Finite Group DatabasebetaFinite Group DatabasebetaOrder 15300.
212 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 56 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 | D5×D255 |
| commutator, cosocle, hypocenter | C3×C52×C17 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C22 |
| LCS | G ▷ C3×C52×C17 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C3⋊(C5⋊D85) | C2 | semidirect |
| 2. C3×C5×D255 | C2 | semidirect |
| 3. C32×C5×D5×C17 | C2 | semidirect |
| 4. D5×D255 | C3 | direct (N × H) |
| 6. C32×C52×C17 | C22 | semidirect |
| 9. C3⋊(C5⋊D85) | C2×C3 | semidirect |
| 10. C5×D255 | C2×C3 | semidirect |
| 14. C3×C5×D5×C17 | D3 | semidirect |
| 15. C3×C5×D5×C17 | C2×C3 | semidirect |
| 21. C3×D255 | D5 | direct (N × H) |
| 23. C32×D5×C17 | D5 | semidirect |
| 25. C3×C52×C17 | C2×D3 | semidirect |
| 26. C3×C52×C17 | C22×C3 | semidirect |
| 34. C5×D5×C17 | C3×D3 | semidirect |
| 36. C32×C5×C17 | C2×D5 | semidirect |
| 37. C32×C5×C17 | C2×D5 | semidirect |
| 45. D255 | C3×D5 | direct (N × H) |
| 52. C3×D5×C17 | C3×D5 | semidirect |
| 53. C3×D5×C17 | D15 | semidirect |
| 57. C32×C5×D5 | D17 | semidirect |
| 58. C52×C17 | C2×C3×D3 | semidirect |
| 71. C3×C5×C17 | D3×D5 | semidirect |
| 72. C3×C5×C17 | C2×C3×D5 | semidirect |
| 73. C3×C5×C17 | C2×C3×D5 | semidirect |
| 74. C3×C5×C17 | C2×D15 | semidirect |
| 75. C32×C52 | C2×D17 | semidirect |
| 86. D5×C17 | C3×D15 | semidirect |
| 87. C32×C17 | D52 | semidirect |
| 93. C3×C5×D5 | C3×D17 | semidirect |
| 94. C3×C5×D5 | D51 | semidirect |
| 109. C32×D5 | D85 | semidirect |
| 111. C5×C17 | C3×D3×D5 | semidirect |
| 112. C5×C17 | C2×C3×D15 | semidirect |
| 114. C3×C52 | C2×C3×D17 | semidirect |
| 115. C3×C52 | C2×D51 | semidirect |
| 122. C3×C17 | C3×D52 | semidirect |
| 123. C3×C17 | D5×D15 | semidirect |
| 126. C5×D5 | C3×D51 | semidirect |
| 128. C32×C5 | D5×D17 | semidirect |
| 129. C32×C5 | C2×D85 | semidirect |
| 147. C3×D5 | C3×D85 | semidirect |
| 148. C3×D5 | D255 | direct (N × H) |
| 150. C52 | C2×C3×D51 | semidirect |
| 156. C17 | C3×D5×D15 | semidirect |
| 162. C3×C5 | C3×D5×D17 | semidirect |
| 163. C3×C5 | D5×D51 | semidirect |
| 164. C3×C5 | C2×C3×D85 | semidirect |
| 165. C3×C5 | C2×D255 | semidirect |
| 174. D5 | C3×D255 | direct (N × H) |
| 175. C32 | D5×D85 | semidirect |
| 184. C5 | C3×D5×D51 | semidirect |
| 185. C5 | C2×C3×D255 | semidirect |
| 188. C3 | C3×D5×D85 | semidirect |
| 189. C3 | D5×D255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C3⋊(C5⋊D85) | 2 |
| C3×C5×D255 | 2 |
| C32×C5×D5×C17 | 2 |
| D5×D255 | 3 |
| C3×D5×D85 | 3 |
| C2×C3×D255 | 5 |
| C3×D5×D51 | 5 |
| C3×D5×D15 | 17 |