Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
238 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10604067 | C2 | semidirect |
| 3. #10598644 | C2 | semidirect |
| 4. C16×#170 | C2 | semidirect |
| 5. #10598609 | C2 | semidirect |
| 51. C5×C16 | M16 | semidirect |
| 75. #170 | D16 | semidirect |
| 119. C16 | #700 | semidirect |
| 140. C5 | #12081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604067 | 2 |
| #10600110 | 2 |
| #10598644 | 2 |
| C16×#170 | 2 |
| #10598609 | 2 |
| #12081 | 5 |