Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 102 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. C5×#5183 | C2 | semidirect |
| 5. C5×#4564 | C2 | semidirect |
| 6. C5×#4503 | C2 | semidirect |
| 7. C5×Dic3⋊C16 | C2 | semidirect |
| 22. #71476 | C5 | direct (N × H) |
| 51. #5183 | C2×C5 | semidirect |
| 54. #4564 | C2×C5 | semidirect |
| 55. #4503 | C2×C5 | semidirect |
| 56. Dic3⋊C16 | C2×C5 | semidirect |
| 138. C5×Dic3 | SD32 | semidirect |
| 241. C3×C5 | #2208 | semidirect |
| 252. Dic3 | C5×SD32 | semidirect |
| 278. C5 | #71476 | direct (N × H) |
| 290. C3 | C5×#2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD32 | 2 |
| C5×#5183 | 2 |
| C5×Dic3×D8 | 2 |
| C2×C5×#827 | 2 |
| C5×#4564 | 2 |
| C5×#4503 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#2208 | 3 |
| #71476 | 5 |