Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
204 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10604862 | C2 | semidirect |
| 3. #10598816 | C2 | semidirect |
| 4. #10598648 | C2 | semidirect |
| 5. #10598638 | C2 | semidirect |
| 24. C5×Q32 | C8 | semidirect |
| 25. C5×SD32 | C8 | semidirect |
| 26. C5×D16 | C8 | semidirect |
| 76. Q32 | #170 | semidirect |
| 77. SD32 | #170 | semidirect |
| 78. D16 | #170 | semidirect |
| 125. C5 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604862 | 2 |
| #10602305 | 2 |
| #10598816 | 2 |
| #10598648 | 2 |
| #10598638 | 2 |
| #12068 | 5 |