Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
302 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 4. #10598638 | C2 | direct (N × H) |
| 25. C2×C5×C16 | C8 | semidirect |
| 31. C2×#672 | C8 | semidirect |
| 52. C5×C16 | C2×C8 | semidirect |
| 53. #672 | C2×C8 | semidirect |
| 87. C2×C16 | #170 | semidirect |
| 119. C16 | C2×#170 | semidirect |
| 120. C2×C5 | #1313 | semidirect |
| 137. C5 | C2×#1313 | semidirect |
| 146. C2 | #10598638 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64886 | 2 |
| C2×#64879 | 2 |
| C2×#64722 | 2 |
| #10598638 | 2 |
| C2×#1313 | 5 |