Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5183 | C2 | semidirect |
| 5. C3×C5×#358 | C2 | semidirect |
| 6. C5×Dic3⋊C16 | C2 | semidirect |
| 7. C5×#4492 | C2 | semidirect |
| 22. #69234 | C5 | direct (N × H) |
| 29. C5×#358 | D3 | semidirect |
| 50. #5183 | C2×C5 | semidirect |
| 54. C3×#358 | C2×C5 | semidirect |
| 55. Dic3⋊C16 | C2×C5 | semidirect |
| 56. #4492 | C2×C5 | semidirect |
| 127. #358 | C5×D3 | semidirect |
| 138. C5×Dic3 | SD32 | semidirect |
| 241. C3×C5 | #2208 | semidirect |
| 252. Dic3 | C5×SD32 | semidirect |
| 278. C5 | #69234 | 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 |
|---|---|
| C5×#5183 | 2 |
| C2×C5×#828 | 2 |
| C2×C5×#800 | 2 |
| C5×#4872 | 2 |
| C3×C5×#358 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#4492 | 2 |
| C5×#2208 | 3 |
| #69234 | 5 |