Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
258 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 88 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. D4×#674 | C2 | semidirect |
| 2. #10604021 | C2 | semidirect |
| 4. D4⋊#674 | C2 | semidirect |
| 5. #10598579 | C2 | semidirect |
| 6. #10598525 | C2 | semidirect |
| 7. C8×#674 | C2 | semidirect |
| 62. #686 | C16 | semidirect |
| 78. #674 | D8 | semidirect |
| 97. C5×D4 | C2×C16 | semidirect |
| 106. D20 | C2×C16 | semidirect |
| 114. #168 | C2×C16 | semidirect |
| 189. D4 | D5⋊C16 | semidirect |
| 207. C5 | C16×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#674 | 2 |
| #10604021 | 2 |
| #10598941 | 2 |
| D4⋊#674 | 2 |
| #10598579 | 2 |
| #10598525 | 2 |
| C8×#674 | 2 |
| C16×D8 | 5 |