Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
224 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 224 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.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D15×D19 |
| commutator, cosocle, hypocenter | C3×C5×C19 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C19 | C22 |
| LCS | G ▷ C3×C5×C19 | |
| UCS | C1 ◁ C3×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×D285 | C2 | semidirect |
| 2. C3×C5×C19×D15 | C2 | semidirect |
| 3. C32×C52×D19 | C2 | semidirect |
| 4. C5×D15×D19 | C3 | direct (N × H) |
| 6. C32×C52×C19 | C22 | semidirect |
| 7. C3×D15×D19 | C5 | direct (N × H) |
| 9. C5×D285 | C2×C3 | semidirect |
| 10. C5×C19×D15 | C2×C3 | semidirect |
| 14. C3×C52×D19 | D3 | semidirect |
| 15. C3×C52×D19 | C2×C3 | semidirect |
| 17. C3×D285 | C2×C5 | semidirect |
| 18. C3×C19×D15 | C2×C5 | semidirect |
| 22. C32×C5×D19 | D5 | semidirect |
| 23. C32×C5×D19 | C2×C5 | semidirect |
| 25. C3×C52×C19 | C2×D3 | semidirect |
| 26. C3×C52×C19 | C22×C3 | semidirect |
| 28. D15×D19 | C3×C5 | direct (N × H) |
| 33. C52×D19 | C3×D3 | semidirect |
| 36. C32×C5×C19 | C2×D5 | semidirect |
| 37. C32×C5×C19 | C22×C5 | semidirect |
| 40. D285 | C2×C3×C5 | semidirect |
| 41. C19×D15 | C2×C3×C5 | semidirect |
| 52. C3×C5×D19 | C5×D3 | semidirect |
| 53. C3×C5×D19 | C3×D5 | semidirect |
| 54. C3×C5×D19 | D15 | direct (N × H) |
| 55. C3×C5×D19 | C2×C3×C5 | semidirect |
| 56. C52×C19 | C2×C3×D3 | semidirect |
| 59. C3×C5×D15 | D19 | direct (N × H) |
| 64. C32×D19 | C5×D5 | semidirect |
| 72. C3×C5×C19 | C2×C3×D5 | semidirect |
| 73. C3×C5×C19 | C2×C5×D3 | semidirect |
| 74. C3×C5×C19 | C2×D15 | semidirect |
| 75. C3×C5×C19 | C22×C3×C5 | semidirect |
| 78. C32×C52 | C2×D19 | semidirect |
| 83. C5×D19 | C3×C5×D3 | semidirect |
| 84. C5×D19 | C3×D15 | direct (N × H) |
| 88. C32×C19 | C2×C5×D5 | semidirect |
| 93. C5×D15 | C3×D19 | direct (N × H) |
| 100. C3×D19 | C3×C5×D5 | semidirect |
| 101. C3×D19 | C5×D15 | direct (N × H) |
| 105. C5×C19 | C2×C3×C5×D3 | semidirect |
| 106. C5×C19 | C2×C3×D15 | semidirect |
| 111. C3×D15 | C5×D19 | direct (N × H) |
| 116. C3×C52 | D3×D19 | semidirect |
| 117. C3×C52 | C2×C3×D19 | semidirect |
| 123. C3×C19 | C2×C3×C5×D5 | semidirect |
| 124. C3×C19 | C2×C5×D15 | semidirect |
| 129. C32×C5 | D5×D19 | semidirect |
| 130. C32×C5 | C2×C5×D19 | semidirect |
| 133. D19 | C3×C5×D15 | direct (N × H) |
| 147. D15 | C3×C5×D19 | direct (N × H) |
| 152. C52 | C3×D3×D19 | semidirect |
| 155. C19 | C2×C3×C5×D15 | semidirect |
| 164. C3×C5 | C3×D5×D19 | semidirect |
| 165. C3×C5 | C5×D3×D19 | semidirect |
| 166. C3×C5 | D15×D19 | direct (N × H) |
| 167. C3×C5 | C2×C3×C5×D19 | semidirect |
| 177. C32 | C5×D5×D19 | semidirect |
| 186. C5 | C3×C5×D3×D19 | semidirect |
| 187. C5 | C3×D15×D19 | direct (N × H) |
| 190. C3 | C3×C5×D5×D19 | semidirect |
| 191. C3 | C5×D15×D19 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D285 | 2 |
| C3×C5×C19×D15 | 2 |
| C32×C52×D19 | 2 |
| C5×D15×D19 | 3 |
| C3×C5×D5×D19 | 3 |
| C3×D15×D19 | 5 |
| C3×C5×D3×D19 | 5 |
| C2×C3×C5×D15 | 19 |