Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 1. C2×C5×#912 | C2 | semidirect |
| 2. C2×C3×C5×D16 | C2 | semidirect |
| 3. C5×#5157 | C2 | semidirect |
| 4. C2×C5×#827 | C2 | semidirect |
| 5. C5×#4562 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 7. C5×#4503 | C2 | semidirect |
| 24. #71468 | C5 | direct (N × H) |
| 27. C2×C5×D16 | D3 | semidirect |
| 44. C3×C5×D8 | D4 | semidirect |
| 51. C5×Dic12 | D4 | semidirect |
| 56. C2×#912 | C2×C5 | semidirect |
| 57. C2×C3×D16 | C2×C5 | semidirect |
| 58. #5157 | C2×C5 | semidirect |
| 59. C2×#827 | C2×C5 | semidirect |
| 60. #4562 | C2×C5 | semidirect |
| 61. (C2×D3)⋊C16 | C2×C5 | semidirect |
| 62. #4503 | C2×C5 | semidirect |
| 130. C5×D8 | #67 | semidirect |
| 141. C2×D16 | C5×D3 | semidirect |
| 173. C3×D8 | C5×D4 | semidirect |
| 180. Dic12 | C5×D4 | semidirect |
| 278. D8 | C5×#67 | semidirect |
| 287. C3×C5 | #2186 | semidirect |
| 336. C5 | #71468 | direct (N × H) |
| 352. C3 | C5×#2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#912 | 2 |
| C2×C3×C5×D16 | 2 |
| C5×#5157 | 2 |
| C2×C5×#827 | 2 |
| C5×#4562 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C5×#4503 | 2 |
| C5×#2186 | 3 |
| #71468 | 5 |