Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
212 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 212 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×C5×#508 | C2 | semidirect |
| 2. C5×#4904 | C2 | semidirect |
| 3. C5×#4522 | C2 | semidirect |
| 4. C5×#4521 | C2 | semidirect |
| 5. C5×#4520 | C2 | semidirect |
| 6. C5×#4519 | C2 | semidirect |
| 7. C2×C5×C3⋊C32 | C2 | semidirect |
| 20. #71508 | C5 | direct (N × H) |
| 22. C5×#508 | D3 | semidirect |
| 39. C3×#508 | C2×C5 | semidirect |
| 40. #4904 | C2×C5 | semidirect |
| 41. #4522 | C2×C5 | semidirect |
| 42. #4521 | C2×C5 | semidirect |
| 43. #4520 | C2×C5 | semidirect |
| 44. #4519 | C2×C5 | semidirect |
| 45. C2×C3⋊C32 | C2×C5 | semidirect |
| 92. #508 | C5×D3 | semidirect |
| 171. C3×C5 | #2262 | semidirect |
| 198. C5 | #71508 | direct (N × H) |
| 206. C3 | C5×#2262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| C5×#4904 | 2 |
| C5×#4522 | 2 |
| C5×#4521 | 2 |
| C5×#4520 | 2 |
| C5×#4519 | 2 |
| C2×C5×C3⋊C32 | 2 |
| C5×#2262 | 3 |
| #71508 | 5 |