Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
264 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 7. C2×C3×C5×C16 | C4 | semidirect |
| 9. C5×#817 | C4 | semidirect |
| 10. #67818 | C5 | direct (N × H) |
| 27. C2×C5×C16 | Dic3 | semidirect |
| 43. C2×C3×C16 | C4×C5 | semidirect |
| 45. #817 | C4×C5 | semidirect |
| 85. C2×C16 | C5×Dic3 | semidirect |
| 116. C3×C5 | #1384 | semidirect |
| 139. C5 | #67818 | direct (N × H) |
| 147. C3 | C5×#1384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×M32 | 2 |
| C5×#5106 | 2 |
| C5×#1384 | 3 |
| #67818 | 5 |