Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
212 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. #10604861 | C2 | semidirect |
| 3. #10598815 | C2 | semidirect |
| 4. #10598650 | C2 | semidirect |
| 5. #10598636 | C2 | semidirect |
| 25. C5×Q32 | C8 | semidirect |
| 26. C5×SD32 | C8 | semidirect |
| 27. C5×D16 | C8 | semidirect |
| 79. Q32 | #170 | semidirect |
| 80. SD32 | #170 | semidirect |
| 81. D16 | #170 | semidirect |
| 131. C5 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604861 | 2 |
| #10602304 | 2 |
| #10598815 | 2 |
| #10598650 | 2 |
| #10598636 | 2 |
| #12047 | 5 |