Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 98 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×#64909 | C2 | semidirect |
| 3. C4×#3996 | C2 | semidirect |
| 4. D5⋊(C4⋊C16) | C2 | semidirect |
| 47. #3996 | D4 | semidirect |
| 177. C4×C5 | #359 | semidirect |
| 252. C5 | #13251 | semidirect |
| 265. C4 | #64909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613530 | 2 |
| C2×#64909 | 2 |
| C4×#3996 | 2 |
| D5⋊(C4⋊C16) | 2 |
| #13251 | 5 |