Finite Group DatabasebetaFinite Group Databasebeta← C2×D3×D5⋊AGL(1,𝔽5) #72222615
Order 2400.
1052 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C3×C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C22×C4 |
| prime radical | C2×D3×D52 | C2 |
| cosocle | C3×C5⋊D5 | C24 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#10597183 | C2 | semidirect |
| 3. C2×#10597182 | C2 | semidirect |
| 4. C2×D5⋊ΓL(1,𝔽16) | C2 | semidirect |
| 5. C2×D3×#1044 | C2 | semidirect |
| 6. C2×D3×#1043 | C2 | semidirect |
| 7. C2×C3×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 8. D3×D5⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 11. C2×D5×D15 | C4 | semidirect |
| 13. C2×C5×D3×D5 | C4 | semidirect |
| 15. C2×C3⋊#1044 | C22 | semidirect |
| 16. C2×C3⋊#1043 | C22 | semidirect |
| 17. C2×C3×#1044 | C22 | semidirect |
| 18. C2×C3×#1043 | C22 | semidirect |
| 19. D3×D52 | C4 | semidirect |
| 21. #10597183 | C22 | semidirect |
| 22. #10597182 | C22 | semidirect |
| 23. D5⋊ΓL(1,𝔽16) | C22 | semidirect |
| 24. D3×#1044 | C22 | semidirect |
| 25. D3×#1043 | C22 | semidirect |
| 26. C3×D5⋊AGL(1,𝔽5) | C22 | semidirect |
| 35. C2×D5⋊AGL(1,𝔽5) | D3 | direct (N × H) |
| 36. C2×C3⋊(C5⋊D5) | C2×C4 | semidirect |
| 37. C2×C5×D15 | C2×C4 | semidirect |
| 38. C2×C52×D3 | C2×C4 | semidirect |
| 40. C2×C3×C5×D5 | C2×C4 | semidirect |
| 41. D15⋊D5 | C2×C4 | semidirect |
| 43. D5×D15 | C2×C4 | semidirect |
| 44. D3×C5⋊D5 | C2×C4 | semidirect |
| 46. C5×D3×D5 | C2×C4 | semidirect |
| 47. C3×D52 | C2×C4 | semidirect |
| 49. C3⋊#1044 | C23 | semidirect |
| 50. C3⋊#1043 | C23 | semidirect |
| 51. C3×#1044 | C23 | semidirect |
| 52. C3×#1043 | C23 | semidirect |
| 71. C2×#1044 | C2×D3 | semidirect |
| 74. C2×#1043 | C2×D3 | semidirect |
| 78. D5⋊AGL(1,𝔽5) | C2×D3 | direct (N × H) |
| 80. C2×C3×C52 | C22×C4 | semidirect |
| 81. C3⋊(C5⋊D5) | C22×C4 | semidirect |
| 82. C5×D15 | C22×C4 | semidirect |
| 83. C52×D3 | C22×C4 | semidirect |
| 84. C3×C5⋊D5 | C22×C4 | semidirect |
| 86. C3×C5×D5 | C22×C4 | semidirect |
| 96. C2×D3×D5 | AGL(1,𝔽5) | semidirect |
| 117. C2×C5×D5 | C4×D3 | semidirect |
| 121. D52 | C4×D3 | semidirect |
| 124. #1044 | C22×D3 | semidirect |
| 126. #1043 | C22×D3 | semidirect |
| 137. C3×C52 | C23×C4 | semidirect |
| 142. C2×D15 | C2×AGL(1,𝔽5) | semidirect |
| 146. C2×C5×D3 | C2×AGL(1,𝔽5) | semidirect |
| 151. C2×C3×D5 | C2×AGL(1,𝔽5) | semidirect |
| 159. D3×D5 | C2×AGL(1,𝔽5) | semidirect |
| 167. C2×C52 | C2×C4×D3 | semidirect |
| 169. C5⋊D5 | C2×C4×D3 | semidirect |
| 172. C5×D5 | C2×C4×D3 | semidirect |
| 207. C2×C3×C5 | C22×AGL(1,𝔽5) | semidirect |
| 210. D15 | C22×AGL(1,𝔽5) | semidirect |
| 215. C3×D5 | C22×AGL(1,𝔽5) | semidirect |
| 218. C5×D3 | C22×AGL(1,𝔽5) | semidirect |
| 219. C52 | C22×C4×D3 | semidirect |
| 258. C2×D5 | D3×AGL(1,𝔽5) | semidirect |
| 274. C3×C5 | C23×AGL(1,𝔽5) | semidirect |
| 287. C2×D3 | D5⋊AGL(1,𝔽5) | direct (N × H) |
| 297. C2×C5 | C2×D3×AGL(1,𝔽5) | semidirect |
| 305. D5 | C2×D3×AGL(1,𝔽5) | semidirect |
| 326. C2×C3 | C2×D5⋊AGL(1,𝔽5) | semidirect |
| 329. D3 | C2×D5⋊AGL(1,𝔽5) | direct (N × H) |
| 331. C5 | C22×D3×AGL(1,𝔽5) | semidirect |
| 349. C3 | C22×D5⋊AGL(1,𝔽5) | semidirect |
| 356. C2 | D3×D5⋊AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D52 | 2 |
| C2×#10597183 | 2 |
| C2×#10597182 | 2 |
| C2×D5⋊ΓL(1,𝔽16) | 2 |
| C2×D3×#1044 | 2 |
| C2×D3×#1043 | 2 |
| C2×C3×D5⋊AGL(1,𝔽5) | 2 |
| D3×D5⋊AGL(1,𝔽5) | 2 |
| C22×D5⋊AGL(1,𝔽5) | 3 |
| C22×D3×AGL(1,𝔽5) | 5 |