Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×Dic15 | C2 | semidirect |
| 3. C32×C5×Dic5 | C2 | semidirect |
| 4. #10597120 | C3 | direct (N × H) |
| 7. C3×C3⋊(C5⋊D5) | C4 | semidirect |
| 12. C5×Dic15 | C2×C3 | semidirect |
| 15. C3×C5×Dic5 | D3 | semidirect |
| 16. C3×C5×Dic5 | C2×C3 | semidirect |
| 17. C32×C52 | C2×C4 | semidirect |
| 23. C3×Dic15 | D5 | semidirect |
| 25. C32×Dic5 | D5 | semidirect |
| 29. C3⋊(C5⋊D5) | C3×C4 | semidirect |
| 37. C5×Dic5 | C3×D3 | semidirect |
| 45. C3×C52 | C4×D3 | semidirect |
| 46. C3×C52 | C2×C3×C4 | semidirect |
| 58. Dic15 | C3×D5 | semidirect |
| 61. C3×Dic5 | C3×D5 | semidirect |
| 62. C3×Dic5 | D15 | semidirect |
| 67. C32×C5 | C4×D5 | semidirect |
| 68. C32×C5 | C4×D5 | semidirect |
| 89. C52 | C3×C4×D3 | semidirect |
| 98. Dic5 | C3×D15 | semidirect |
| 106. C3×C5 | #1200 | semidirect |
| 107. C3×C5 | C3×C4×D5 | semidirect |
| 108. C3×C5 | C3×C4×D5 | semidirect |
| 109. C3×C5 | C4×D15 | semidirect |
| 123. C32 | #6036 | semidirect |
| 131. C5 | C3×#1200 | semidirect |
| 132. C5 | C3×C4×D15 | semidirect |
| 137. C3 | C3×#6036 | semidirect |
| 138. C3 | #10597120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊(C5⋊D5) | 2 |
| C3×C5×Dic15 | 2 |
| C32×C5×Dic5 | 2 |
| #10597120 | 3 |
| C3×#6036 | 3 |
| C3×C4×D15 | 5 |
| C3×#1200 | 5 |