Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 20. #90946 | C4 | direct (N × H) |
| 118. C3×C4×C5 | Q32 | semidirect |
| 189. C4×C5 | #829 | semidirect |
| 211. C3×C5 | C4×Q32 | semidirect |
| 216. C3×C4 | #3961 | semidirect |
| 241. C5 | C4×#829 | semidirect |
| 248. C4 | #90946 | direct (N × H) |
| 251. C3 | C4×#3961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Dic12 | 2 |
| C3×C4×Dic20 | 2 |
| C2×#90946 | 2 |
| C4×C3⋊#672 | 2 |
| #11745940 | 2 |
| #11745899 | 2 |
| #11745897 | 2 |
| C4×#3961 | 3 |
| C4×#829 | 5 |