Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1394 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1394 conjugacy classes of subgroups — too many to draw. Only its 224 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. #10617046 | C2 | semidirect |
| 3. #10604944 | C2 | semidirect |
| 4. #10604942 | C2 | semidirect |
| 6. C2×C5×#127 | C4 | semidirect |
| 8. C2×#4082 | C4 | semidirect |
| 9. C2×D4×Dic5 | C4 | semidirect |
| 15. C2×#4015 | C4 | semidirect |
| 127. C2×#127 | AGL(1,𝔽5) | semidirect |
| 330. C5 | #21794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66050 | 2 |
| #10617046 | 2 |
| #10604944 | 2 |
| #10604942 | 2 |
| #21794 | 5 |