Finite Group DatabasebetaFinite Group DatabasebetaOrder 22050.
184 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C5⋊#64418 |
| commutator, cosocle, hypocenter | C5×#3862 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | D3 |
| LCS | G ▷ C5×#3862 | |
| UCS | C1 ◁ C3×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C52×#3862 | C2 | semidirect |
| 3. C5×C5⋊#64418 | C3 | direct (N × H) |
| 4. C3×C5⋊#64418 | C5 | direct (N × H) |
| 7. C52×#3862 | C2×C3 | semidirect |
| 8. C3×C52×C72 | D3 | semidirect |
| 11. C3×C5×#3862 | D5 | semidirect |
| 12. C3×C5×#3862 | C2×C5 | semidirect |
| 16. C5⋊#64418 | C3×C5 | direct (N × H) |
| 18. C52×C72 | C3×D3 | semidirect |
| 23. C3×C5×C72 | C5×D3 | semidirect |
| 24. C3×C5×C72 | D15 | semidirect |
| 29. C5×#3862 | C3×D5 | semidirect |
| 30. C5×#3862 | C2×C3×C5 | semidirect |
| 39. C3×#3862 | C5×D5 | semidirect |
| 48. C5×C72 | C3×C5×D3 | semidirect |
| 49. C5×C72 | C3×D15 | semidirect |
| 60. C3×C72 | C5×D15 | semidirect |
| 62. #3862 | C3×C5×D5 | semidirect |
| 83. C3×C52 | #64418 | semidirect |
| 90. C72 | C3×C5×D15 | semidirect |
| 109. C52 | C3×#64418 | semidirect |
| 123. C3×C5 | C5×#64418 | semidirect |
| 124. C3×C5 | C5⋊#64418 | direct (N × H) |
| 136. C5 | C3×C5×#64418 | semidirect |
| 137. C5 | C3×C5⋊#64418 | direct (N × H) |
| 140. C3 | C5×C5⋊#64418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C52×#3862 | 2 |
| C3×C5×C7×D35 | 3 |
| C5×C5⋊#64418 | 3 |
| C3×C5⋊#64418 | 5 |
| C3×C5×#64418 | 5 |
| C3×C5×D15 | 49 |