Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
428 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 146 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×#498 | C2 | semidirect |
| 3. C5×#5080 | C2 | semidirect |
| 5. C5×C8×C3⋊C8 | C2 | semidirect |
| 16. #71332 | C5 | direct (N × H) |
| 18. C5×#498 | D3 | semidirect |
| 34. C3×#498 | C2×C5 | semidirect |
| 36. #5080 | C2×C5 | semidirect |
| 38. C8×C3⋊C8 | C2×C5 | semidirect |
| 58. C3×C5×C8 | SD16 | semidirect |
| 59. C5×C3⋊C8 | SD16 | semidirect |
| 82. #498 | C5×D3 | semidirect |
| 115. C5×C8 | #215 | semidirect |
| 137. C3×C8 | C5×SD16 | semidirect |
| 138. C3⋊C8 | C5×SD16 | semidirect |
| 158. C3×C5 | #1705 | semidirect |
| 179. C8 | C5×#215 | semidirect |
| 183. C5 | #71332 | direct (N × H) |
| 191. C3 | C5×#1705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#498 | 2 |
| C5×#5085 | 2 |
| C5×#5080 | 2 |
| C5×#4693 | 2 |
| C5×C8×C3⋊C8 | 2 |
| C5×#1705 | 3 |
| #71332 | 5 |