Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10604024 | C2 | semidirect |
| 5. #10598581 | C2 | semidirect |
| 6. #10598523 | C2 | semidirect |
| 7. #10598512 | C2 | semidirect |
| 75. #674 | SD16 | semidirect |
| 103. Dic10 | M32 | semidirect |
| 194. C5 | #12050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604414 | 2 |
| #10604024 | 2 |
| #10598942 | 2 |
| D4⋊#674 | 2 |
| #10598581 | 2 |
| #10598523 | 2 |
| #10598512 | 2 |
| #12050 | 5 |