Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×#65163 | C2 | semidirect |
| 4. C5×#4490 | C2 | semidirect |
| 5. #11745943 | C2 | semidirect |
| 6. #11745927 | C2 | semidirect |
| 21. #65163 | D3 | semidirect |
| 34. D120 | Q8 | semidirect |
| 48. #4490 | D5 | semidirect |
| 204. C3×C5 | #2226 | semidirect |
| 238. C5 | #71388 | semidirect |
| 250. C3 | #10600146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65163 | 2 |
| #11747766 | 2 |
| #11746312 | 2 |
| C5×#4490 | 2 |
| #11745943 | 2 |
| #11745927 | 2 |
| #11745895 | 2 |
| #10600146 | 3 |
| #71388 | 5 |