| 20. C5×C4⋊C16 | C22 | semidirect |
| 23. C4×#672 | C22 | semidirect |
| 24. #64678 | C22 | semidirect |
| 59. #2208 | D5 | semidirect |
| 108. #494 | C2×D5 | semidirect |
| 116. C4⋊C16 | C2×D5 | semidirect |
| 147. D20 | SD32 | semidirect |
| 285. C5 | #12320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D20 | 2 |
| C5×#2208 | 2 |
| #10602106 | 2 |
| #10602098 | 2 |
| #10598254 | 2 |
| #10598051 | 2 |
| #10598047 | 2 |
| #12320 | 5 |