Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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. Q16×#170 | C2 | semidirect |
| 4. #10598809 | C2 | semidirect |
| 5. #10598644 | C2 | semidirect |
| 6. #170⋊C16 | C2 | semidirect |
| 62. C5×Q16 | M16 | semidirect |
| 149. Q16 | #700 | semidirect |
| 194. C5 | #12075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#170 | 2 |
| #10604067 | 2 |
| #10599999 | 2 |
| #10598809 | 2 |
| #10598644 | 2 |
| #170⋊C16 | 2 |
| #10598609 | 2 |
| #12075 | 5 |