Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
264 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. C5×#4564 | C2 | semidirect |
| 4. C3×#64784 | C2 | semidirect |
| 5. #11745942 | C2 | semidirect |
| 6. #11745941 | C2 | semidirect |
| 24. #64784 | D3 | semidirect |
| 48. #4564 | D5 | semidirect |
| 212. C3×C5 | #2237 | semidirect |
| 246. C5 | #69233 | semidirect |
| 258. C3 | #10600007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751289 | 2 |
| #11747690 | 2 |
| C5×#4564 | 2 |
| C3×#64784 | 2 |
| #11745942 | 2 |
| #11745941 | 2 |
| #11745881 | 2 |
| #10600007 | 3 |
| #69233 | 5 |