Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 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×C3×C5×SD32 | C2 | semidirect |
| 2. C5×Dic3×Q16 | C2 | semidirect |
| 3. C2×C5×#828 | C2 | semidirect |
| 5. C5×#4562 | C2 | semidirect |
| 6. C5×#4509 | C2 | semidirect |
| 7. C5×Dic3⋊C16 | C2 | semidirect |
| 22. #71475 | C5 | direct (N × H) |
| 24. C2×C5×SD32 | D3 | semidirect |
| 36. C3×C5×Q16 | D4 | semidirect |
| 50. C2×C3×SD32 | C2×C5 | semidirect |
| 51. Dic3×Q16 | C2×C5 | semidirect |
| 52. C2×#828 | C2×C5 | semidirect |
| 54. #4562 | C2×C5 | semidirect |
| 55. #4509 | C2×C5 | semidirect |
| 56. Dic3⋊C16 | C2×C5 | semidirect |
| 108. C5×Q16 | #67 | semidirect |
| 123. C2×SD32 | C5×D3 | semidirect |
| 141. C5×Dic3 | SD32 | semidirect |
| 148. C3×Q16 | C5×D4 | semidirect |
| 235. Q16 | C5×#67 | semidirect |
| 249. C3×C5 | #2207 | semidirect |
| 262. Dic3 | C5×SD32 | semidirect |
| 291. C5 | #71475 | direct (N × H) |
| 305. C3 | C5×#2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD32 | 2 |
| C5×Dic3×Q16 | 2 |
| C2×C5×#828 | 2 |
| C5×#5151 | 2 |
| C5×#4562 | 2 |
| C5×#4509 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#2207 | 3 |
| #71475 | 5 |