Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
922 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 3. #10598696 | C2 | semidirect |
| 10. #65683 | C4 | semidirect |
| 11. #65681 | C4 | semidirect |
| 43. C4⋊#170 | C2×C4 | semidirect |
| 73. C42×C5 | M16 | semidirect |
| 82. C4×Dic5 | M16 | semidirect |
| 206. C42 | #700 | semidirect |
| 243. C5 | #7867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617038 | 2 |
| C43×D5 | 2 |
| #10598696 | 2 |
| #7867 | 5 |