Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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×#65395 | C2 | semidirect |
| 3. C5×#2112 | C2 | semidirect |
| 4. #10602232 | C2 | semidirect |
| 5. #10602221 | C2 | semidirect |
| 6. #10599893 | C2 | semidirect |
| 7. #10599890 | C2 | semidirect |
| 23. #64729 | C22 | semidirect |
| 24. #64725 | C22 | semidirect |
| 25. #64724 | C22 | semidirect |
| 26. #64723 | C22 | semidirect |
| 65. #2112 | D5 | semidirect |
| 265. C5 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615473 | 2 |
| C2×#65395 | 2 |
| C5×#2112 | 2 |
| #10602232 | 2 |
| #10602221 | 2 |
| #10599893 | 2 |
| #10599890 | 2 |
| #33647 | 5 |