Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
380 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. C2×#64852 | C2 | semidirect |
| 4. #10604092 | C2 | semidirect |
| 6. #10598662 | C2 | semidirect |
| 7. #10598631 | C2 | semidirect |
| 25. C5×#359 | C4 | semidirect |
| 26. #64787 | C4 | semidirect |
| 27. #64730 | C4 | semidirect |
| 28. #64717 | C4 | semidirect |
| 148. #359 | AGL(1,𝔽5) | semidirect |
| 330. C5 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617445 | 2 |
| #10604858 | 2 |
| C2×#64852 | 2 |
| #10604092 | 2 |
| D5×#359 | 2 |
| #10598662 | 2 |
| #10598631 | 2 |
| #12947 | 5 |