Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C3×C5×#346 | C2 | semidirect |
| 3. #11746278 | C2 | semidirect |
| 14. C5×#346 | D3 | semidirect |
| 25. D120 | C8 | semidirect |
| 28. C3×#346 | D5 | semidirect |
| 69. #346 | D15 | semidirect |
| 146. C3×C5 | #1333 | semidirect |
| 176. C5 | #67516 | semidirect |
| 186. C3 | #10598007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D120 | 2 |
| C3×C5×#346 | 2 |
| #11746278 | 2 |
| #10598007 | 3 |
| #67516 | 5 |