Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
548 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 238 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. Q8×#674 | C2 | semidirect |
| 3. #10604023 | C2 | semidirect |
| 4. #10603831 | C2 | semidirect |
| 5. C4×#3990 | C2 | semidirect |
| 64. #674 | #41 | semidirect |
| 79. C5×Q8 | M32 | semidirect |
| 151. Q8 | #3990 | semidirect |
| 167. C5 | #33485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#713 | 2 |
| Q8×#674 | 2 |
| #10604023 | 2 |
| #10603831 | 2 |
| C4×#3990 | 2 |
| #33485 | 5 |