Finite Group DatabasebetaFinite Group DatabasebetaOrder 23940.
176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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×C19 | (C3⋊D3)⋊D7 |
| commutator, cosocle, hypocenter | C32×C7 | C22×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C19 | C22 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C5×C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C19×D21 | C2 | semidirect |
| 2. C5×C7×C3⋊D3×C19 | C2 | semidirect |
| 4. C32×C5×C7×C19 | C22 | semidirect |
| 5. C19×(C3⋊D3)⋊D7 | C5 | direct (N × H) |
| 6. C5×C19×D21 | D3 | semidirect |
| 12. C7×C3⋊D3×C19 | C2×C5 | semidirect |
| 13. C3×C19×D21 | C2×C5 | semidirect |
| 15. C3×C5×C7×C19 | C2×D3 | semidirect |
| 16. C5×C3⋊D3×C19 | D7 | semidirect |
| 21. C5×(C3⋊D3)⋊D7 | C19 | direct (N × H) |
| 22. C32×C7×C19 | C22×C5 | semidirect |
| 24. C32×C5×C19 | C2×D7 | semidirect |
| 25. C19×D21 | C5×D3 | semidirect |
| 30. C5×C7×C19 | D32 | semidirect |
| 31. C5×C7×C3⋊D3 | C2×C19 | semidirect |
| 32. C3×C5×D21 | C2×C19 | semidirect |
| 40. C3×C7×C19 | C2×C5×D3 | semidirect |
| 42. C3⋊D3×C19 | C5×D7 | semidirect |
| 44. C32×C5×C7 | C22×C19 | semidirect |
| 46. C3×C5×C19 | D3×D7 | semidirect |
| 49. (C3⋊D3)⋊D7 | C5×C19 | direct (N × H) |
| 51. C5×D21 | D3×C19 | semidirect |
| 58. C32×C19 | C2×C5×D7 | semidirect |
| 60. C7×C19 | C5×D32 | semidirect |
| 61. C7×C3⋊D3 | C2×C5×C19 | semidirect |
| 62. C3×D21 | C2×C5×C19 | semidirect |
| 68. C3×C5×C7 | C2×D3×C19 | semidirect |
| 69. C5×C19 | (C3⋊D3)⋊D7 | direct (N × H) |
| 70. C5×C3⋊D3 | D7×C19 | semidirect |
| 76. C32×C7 | C22×C5×C19 | semidirect |
| 79. C3×C19 | C5×D3×D7 | semidirect |
| 80. C32×C5 | C2×D7×C19 | semidirect |
| 81. D21 | C5×D3×C19 | semidirect |
| 88. C5×C7 | D32×C19 | semidirect |
| 95. C3×C7 | C2×C5×D3×C19 | semidirect |
| 97. C19 | C5×(C3⋊D3)⋊D7 | direct (N × H) |
| 98. C3⋊D3 | C5×D7×C19 | semidirect |
| 101. C3×C5 | D3×D7×C19 | semidirect |
| 107. C32 | C2×C5×D7×C19 | semidirect |
| 108. C7 | C5×D32×C19 | semidirect |
| 113. C5 | C19×(C3⋊D3)⋊D7 | direct (N × H) |
| 116. C3 | C5×D3×D7×C19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C19×D21 | 2 |
| C5×C7×C3⋊D3×C19 | 2 |
| C5×D3×D7×C19 | 3 |
| C19×(C3⋊D3)⋊D7 | 5 |
| C5×D32×C19 | 7 |
| C5×(C3⋊D3)⋊D7 | 19 |