Finite Group DatabasebetaFinite Group DatabasebetaOrder 37620.
120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 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×C19 | C22 |
| Frattini | C3 | D55⋊D57 |
| socle | C3×C5×C11×C19 | C2×D3 |
| LCS | G ▷ C5×C9×C11×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×D855 | C2 | semidirect |
| 2. C5×D1881 | C2 | semidirect |
| 3. C9×C19×D55 | C2 | semidirect |
| 5. C5×C9×C11×C19 | C22 | semidirect |
| 11. D1881 | D5 | semidirect |
| 17. C19×D55 | D9 | semidirect |
| 21. C9×C11×C19 | C2×D5 | semidirect |
| 22. D855 | D11 | semidirect |
| 29. C5×C11×C19 | C2×D9 | semidirect |
| 32. C9×D55 | D19 | semidirect |
| 33. C5×C9×C19 | C2×D11 | semidirect |
| 41. C5×C9×C11 | C2×D19 | semidirect |
| 56. C11×C19 | D5×D9 | semidirect |
| 64. C9×C19 | D5×D11 | semidirect |
| 70. D55 | D171 | semidirect |
| 73. C9×C11 | D5×D19 | semidirect |
| 74. C5×C19 | D9×D11 | semidirect |
| 84. C5×C11 | C2×D171 | semidirect |
| 85. C5×C9 | D11×D19 | semidirect |
| 99. C19 | D45⋊D11 | semidirect |
| 105. C11 | D5×D171 | semidirect |
| 109. C9 | D55⋊D19 | semidirect |
| 113. C5 | D11×D171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×D855 | 2 |
| C5×D1881 | 2 |
| C9×C19×D55 | 2 |
| D55⋊D57 | 3 |
| D11×D171 | 5 |
| D5×D171 | 11 |
| D45⋊D11 | 19 |