Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. #10603829 | C2 | semidirect |
| 3. C4×D5⋊C16 | C2 | semidirect |
| 4. Q8⋊#674 | C2 | semidirect |
| 5. #10598579 | C2 | semidirect |
| 63. #713 | C16 | semidirect |
| 118. C5×Q8 | C2×C16 | semidirect |
| 130. D20 | C2×C16 | semidirect |
| 241. Q8 | D5⋊C16 | semidirect |
| 269. C5 | #11613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#713 | 2 |
| #10603829 | 2 |
| C4×D5⋊C16 | 2 |
| Q8⋊#674 | 2 |
| #10598579 | 2 |
| #11613 | 5 |