Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
212 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C19 | C22×C3 |
| LCS | G ▷ C3×C52×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19⋊C3×C3⋊(C5⋊D5) | C2 | semidirect |
| 2. C5×D15×C19⋊C3 | C2 | semidirect |
| 3. C3×C5×D5×C19⋊C3 | C2 | semidirect |
| 4. D5×C19×D15 | C3 | semidirect |
| 6. C3×C52×C19⋊C3 | C22 | semidirect |
| 9. C19×C3⋊(C5⋊D5) | C2×C3 | semidirect |
| 10. C5×C19×D15 | C2×C3 | semidirect |
| 11. C3×C5×D5×C19 | C2×C3 | semidirect |
| 15. C5×D5×C19⋊C3 | D3 | semidirect |
| 21. D15×C19⋊C3 | D5 | direct (N × H) |
| 23. C3×D5×C19⋊C3 | D5 | semidirect |
| 24. C3×C52×C19 | C22×C3 | semidirect |
| 26. C52×C19⋊C3 | C2×D3 | semidirect |
| 33. C5×D5×C19 | C3×D3 | semidirect |
| 36. C3×C5×C19⋊C3 | C2×D5 | semidirect |
| 37. C3×C5×C19⋊C3 | C2×D5 | semidirect |
| 43. C19×D15 | C3×D5 | semidirect |
| 45. C3×D5×C19 | C3×D5 | semidirect |
| 54. D5×C19⋊C3 | D15 | direct (N × H) |
| 55. C52×C19 | C2×C3×D3 | semidirect |
| 64. D5×D15 | C19⋊C3 | direct (N × H) |
| 67. C3×C5×C19 | C2×C3×D5 | semidirect |
| 68. C3×C5×C19 | C2×C3×D5 | semidirect |
| 73. C5×C19⋊C3 | D3×D5 | semidirect |
| 74. C5×C19⋊C3 | C2×D15 | semidirect |
| 84. D5×C19 | C3×D15 | semidirect |
| 87. C3×C19⋊C3 | D52 | semidirect |
| 88. C3⋊(C5⋊D5) | C2×C19⋊C3 | semidirect |
| 89. C5×D15 | C2×C19⋊C3 | semidirect |
| 94. C3×C5×D5 | C2×C19⋊C3 | semidirect |
| 104. C5×C19 | C3×D3×D5 | semidirect |
| 105. C5×C19 | C2×C3×D15 | semidirect |
| 116. C3×C52 | C22×C19⋊C3 | semidirect |
| 121. C3×C19 | C3×D52 | semidirect |
| 123. C19⋊C3 | D5×D15 | direct (N × H) |
| 126. C5×D5 | D3×C19⋊C3 | semidirect |
| 141. D15 | D5×C19⋊C3 | direct (N × H) |
| 148. C3×D5 | D5×C19⋊C3 | semidirect |
| 150. C52 | C2×D3×C19⋊C3 | semidirect |
| 153. C19 | C3×D5×D15 | semidirect |
| 164. C3×C5 | C2×D5×C19⋊C3 | semidirect |
| 165. C3×C5 | C2×D5×C19⋊C3 | semidirect |
| 174. D5 | D15×C19⋊C3 | direct (N × H) |
| 184. C5 | D3×D5×C19⋊C3 | semidirect |
| 185. C5 | C2×D15×C19⋊C3 | semidirect |
| 189. C3 | D52×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊C3×C3⋊(C5⋊D5) | 2 |
| C5×D15×C19⋊C3 | 2 |
| C3×C5×D5×C19⋊C3 | 2 |
| D5×C19×D15 | 3 |
| D52×C19⋊C3 | 3 |
| C2×D15×C19⋊C3 | 5 |
| D3×D5×C19⋊C3 | 5 |
| C3×D5×D15 | 19 |