Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
258 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
| 3. D4⋊#674 | C2 | semidirect |
| 4. #10598524 | C2 | semidirect |
| 5. C8×#674 | C2 | semidirect |
| 39. C5×D8 | C16 | semidirect |
| 54. #674 | D8 | direct (N × H) |
| 67. C5×D4 | C2×C16 | semidirect |
| 75. C5×C8 | C2×C16 | semidirect |
| 108. D8 | #674 | direct (N × H) |
| 130. D4 | C2×#674 | semidirect |
| 143. C8 | C2×#674 | semidirect |
| 144. 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 |
| D8×#168 | 2 |
| D4⋊#674 | 2 |
| #10598524 | 2 |
| C8×#674 | 2 |
| C16×D8 | 5 |