Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
538 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 124 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×C3 | D3×D52 |
| commutator, hypocenter | C3×C52 | C22×C3×C4 |
| Frattini | C2 | C3×D3×D52 |
| Fitting, socle | C2×C32×C52 | C23 |
| prime radical | C2×C3×D15⋊D5 | C2 |
| cosocle | C2×C3×C52 | C23×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×Dic5×D15 | C2 | semidirect |
| 3. C3×Dic3×C5⋊D5 | C2 | semidirect |
| 4. C3×C5×#1200 | C2 | semidirect |
| 5. C32×#6036 | C2 | semidirect |
| 7. #11925416 | C3 | direct (N × H) |
| 10. C3×D15⋊D5 | C4 | semidirect |
| 11. C3×C3⋊#1039 | C22 | semidirect |
| 12. C3×C52×Dic3 | C22 | semidirect |
| 13. C32×C5×Dic5 | C22 | semidirect |
| 19. Dic5×D15 | C2×C3 | semidirect |
| 20. Dic3×C5⋊D5 | C2×C3 | semidirect |
| 21. C5×#1200 | C2×C3 | semidirect |
| 23. C3×#6036 | D3 | semidirect |
| 24. C3×#6036 | C2×C3 | semidirect |
| 27. C3×C5×D15 | C2×C4 | semidirect |
| 28. C32×C5⋊D5 | C2×C4 | semidirect |
| 34. C3×#1200 | D5 | semidirect |
| 43. D15⋊D5 | C3×C4 | semidirect |
| 46. C3⋊#1039 | C22×C3 | semidirect |
| 47. C52×Dic3 | C22×C3 | semidirect |
| 50. C3×C5×Dic5 | C2×D3 | semidirect |
| 51. C3×C5×Dic5 | C22×C3 | semidirect |
| 54. C32×C52 | C22×C4 | semidirect |
| 58. #6036 | C3×D3 | semidirect |
| 69. C3×C5×Dic3 | C2×D5 | semidirect |
| 70. C32×Dic5 | C2×D5 | semidirect |
| 74. C5×D15 | C2×C3×C4 | semidirect |
| 76. C3×C5⋊D5 | C4×D3 | semidirect |
| 77. C3×C5⋊D5 | C2×C3×C4 | semidirect |
| 93. #1200 | C3×D5 | semidirect |
| 102. C5×Dic5 | C2×C3×D3 | semidirect |
| 105. C3×D15 | C4×D5 | semidirect |
| 111. C3×C52 | C2×C4×D3 | semidirect |
| 112. C3×C52 | C22×C3×C4 | semidirect |
| 140. C3×Dic5 | D3×D5 | semidirect |
| 141. C3×Dic5 | C2×C3×D5 | semidirect |
| 143. C5×Dic3 | C2×C3×D5 | semidirect |
| 145. C5⋊D5 | C3×C4×D3 | semidirect |
| 150. C32×C5 | C2×C4×D5 | semidirect |
| 164. C3×Dic3 | D52 | semidirect |
| 172. D15 | C3×C4×D5 | semidirect |
| 181. C52 | C2×C3×C4×D3 | semidirect |
| 203. Dic5 | C3×D3×D5 | semidirect |
| 212. C3×C5 | C4×D3×D5 | semidirect |
| 213. C3×C5 | C2×C3×C4×D5 | semidirect |
| 227. Dic3 | C3×D52 | semidirect |
| 234. C32 | C4×D52 | semidirect |
| 249. C5 | C3×C4×D3×D5 | semidirect |
| 257. C3 | #11925416 | direct (N × H) |
| 258. C3 | C3×C4×D52 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D15⋊D5 | 2 |
| C3×Dic5×D15 | 2 |
| C3×Dic3×C5⋊D5 | 2 |
| C3×C5×#1200 | 2 |
| C32×#6036 | 2 |
| C3×C4×D52 | 3 |
| #11925416 | 3 |
| C3×C4×D3×D5 | 5 |