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. C3×#64725 | C2 | semidirect |
| 6. #11745944 | C2 | semidirect |
| 7. #11745941 | C2 | semidirect |
| 16. C5×#798 | C4 | semidirect |
| 26. #64725 | D3 | semidirect |
| 42. C3×C5×C16 | C2×C4 | semidirect |
| 43. C5×C3⋊C16 | C2×C4 | semidirect |
| 88. #798 | Dic5 | semidirect |
| 103. C5×C16 | C4×D3 | semidirect |
| 135. C3×C16 | C2×Dic5 | semidirect |
| 136. C3⋊C16 | C2×Dic5 | semidirect |
| 204. C16 | D3×Dic5 | semidirect |
| 205. C3×C5 | #2159 | semidirect |
| 238. C5 | #69346 | semidirect |
| 250. C3 | #10602221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#798 | 2 |
| #11747682 | 2 |
| D3×#3950 | 2 |
| #11746325 | 2 |
| C3×#64725 | 2 |
| #11745944 | 2 |
| #11745941 | 2 |
| #10602221 | 3 |
| #69346 | 5 |