Finite Group DatabasebetaFinite Group DatabasebetaOrder 22050.
208 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 34 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 | C3⋊(C5⋊#64418) |
| commutator, cosocle, hypocenter | C3×C5×#3862 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | D3 |
| LCS | G ▷ C3×C5×#3862 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C52×#3862 | C2 | semidirect |
| 5. C3⋊(C5⋊#64418) | C5 | direct (N × H) |
| 7. C52×#3862 | D3 | semidirect |
| 8. C52×#3862 | D3 | semidirect |
| 9. C3×C52×C72 | D3 | semidirect |
| 12. C3×C5×#3862 | D5 | semidirect |
| 13. C3×C5×#3862 | C2×C5 | semidirect |
| 21. C52×C72 | C3⋊D3 | semidirect |
| 26. C3×C5×C72 | C5×D3 | semidirect |
| 27. C3×C5×C72 | D15 | semidirect |
| 30. C5×#3862 | C5×D3 | semidirect |
| 31. C5×#3862 | C5×D3 | semidirect |
| 32. C5×#3862 | D15 | semidirect |
| 33. C5×#3862 | D15 | semidirect |
| 42. C3×#3862 | C5×D5 | semidirect |
| 52. C5×C72 | C5×C3⋊D3 | semidirect |
| 53. C5×C72 | C3⋊D15 | semidirect |
| 65. C3×C72 | C5×D15 | semidirect |
| 66. #3862 | C5×D15 | semidirect |
| 67. #3862 | C5×D15 | semidirect |
| 88. C3×C52 | #64418 | semidirect |
| 95. C72 | C5×C3⋊D15 | semidirect |
| 116. C52 | C3⋊#64418 | semidirect |
| 130. C3×C5 | C5×#64418 | semidirect |
| 131. C3×C5 | C5⋊#64418 | semidirect |
| 144. C5 | C5×C3⋊#64418 | semidirect |
| 145. C5 | C3⋊(C5⋊#64418) | direct (N × H) |
| 148. C3 | C5×C5⋊#64418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C52×#3862 | 2 |
| C5×C7×D105 | 3 |
| C5×C5⋊#64418 | 3 |
| C3⋊(C5⋊#64418) | 5 |
| C5×C3⋊#64418 | 5 |
| C5×C3⋊D15 | 49 |