Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
224 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D15×D19⋊C3 |
| commutator, cosocle, hypocenter | C3×C5×C19 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C22×C3 |
| LCS | G ▷ C3×C5×C19 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×D15×C19⋊C3 | C2 | semidirect |
| 2. C5×C3⋊(C5⋊(D19⋊C3)) | C2 | semidirect |
| 3. C3×C52×D19⋊C3 | C2 | semidirect |
| 4. C5×D15×D19 | C3 | semidirect |
| 6. C3×C52×C19⋊C3 | C22 | semidirect |
| 7. D15×D19⋊C3 | C5 | direct (N × H) |
| 9. C5×D285 | C2×C3 | semidirect |
| 10. C5×C19×D15 | C2×C3 | semidirect |
| 11. C3×C52×D19 | C2×C3 | semidirect |
| 15. C52×D19⋊C3 | D3 | semidirect |
| 17. C3⋊(C5⋊(D19⋊C3)) | C2×C5 | semidirect |
| 18. D15×C19⋊C3 | C2×C5 | semidirect |
| 23. C3×C5×D19⋊C3 | D5 | semidirect |
| 24. C3×C5×D19⋊C3 | C2×C5 | semidirect |
| 25. C3×C52×C19 | C22×C3 | semidirect |
| 27. C52×C19⋊C3 | C2×D3 | semidirect |
| 28. D15×D19 | C3×C5 | semidirect |
| 34. C52×D19 | C3×D3 | semidirect |
| 38. C3×C5×C19⋊C3 | C2×D5 | semidirect |
| 39. C3×C5×C19⋊C3 | C22×C5 | semidirect |
| 41. D285 | C2×C3×C5 | semidirect |
| 42. C19×D15 | C2×C3×C5 | semidirect |
| 47. C3×C5×D19 | C3×D5 | semidirect |
| 48. C3×C5×D19 | C2×C3×C5 | semidirect |
| 60. C5×D19⋊C3 | C5×D3 | semidirect |
| 61. C5×D19⋊C3 | D15 | direct (N × H) |
| 62. C52×C19 | C2×C3×D3 | semidirect |
| 70. C3×D19⋊C3 | C5×D5 | semidirect |
| 75. C3×C5×C19 | C2×C3×D5 | semidirect |
| 76. C3×C5×C19 | C22×C3×C5 | semidirect |
| 84. C5×C19⋊C3 | C2×C5×D3 | semidirect |
| 85. C5×C19⋊C3 | C2×D15 | semidirect |
| 94. C5×D19 | C3×C5×D3 | semidirect |
| 95. C5×D19 | C3×D15 | semidirect |
| 99. C3×C19⋊C3 | C2×C5×D5 | semidirect |
| 104. C5×D15 | D19⋊C3 | direct (N × H) |
| 108. C3×D19 | C3×C5×D5 | semidirect |
| 113. D19⋊C3 | C5×D15 | direct (N × H) |
| 117. C5×C19 | C2×C3×C5×D3 | semidirect |
| 118. C5×C19 | C2×C3×D15 | semidirect |
| 130. C3×C52 | C2×D19⋊C3 | semidirect |
| 135. C3×C19 | C2×C3×C5×D5 | semidirect |
| 137. C19⋊C3 | C2×C5×D15 | semidirect |
| 147. D19 | C3×C5×D15 | semidirect |
| 165. D15 | C5×D19⋊C3 | direct (N × H) |
| 170. C52 | D3×D19⋊C3 | semidirect |
| 173. C19 | C2×C3×C5×D15 | semidirect |
| 188. C3×C5 | D5×D19⋊C3 | semidirect |
| 189. C3×C5 | C2×C5×D19⋊C3 | semidirect |
| 210. C5 | C5×D3×D19⋊C3 | semidirect |
| 211. C5 | D15×D19⋊C3 | direct (N × H) |
| 215. C3 | C5×D5×D19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D15×C19⋊C3 | 2 |
| C5×C3⋊(C5⋊(D19⋊C3)) | 2 |
| C3×C52×D19⋊C3 | 2 |
| C5×D15×D19 | 3 |
| C5×D5×D19⋊C3 | 3 |
| D15×D19⋊C3 | 5 |
| C5×D3×D19⋊C3 | 5 |
| C2×C3×C5×D15 | 19 |