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. C2×C3×C5×D16 | C2 | semidirect |
| 2. C5×#4904 | C2 | semidirect |
| 3. C5×#4520 | C2 | semidirect |
| 4. C5×#4519 | C2 | semidirect |
| 5. C5×#4499 | C2 | semidirect |
| 12. C5×Dic24 | C22 | semidirect |
| 14. C5×D48 | C22 | semidirect |
| 15. C5×C3⋊C32 | C22 | semidirect |
| 16. #71458 | C5 | direct (N × H) |
| 18. C2×C5×D16 | D3 | semidirect |
| 32. C2×C3×D16 | C2×C5 | semidirect |
| 33. #4904 | C2×C5 | semidirect |
| 34. #4520 | C2×C5 | semidirect |
| 35. #4519 | C2×C5 | semidirect |
| 36. #4499 | C2×C5 | semidirect |
| 62. Dic24 | C22×C5 | semidirect |
| 64. D48 | C22×C5 | semidirect |
| 65. C3⋊C32 | C22×C5 | semidirect |
| 77. C2×D16 | C5×D3 | semidirect |
| 148. C3×C5 | #2263 | semidirect |
| 174. C5 | #71458 | 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 |
|---|---|
| C2×C3×C5×D16 | 2 |
| C5×#4904 | 2 |
| C5×#4520 | 2 |
| C5×#4519 | 2 |
| C5×#4499 | 2 |
| C5×#2263 | 3 |
| #71458 | 5 |