Finite Group DatabasebetaFinite Group DatabasebetaOrder 27300.
192 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 52 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×D91 |
| commutator, cosocle, hypocenter | C3×C5×C7×C13 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C13 | C22 |
| LCS | G ▷ C3×C5×C7×C13 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C52×D91 | C2 | semidirect |
| 2. C5×C7×C13×D15 | C2 | semidirect |
| 3. C5×D1365 | C2 | semidirect |
| 5. C3×C52×C7×C13 | C22 | semidirect |
| 6. D15×D91 | C5 | direct (N × H) |
| 10. C52×D91 | D3 | semidirect |
| 12. D1365 | C2×C5 | semidirect |
| 13. C7×C13×D15 | C2×C5 | semidirect |
| 17. C3×C5×D91 | D5 | semidirect |
| 18. C3×C5×D91 | C2×C5 | semidirect |
| 19. C52×C7×C13 | C2×D3 | semidirect |
| 22. C5×C13×D15 | D7 | semidirect |
| 27. C3×C5×C7×C13 | C2×D5 | semidirect |
| 28. C3×C5×C7×C13 | C22×C5 | semidirect |
| 32. C5×C7×D15 | D13 | semidirect |
| 34. C3×C52×C13 | C2×D7 | semidirect |
| 40. C5×D91 | C5×D3 | semidirect |
| 41. C5×D91 | D15 | direct (N × H) |
| 50. C3×D91 | C5×D5 | semidirect |
| 51. C3×C52×C7 | C2×D13 | semidirect |
| 53. C5×C7×C13 | C2×C5×D3 | semidirect |
| 54. C5×C7×C13 | C2×D15 | semidirect |
| 58. C13×D15 | C5×D7 | semidirect |
| 68. C52×C13 | D3×D7 | semidirect |
| 70. C3×C7×C13 | C2×C5×D5 | semidirect |
| 74. C7×D15 | C5×D13 | semidirect |
| 81. C3×C5×C13 | D5×D7 | semidirect |
| 82. C3×C5×C13 | C2×C5×D7 | semidirect |
| 85. D91 | C5×D15 | direct (N × H) |
| 86. C52×C7 | D3×D13 | semidirect |
| 90. C5×D15 | D91 | direct (N × H) |
| 101. C3×C5×C7 | D5×D13 | semidirect |
| 102. C3×C5×C7 | C2×C5×D13 | semidirect |
| 104. C7×C13 | C2×C5×D15 | semidirect |
| 109. C3×C52 | C2×D91 | semidirect |
| 118. C5×C13 | C5×D3×D7 | semidirect |
| 119. C5×C13 | D7×D15 | semidirect |
| 129. C3×C13 | C5×D5×D7 | semidirect |
| 131. C5×C7 | C5×D3×D13 | semidirect |
| 132. C5×C7 | D13×D15 | semidirect |
| 137. D15 | C5×D91 | direct (N × H) |
| 144. C52 | D3×D91 | semidirect |
| 145. C3×C7 | C5×D5×D13 | semidirect |
| 149. C3×C5 | D5×D91 | semidirect |
| 150. C3×C5 | C2×C5×D91 | semidirect |
| 154. C13 | C5×D7×D15 | semidirect |
| 163. C7 | C5×D13×D15 | semidirect |
| 168. C5 | C5×D3×D91 | semidirect |
| 169. C5 | D15×D91 | direct (N × H) |
| 171. C3 | C5×D5×D91 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C52×D91 | 2 |
| C5×C7×C13×D15 | 2 |
| C5×D1365 | 2 |
| C5×D5×D91 | 3 |
| D15×D91 | 5 |
| C5×D3×D91 | 5 |
| C5×D13×D15 | 7 |
| C5×D7×D15 | 13 |