Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 224 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. C2×C5×D48 | C2 | semidirect |
| 3. C5×#4521 | C2 | semidirect |
| 4. C5×#4519 | C2 | semidirect |
| 5. C5×#4499 | C2 | semidirect |
| 9. C3×C5×Q32 | C22 | semidirect |
| 11. C3×C5×D16 | C22 | semidirect |
| 15. C5×C3⋊C32 | C22 | semidirect |
| 16. #71509 | C5 | direct (N × H) |
| 17. C5×#508 | D3 | semidirect |
| 32. C3×#508 | C2×C5 | semidirect |
| 33. C2×D48 | C2×C5 | semidirect |
| 34. #4521 | C2×C5 | semidirect |
| 35. #4519 | C2×C5 | semidirect |
| 36. #4499 | C2×C5 | semidirect |
| 39. C5×Q32 | C2×D3 | semidirect |
| 43. C5×D16 | C2×D3 | semidirect |
| 59. C3×Q32 | C22×C5 | semidirect |
| 61. C3×D16 | C22×C5 | semidirect |
| 65. C3⋊C32 | C22×C5 | semidirect |
| 76. #508 | C5×D3 | semidirect |
| 110. Q32 | C2×C5×D3 | semidirect |
| 114. D16 | C2×C5×D3 | semidirect |
| 148. C3×C5 | #2263 | semidirect |
| 174. C5 | #71509 | direct (N × H) |
| 182. C3 | C5×#2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| C2×C5×D48 | 2 |
| C5×#4521 | 2 |
| C5×#4519 | 2 |
| C5×#4499 | 2 |
| C5×#2263 | 3 |
| #71509 | 5 |