Finite Group DatabasebetaFinite Group DatabasebetaOrder 25740.
120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C11×C13 | C22 |
| Frattini | C3 | D15×D143 |
| socle | C3×C5×C11×C13 | C2×D3 |
| LCS | G ▷ C5×C9×C11×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D6435 | C2 | semidirect |
| 2. C11×C13×D45 | C2 | semidirect |
| 3. C5×C9×D143 | C2 | semidirect |
| 5. C5×C9×C11×C13 | C22 | semidirect |
| 13. C9×D143 | D5 | semidirect |
| 20. C5×D143 | D9 | semidirect |
| 21. C9×C11×C13 | C2×D5 | semidirect |
| 23. C13×D45 | D11 | semidirect |
| 26. C11×D45 | D13 | semidirect |
| 32. C5×C11×C13 | C2×D9 | semidirect |
| 34. C5×C9×C13 | C2×D11 | semidirect |
| 36. C5×C9×C11 | C2×D13 | semidirect |
| 48. D143 | D45 | direct (N × H) |
| 61. C11×C13 | C2×D45 | semidirect |
| 66. C9×C13 | D5×D11 | semidirect |
| 70. C9×C11 | D5×D13 | semidirect |
| 73. D45 | D143 | direct (N × H) |
| 80. C5×C13 | D9×D11 | semidirect |
| 82. C5×C11 | D9×D13 | semidirect |
| 84. C5×C9 | C2×D143 | semidirect |
| 103. C13 | D11×D45 | semidirect |
| 105. C11 | D13×D45 | semidirect |
| 109. C9 | D5×D143 | semidirect |
| 113. C5 | D9×D143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D6435 | 2 |
| C11×C13×D45 | 2 |
| C5×C9×D143 | 2 |
| D15×D143 | 3 |
| D9×D143 | 5 |
| D13×D45 | 11 |
| D11×D45 | 13 |