Finite Group DatabasebetaFinite Group DatabasebetaOrder 35700.
192 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D15×D85 |
| commutator, cosocle, hypocenter | C3×C52×C17 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C17 | C22 |
| LCS | G ▷ C3×C52×C17 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C7×D85 | C2 | semidirect |
| 2. C5×C7×C17×D15 | C2 | semidirect |
| 3. C7×C3⋊(C5⋊D85) | C2 | semidirect |
| 5. C3×C52×C7×C17 | C22 | semidirect |
| 9. C5×C7×D85 | D3 | semidirect |
| 11. D15×D85 | C7 | direct (N × H) |
| 15. C7×C17×D15 | D5 | semidirect |
| 17. C3×C7×D85 | D5 | semidirect |
| 19. C52×C7×C17 | C2×D3 | semidirect |
| 20. C3⋊(C5⋊D85) | C2×C7 | semidirect |
| 21. C5×C17×D15 | C2×C7 | semidirect |
| 22. C3×C5×D85 | C2×C7 | semidirect |
| 27. C3×C5×C7×C17 | C2×D5 | semidirect |
| 28. C3×C5×C7×C17 | C2×D5 | semidirect |
| 31. C3×C52×C17 | C22×C7 | semidirect |
| 36. C7×D85 | D15 | direct (N × H) |
| 40. C5×C7×D15 | D17 | semidirect |
| 45. C5×D85 | D3×C7 | semidirect |
| 52. C5×C7×C17 | D3×D5 | semidirect |
| 53. C5×C7×C17 | C2×D15 | semidirect |
| 54. C3×C52×C7 | C2×D17 | semidirect |
| 58. C17×D15 | C7×D5 | semidirect |
| 60. C3×D85 | C7×D5 | semidirect |
| 63. C52×C17 | C2×D3×C7 | semidirect |
| 66. C3×C7×C17 | D52 | semidirect |
| 74. C3×C5×C17 | C2×C7×D5 | semidirect |
| 75. C3×C5×C17 | C2×C7×D5 | semidirect |
| 83. C7×D15 | D85 | direct (N × H) |
| 87. C52×C7 | D3×D17 | semidirect |
| 92. D85 | C7×D15 | direct (N × H) |
| 96. C5×D15 | C7×D17 | semidirect |
| 100. C7×C17 | D5×D15 | semidirect |
| 102. C3×C5×C7 | D5×D17 | semidirect |
| 103. C3×C5×C7 | C2×D85 | semidirect |
| 109. C5×C17 | D3×C7×D5 | semidirect |
| 110. C5×C17 | C2×C7×D15 | semidirect |
| 112. C3×C52 | C2×C7×D17 | semidirect |
| 123. C3×C17 | C7×D52 | semidirect |
| 131. C5×C7 | D15×D17 | semidirect |
| 132. C5×C7 | D3×D85 | semidirect |
| 140. D15 | C7×D85 | direct (N × H) |
| 144. C52 | D3×C7×D17 | semidirect |
| 145. C3×C7 | D5×D85 | semidirect |
| 148. C17 | C7×D5×D15 | semidirect |
| 150. C3×C5 | C7×D5×D17 | semidirect |
| 151. C3×C5 | C2×C7×D85 | semidirect |
| 163. C7 | D15×D85 | direct (N × H) |
| 168. C5 | C7×D15×D17 | semidirect |
| 169. C5 | D3×C7×D85 | semidirect |
| 171. C3 | C7×D5×D85 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C7×D85 | 2 |
| C5×C7×C17×D15 | 2 |
| C7×C3⋊(C5⋊D85) | 2 |
| C7×D5×D85 | 3 |
| D3×C7×D85 | 5 |
| C7×D15×D17 | 5 |
| D15×D85 | 7 |
| C7×D5×D15 | 17 |