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 |
|---|---|---|
| 16. #91113 | C4 | direct (N × H) |
| 120. 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 | #91113 | 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 |
|---|---|
| C3×C4×C5×Q16 | 2 |
| C2×#91113 | 2 |
| C4×Dic60 | 2 |
| #11746385 | 2 |
| #11746313 | 2 |
| #11746310 | 2 |
| C4×C3⋊#672 | 2 |
| C4×#3961 | 3 |
| C4×#829 | 5 |