Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
290 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 4. #170⋊C16 | C2 | semidirect |
| 5. #10598636 | C2 | semidirect |
| 65. C5×C16 | M16 | semidirect |
| 67. #672 | M16 | semidirect |
| 152. C16 | #700 | semidirect |
| 175. C5 | #11408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603829 | 2 |
| C8×#700 | 2 |
| C4×D5×C16 | 2 |
| #170⋊C16 | 2 |
| #10598636 | 2 |
| #11408 | 5 |