Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 4. #11746325 | C2 | semidirect |
| 5. C5×#4505 | C2 | semidirect |
| 6. #11745942 | C2 | semidirect |
| 7. #11745939 | C2 | semidirect |
| 18. C3×#3930 | C4 | semidirect |
| 42. C3×C5×C16 | C2×C4 | semidirect |
| 43. C3×#672 | C2×C4 | semidirect |
| 48. #4505 | D5 | semidirect |
| 62. #3930 | Dic3 | semidirect |
| 102. C5×C16 | C2×Dic3 | semidirect |
| 103. #672 | C2×Dic3 | semidirect |
| 136. C3×C16 | C4×D5 | semidirect |
| 204. C16 | D5×Dic3 | semidirect |
| 205. C3×C5 | #2159 | semidirect |
| 238. C5 | #71428 | semidirect |
| 250. C3 | #10600139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3930 | 2 |
| #11747672 | 2 |
| D5×#818 | 2 |
| #11746325 | 2 |
| C5×#4505 | 2 |
| #11745942 | 2 |
| #11745939 | 2 |
| #10600139 | 3 |
| #71428 | 5 |