Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 4. C2×#64707 | C2 | semidirect |
| 5. #10600694 | C2 | semidirect |
| 6. #10598211 | C2 | semidirect |
| 7. #10598163 | C2 | semidirect |
| 21. #64787 | C4 | semidirect |
| 56. #3951 | C2×C4 | semidirect |
| 62. C2×#672 | C2×C4 | semidirect |
| 283. C5 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2952 | 2 |
| #10602874 | 2 |
| #10602873 | 2 |
| C2×#64707 | 2 |
| #10600694 | 2 |
| #10598211 | 2 |
| #10598163 | 2 |
| #12949 | 5 |