Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
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×D555 |
| commutator, cosocle, hypocenter | C3×C52×C37 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C22 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C5×D5×C37 | C2 | semidirect |
| 2. C3×C5×D555 | C2 | semidirect |
| 3. C3×C3⋊(C5⋊D185) | C2 | semidirect |
| 4. D5×D555 | C3 | direct (N × H) |
| 6. C32×C52×C37 | C22 | semidirect |
| 9. C3⋊(C5⋊D185) | C2×C3 | semidirect |
| 10. C5×D555 | C2×C3 | semidirect |
| 14. C3×C5×D5×C37 | D3 | semidirect |
| 15. C3×C5×D5×C37 | C2×C3 | semidirect |
| 20. C3×D555 | D5 | direct (N × H) |
| 22. C32×D5×C37 | D5 | semidirect |
| 25. C3×C52×C37 | C2×D3 | semidirect |
| 26. C3×C52×C37 | C22×C3 | semidirect |
| 33. C5×D5×C37 | C3×D3 | semidirect |
| 35. C32×C5×C37 | C2×D5 | semidirect |
| 36. C32×C5×C37 | C2×D5 | semidirect |
| 44. D555 | C3×D5 | direct (N × H) |
| 51. C3×D5×C37 | C3×D5 | semidirect |
| 52. C3×D5×C37 | D15 | semidirect |
| 54. C52×C37 | C2×C3×D3 | semidirect |
| 66. C3×C5×C37 | D3×D5 | semidirect |
| 67. C3×C5×C37 | C2×C3×D5 | semidirect |
| 68. C3×C5×C37 | C2×C3×D5 | semidirect |
| 69. C3×C5×C37 | C2×D15 | semidirect |
| 72. C32×C5×D5 | D37 | semidirect |
| 81. D5×C37 | C3×D15 | semidirect |
| 82. C32×C37 | D52 | semidirect |
| 85. C32×C52 | C2×D37 | semidirect |
| 94. C5×C37 | C3×D3×D5 | semidirect |
| 95. C5×C37 | C2×C3×D15 | semidirect |
| 103. C3×C5×D5 | C3×D37 | semidirect |
| 104. C3×C5×D5 | D111 | semidirect |
| 107. C3×C37 | C3×D52 | semidirect |
| 108. C3×C37 | D5×D15 | semidirect |
| 116. C32×D5 | D185 | semidirect |
| 118. C3×C52 | C2×C3×D37 | semidirect |
| 119. C3×C52 | C2×D111 | semidirect |
| 129. C5×D5 | C3×D111 | semidirect |
| 131. C32×C5 | D5×D37 | semidirect |
| 132. C32×C5 | C2×D185 | semidirect |
| 133. C37 | C3×D5×D15 | semidirect |
| 148. C3×D5 | C3×D185 | semidirect |
| 149. C3×D5 | D555 | direct (N × H) |
| 151. C52 | C2×C3×D111 | semidirect |
| 162. C3×C5 | C3×D5×D37 | semidirect |
| 163. C3×C5 | D5×D111 | semidirect |
| 164. C3×C5 | C2×C3×D185 | semidirect |
| 165. C3×C5 | C2×D555 | semidirect |
| 174. D5 | C3×D555 | direct (N × H) |
| 175. C32 | D5×D185 | semidirect |
| 184. C5 | C3×D5×D111 | semidirect |
| 185. C5 | C2×C3×D555 | semidirect |
| 188. C3 | C3×D5×D185 | semidirect |
| 189. C3 | D5×D555 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×D5×C37 | 2 |
| C3×C5×D555 | 2 |
| C3×C3⋊(C5⋊D185) | 2 |
| D5×D555 | 3 |
| C3×D5×D185 | 3 |
| C2×C3×D555 | 5 |
| C3×D5×D111 | 5 |
| C3×D5×D15 | 37 |