Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 1. C4×C5×Dic12 | C2 | semidirect |
| 4. C4×C3⋊#672 | C2 | semidirect |
| 5. #11745943 | C2 | semidirect |
| 6. #11745899 | C2 | semidirect |
| 20. #90940 | C4 | direct (N × H) |
| 39. C5×Dic12 | C2×C4 | semidirect |
| 45. C3⋊#672 | C2×C4 | semidirect |
| 48. C4×Dic12 | D5 | semidirect |
| 122. C3×C4×C5 | SD32 | semidirect |
| 142. Dic12 | C4×D5 | semidirect |
| 198. C4×C5 | #827 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 226. C3×C4 | #3960 | semidirect |
| 254. C5 | C4×#827 | semidirect |
| 263. C4 | #90940 | direct (N × H) |
| 266. C3 | C4×#3960 | 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×D40 | 2 |
| C2×#90940 | 2 |
| C4×C3⋊#672 | 2 |
| #11745943 | 2 |
| #11745899 | 2 |
| #11745891 | 2 |
| C4×#3960 | 3 |
| C4×#827 | 5 |