Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 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 |
|---|---|---|
| 2. #10604188 | C3 | semidirect |
| 10. C5×C42⋊C3 | C8 | semidirect |
| 29. C42×C5 | C3×C8 | semidirect |
| 39. C42⋊C3 | #170 | semidirect |
| 78. C42 | C3×#170 | semidirect |
| 98. C5 | #1839⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic5×C42⋊C3 | 2 |
| #10604188 | 3 |
| A4×#170 | 4 |
| #1839⋊C3 | 5 |