Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C22⋊#674 | C2 | semidirect |
| 3. #10598817 | C2 | semidirect |
| 4. #10598690 | C2 | semidirect |
| 52. C2×C5×D4 | C16 | semidirect |
| 105. C23×C5 | C2×C16 | semidirect |
| 125. C2×C4×C5 | C2×C16 | semidirect |
| 185. C2×D4 | #674 | semidirect |
| 232. C23 | C2×#674 | semidirect |
| 252. C2×C4 | C2×#674 | semidirect |
| 261. C5 | #11465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#168 | 2 |
| C2×C22⋊#674 | 2 |
| #10598817 | 2 |
| #10598690 | 2 |
| #11465 | 5 |