Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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. C5×#4683 | C2 | semidirect |
| 3. #11746284 | C2 | semidirect |
| 4. #11745936 | C2 | semidirect |
| 36. #4683 | D5 | semidirect |
| 165. C3×C5 | #2231 | semidirect |
| 191. C5 | #70920 | semidirect |
| 199. C3 | #10602151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4683 | 2 |
| C3×#64989 | 2 |
| #11746284 | 2 |
| #11745936 | 2 |
| #11745909 | 2 |
| #10602151 | 3 |
| #70920 | 5 |