Finite Group DatabasebetaFinite Group DatabasebetaOrder 26100.
224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 224 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 | D15⋊D87 |
| commutator, cosocle, hypocenter | C32×C5×C29 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C29 | C22 |
| LCS | G ▷ C32×C5×C29 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C29×D15 | C2 | semidirect |
| 2. C3×C5×D435 | C2 | semidirect |
| 3. C52×C3⋊D87 | C2 | semidirect |
| 6. C32×C52×C29 | C22 | semidirect |
| 7. D15⋊D87 | C5 | direct (N × H) |
| 9. C5×D435 | D3 | semidirect |
| 10. C5×C29×D15 | D3 | semidirect |
| 18. C5×C3⋊D87 | D5 | semidirect |
| 19. C5×C3⋊D87 | C2×C5 | semidirect |
| 20. C3×D435 | C2×C5 | semidirect |
| 21. C3×C29×D15 | C2×C5 | semidirect |
| 25. C3×C52×C29 | C2×D3 | semidirect |
| 26. C3×C52×C29 | C2×D3 | semidirect |
| 35. C32×C5×C29 | C2×D5 | semidirect |
| 36. C32×C5×C29 | C22×C5 | semidirect |
| 40. D435 | C5×D3 | semidirect |
| 41. C29×D15 | C5×D3 | semidirect |
| 56. C52×C29 | D32 | semidirect |
| 59. C3⋊D87 | C5×D5 | semidirect |
| 64. C3×C5×D15 | D29 | semidirect |
| 70. C3×C5×C29 | D3×D5 | semidirect |
| 71. C3×C5×C29 | D3×D5 | semidirect |
| 72. C3×C5×C29 | C2×C5×D3 | semidirect |
| 73. C3×C5×C29 | C2×C5×D3 | semidirect |
| 85. C32×C29 | C2×C5×D5 | semidirect |
| 86. C32×C52 | C2×D29 | semidirect |
| 97. C5×D15 | D87 | semidirect |
| 104. C5×C29 | C5×D32 | semidirect |
| 105. C5×C29 | (C3⋊D3)⋊D5 | semidirect |
| 112. C3×D15 | C5×D29 | semidirect |
| 116. C3×C29 | C5×D3×D5 | semidirect |
| 117. C3×C29 | C5×D3×D5 | semidirect |
| 119. C3×C52 | D3×D29 | semidirect |
| 120. C3×C52 | C2×D87 | semidirect |
| 132. C32×C5 | D5×D29 | semidirect |
| 133. C32×C5 | C2×C5×D29 | semidirect |
| 138. D15 | C5×D87 | semidirect |
| 152. C29 | C5×(C3⋊D3)⋊D5 | semidirect |
| 153. C52 | D3×D87 | semidirect |
| 164. C3×C5 | C5×D3×D29 | semidirect |
| 165. C3×C5 | D5×D87 | semidirect |
| 166. C3×C5 | D15⋊D29 | semidirect |
| 167. C3×C5 | C2×C5×D87 | semidirect |
| 177. C32 | C5×D5×D29 | semidirect |
| 186. C5 | C5×D3×D87 | semidirect |
| 187. C5 | D15⋊D87 | direct (N × H) |
| 190. C3 | C5×D5×D87 | semidirect |
| 191. C3 | C5×D15⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C29×D15 | 2 |
| C3×C5×D435 | 2 |
| C52×C3⋊D87 | 2 |
| C5×D15⋊D29 | 3 |
| C5×D5×D87 | 3 |
| D15⋊D87 | 5 |
| C5×D3×D87 | 5 |
| C5×(C3⋊D3)⋊D5 | 29 |