Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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×Dic21 | C2 | semidirect |
| 2. C5×C7×#67 | C2 | semidirect |
| 3. C3×C5×C22⋊D7 | C2 | semidirect |
| 4. C5×#4248 | C2 | semidirect |
| 5. C5×#4245 | C2 | semidirect |
| 6. C5×D3×Dic7 | C2 | semidirect |
| 7. C5×Dic3×D7 | C2 | semidirect |
| 16. #66684 | C5 | direct (N × H) |
| 19. C5×C22⋊D7 | D3 | semidirect |
| 29. C2×Dic21 | C2×C5 | semidirect |
| 30. C7×#67 | C2×C5 | semidirect |
| 31. C3×C22⋊D7 | C2×C5 | semidirect |
| 32. #4248 | C2×C5 | semidirect |
| 33. #4245 | C2×C5 | semidirect |
| 34. D3×Dic7 | C2×C5 | semidirect |
| 35. Dic3×D7 | C2×C5 | semidirect |
| 45. C5×#67 | D7 | semidirect |
| 51. C3×C5×C7 | #41 | semidirect |
| 73. C22⋊D7 | C5×D3 | semidirect |
| 90. C5×C7 | #237 | semidirect |
| 104. #67 | C5×D7 | semidirect |
| 109. C3×C7 | C5×#41 | semidirect |
| 118. C3×C5 | #1159 | semidirect |
| 141. C7 | C5×#237 | semidirect |
| 146. C5 | #66684 | direct (N × H) |
| 154. C3 | C5×#1159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic21 | 2 |
| C5×C7×#67 | 2 |
| C3×C5×C22⋊D7 | 2 |
| C5×#4248 | 2 |
| C5×#4245 | 2 |
| C5×D3×Dic7 | 2 |
| C5×Dic3×D7 | 2 |
| C5×#1159 | 3 |
| #66684 | 5 |
| C5×#237 | 7 |