Finite Group DatabasebetaFinite Group DatabasebetaOrder 22050.
114 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 25 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, cosocle, hypocenter | C3×C25×#3862 | C2 |
| Frattini | C5 | C3⋊(C5⋊#64418) |
| Fitting | C3×C72×C25 | D3 |
| socle | C3×C5×C72 | D15 |
| LCS | G ▷ C3×C25×#3862 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C25×#3862 | C2 | semidirect |
| 7. C25×#3862 | D3 | semidirect |
| 8. C25×#3862 | D3 | semidirect |
| 9. C25×#3862 | D3 | semidirect |
| 10. C3×C72×C25 | D3 | semidirect |
| 18. C72×C25 | C3⋊D3 | semidirect |
| 34. C3×#3862 | D25 | semidirect |
| 53. C3×C72 | D75 | semidirect |
| 54. #3862 | D75 | semidirect |
| 55. #3862 | D75 | semidirect |
| 56. #3862 | D75 | semidirect |
| 68. C3×C25 | #64418 | semidirect |
| 73. C72 | C3⋊D75 | semidirect |
| 84. C25 | C3⋊#64418 | semidirect |
| 111. C3 | C25⋊#64418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C25×#3862 | 2 |
| C7×D525 | 3 |
| C25⋊#64418 | 3 |
| C3⋊(C5⋊#64418) | 5 |
| C3⋊D75 | 49 |