Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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. #10599357 | C2 | semidirect |
| 4. C5×#1371 | C2 | semidirect |
| 5. #10597989 | C2 | semidirect |
| 6. #10597963 | C2 | semidirect |
| 48. #1371 | D5 | semidirect |
| 74. C5×C16 | M16 | semidirect |
| 168. C16 | #676 | semidirect |
| 194. C5 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3932 | 2 |
| #10599357 | 2 |
| #10599356 | 2 |
| C5×#1371 | 2 |
| #10597989 | 2 |
| #10597963 | 2 |
| #10597962 | 2 |
| #12084 | 5 |