Finite Group DatabasebetaFinite Group DatabasebetaOrder 23940.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#11924781 | C2 | semidirect |
| 2. C5⋊#14558804 | C2 | direct (N × H) |
| 3. C5⋊#14558804 | C2 | direct (N × H) |
| 5. C5×#11924781 | C22 | semidirect |
| 11. C2×C19×D35 | C9 | semidirect |
| 12. C2×#11924781 | D5 | semidirect |
| 20. C2×C5×C7×C19 | C2×C9 | semidirect |
| 21. C19×D35 | C2×C9 | semidirect |
| 22. C19×D35 | C2×C9 | semidirect |
| 24. #11924781 | C2×D5 | semidirect |
| 31. C5×C7×C19 | C22×C9 | semidirect |
| 47. C2×C7×C19 | C9×D5 | semidirect |
| 55. C2×C5×C19 | D7⋊C9 | semidirect |
| 60. C2×D35 | #4296 | semidirect |
| 61. C7×C19 | C2×C9×D5 | semidirect |
| 69. C5×C19 | C2×D7⋊C9 | semidirect |
| 75. C2×C5×C7 | C2×#4296 | semidirect |
| 76. D35 | C2×#4296 | semidirect |
| 77. D35 | C2×#4296 | semidirect |
| 87. C2×C19 | C5⋊(D7⋊C9) | semidirect |
| 89. C5×C7 | C22×#4296 | semidirect |
| 96. C19 | C2×C5⋊(D7⋊C9) | semidirect |
| 101. C2×C7 | D5×#4296 | semidirect |
| 105. C2×C5 | #14558804 | semidirect |
| 109. C7 | C2×D5×#4296 | semidirect |
| 113. C5 | C2×#14558804 | semidirect |
| 118. C2 | C5⋊#14558804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#11924781 | 2 |
| C5⋊#14558804 | 2 |
| C2×C19⋊C3×D35 | 3 |
| C2×#14558804 | 5 |
| C2×D5×#4296 | 7 |
| C2×C5⋊(D7⋊C9) | 19 |