Finite Group DatabasebetaFinite Group DatabasebetaOrder 23940.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×#11716326 |
| commutator, hypocenter | C5×C7×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C7×C19 | C22×C3 |
| prime radical | C3×D5×D7×C19 | C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊#14558785 | C2 | semidirect |
| 2. D5×#11924777 | C2 | semidirect |
| 3. C5×#14558785 | C2 | semidirect |
| 5. C5×#11924777 | C22 | semidirect |
| 11. D5×D7×C19 | C9 | semidirect |
| 14. #14558785 | D5 | direct (N × H) |
| 20. C19×D35 | C2×C9 | semidirect |
| 21. C7×D5×C19 | C2×C9 | semidirect |
| 22. C5×D7×C19 | C2×C9 | semidirect |
| 24. #11924777 | C2×D5 | semidirect |
| 31. C5×C7×C19 | C22×C9 | semidirect |
| 49. D7×C19 | C9×D5 | semidirect |
| 57. D5×C19 | D7⋊C9 | semidirect |
| 60. D5×D7 | #4294 | semidirect |
| 61. C7×C19 | C2×C9×D5 | semidirect |
| 69. C5×C19 | C2×D7⋊C9 | semidirect |
| 75. D35 | C2×#4294 | semidirect |
| 76. C5×D7 | C2×#4294 | semidirect |
| 77. C7×D5 | C2×#4294 | semidirect |
| 89. C5×C7 | C22×#4294 | semidirect |
| 96. C19 | D5×D7⋊C9 | semidirect |
| 103. D7 | D5×#4294 | semidirect |
| 107. D5 | #14558785 | direct (N × H) |
| 109. C7 | C2×D5×#4294 | semidirect |
| 113. C5 | C2×#14558785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊#14558785 | 2 |
| D5×#11924777 | 2 |
| C5×#14558785 | 2 |
| C3×D5×D7×C19 | 3 |
| C2×#14558785 | 5 |
| C2×D5×#4294 | 7 |
| D5×D7⋊C9 | 19 |