Finite Group DatabasebetaFinite Group DatabasebetaOrder 23100.
192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 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 | D55⋊D21 |
| commutator, cosocle, hypocenter | C3×C5×C7×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C11 | C22 |
| LCS | G ▷ C3×C5×C7×C11 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C7×D55 | C2 | semidirect |
| 2. C52×D231 | C2 | semidirect |
| 3. C5×C11×D105 | C2 | semidirect |
| 5. C3×C52×C7×C11 | C22 | semidirect |
| 6. D55⋊D21 | C5 | direct (N × H) |
| 9. C5×C7×D55 | D3 | semidirect |
| 12. C11×D105 | C2×C5 | semidirect |
| 14. C5×D231 | D5 | semidirect |
| 15. C5×D231 | C2×C5 | semidirect |
| 17. C3×C7×D55 | C2×C5 | semidirect |
| 20. C52×C7×C11 | C2×D3 | semidirect |
| 23. C3×C5×D55 | D7 | semidirect |
| 27. C3×C5×C7×C11 | C2×D5 | semidirect |
| 28. C3×C5×C7×C11 | C22×C5 | semidirect |
| 30. C5×D105 | D11 | semidirect |
| 34. C3×C52×C11 | C2×D7 | semidirect |
| 36. C7×D55 | C5×D3 | semidirect |
| 45. C5×D55 | D21 | semidirect |
| 48. C3×C52×C7 | C2×D11 | semidirect |
| 49. D231 | C5×D5 | semidirect |
| 55. C5×C7×C11 | D3×D5 | semidirect |
| 56. C5×C7×C11 | C2×C5×D3 | semidirect |
| 65. C3×D55 | C5×D7 | semidirect |
| 69. C52×C11 | C2×D21 | semidirect |
| 70. C3×C7×C11 | C2×C5×D5 | semidirect |
| 74. D105 | C5×D11 | semidirect |
| 80. C52×C7 | D3×D11 | semidirect |
| 82. C3×C5×C11 | D5×D7 | semidirect |
| 83. C3×C5×C11 | C2×C5×D7 | semidirect |
| 94. D55 | C5×D21 | semidirect |
| 101. C3×C5×C7 | D5×D11 | semidirect |
| 102. C3×C5×C7 | C2×C5×D11 | semidirect |
| 105. C7×C11 | C5×D3×D5 | semidirect |
| 106. C3×C52 | D7×D11 | semidirect |
| 120. C5×C11 | D5×D21 | semidirect |
| 121. C5×C11 | C2×C5×D21 | semidirect |
| 130. C5×C7 | C5×D3×D11 | semidirect |
| 131. C5×C7 | D15⋊D11 | semidirect |
| 132. C3×C11 | C5×D5×D7 | semidirect |
| 141. C52 | D11×D21 | semidirect |
| 145. C3×C7 | C5×D5×D11 | semidirect |
| 149. C3×C5 | C5×D7×D11 | semidirect |
| 150. C3×C5 | D35⋊D11 | semidirect |
| 155. C11 | C5×D5×D21 | semidirect |
| 163. C7 | C5×D15⋊D11 | semidirect |
| 168. C5 | C5×D11×D21 | semidirect |
| 169. C5 | D55⋊D21 | direct (N × H) |
| 171. C3 | C5×D35⋊D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C7×D55 | 2 |
| C52×D231 | 2 |
| C5×C11×D105 | 2 |
| C5×D35⋊D11 | 3 |
| D55⋊D21 | 5 |
| C5×D11×D21 | 5 |
| C5×D15⋊D11 | 7 |
| C5×D5×D21 | 11 |