Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11751008 | C2 | semidirect |
| 3. C3×C5×#364 | C2 | semidirect |
| 4. #11746336 | C2 | semidirect |
| 5. #11746282 | C2 | semidirect |
| 20. C5×#364 | D3 | semidirect |
| 38. C3×#364 | D5 | semidirect |
| 88. #364 | D15 | semidirect |
| 164. C3×C5 | #2171 | semidirect |
| 188. C5 | #69301 | semidirect |
| 195. C3 | #10600094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751008 | 2 |
| #11750801 | 2 |
| C3×C5×#364 | 2 |
| #11746336 | 2 |
| #11746282 | 2 |
| #10600094 | 3 |
| #69301 | 5 |