Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 14. Dic120 | C4 | direct (N × H) |
| 82. C3×C4×C5 | Q32 | semidirect |
| 131. C4×C5 | Dic24 | semidirect |
| 147. C3×C5 | C4×Q32 | semidirect |
| 150. C3×C4 | Dic40 | semidirect |
| 171. C5 | C4×Dic24 | semidirect |
| 176. C4 | Dic120 | direct (N × H) |
| 179. C3 | C4×Dic40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic120 | 2 |
| C4×Dic60 | 2 |
| C3×C4×C5×C16 | 2 |
| #11746325 | 2 |
| #11746324 | 2 |
| C4×Dic40 | 3 |
| C4×Dic24 | 5 |