Finite Group DatabasebetaFinite Group DatabasebetaOrder 23940.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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 | #11716321⋊D5 |
| commutator, hypocenter | C5×C7×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C7×C19 | C22×C3 |
| prime radical | C3×D19×D35 | 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⋊#14558786 | C2 | semidirect |
| 2. C5⋊#14558784 | C2 | semidirect |
| 3. C5×#14558780 | C2 | semidirect |
| 5. C5×#11924776 | C22 | semidirect |
| 11. D19×D35 | C9 | semidirect |
| 14. #14558780 | D5 | semidirect |
| 20. D665 | C2×C9 | semidirect |
| 21. C19×D35 | C2×C9 | semidirect |
| 22. C5×C7×D19 | C2×C9 | semidirect |
| 24. #11924776 | C2×D5 | semidirect |
| 31. C5×C7×C19 | C22×C9 | semidirect |
| 48. C7×D19 | C9×D5 | semidirect |
| 56. C5×D19 | D7⋊C9 | semidirect |
| 61. C7×C19 | C2×C9×D5 | semidirect |
| 69. C5×C19 | C2×D7⋊C9 | semidirect |
| 77. D35 | #4294⋊C2 | semidirect |
| 87. D19 | C5⋊(D7⋊C9) | semidirect |
| 89. C5×C7 | C2×#4294⋊C2 | semidirect |
| 96. C19 | C2×C5⋊(D7⋊C9) | semidirect |
| 109. C7 | D5×#4294⋊C2 | semidirect |
| 113. C5 | #14558780⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊#14558786 | 2 |
| C5⋊#14558784 | 2 |
| C5×#14558780 | 2 |
| C3×D19×D35 | 3 |
| #14558780⋊C2 | 5 |
| D5×#4294⋊C2 | 7 |
| C2×C5⋊(D7⋊C9) | 19 |