Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
522 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10610225 | C2 | semidirect |
| 3. C5×#1972 | C2 | semidirect |
| 4. #10602826 | C2 | semidirect |
| 5. C2×#64708 | C2 | semidirect |
| 6. #10598212 | C2 | semidirect |
| 7. #10598155 | C2 | semidirect |
| 17. #65436 | C4 | semidirect |
| 36. C2×C5×D8 | C2×C4 | semidirect |
| 69. #3944 | C2×C4 | semidirect |
| 76. #1972 | D5 | semidirect |
| 123. Dic20 | C22⋊C4 | semidirect |
| 125. D40 | C22⋊C4 | semidirect |
| 201. C2×D8 | C4×D5 | semidirect |
| 343. C5 | #13025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65436 | 2 |
| #10610225 | 2 |
| C5×#1972 | 2 |
| #10602826 | 2 |
| C2×#64708 | 2 |
| #10598212 | 2 |
| #10598155 | 2 |
| #13025 | 5 |