Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
192 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D15⋊D15 |
| commutator, Fitting, socle, cosocle | C2×C32×C52 | C22 |
| hypocenter | C32×C52 | D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×C3⋊D15 | C2 | semidirect |
| 2. C2×C3×C3⋊(C5⋊D5) | C2 | semidirect |
| 3. C3×C5×Dic15 | C2 | semidirect |
| 11. C2×C3⋊(C5⋊D5) | D3 | semidirect |
| 16. C5×Dic15 | D3 | semidirect |
| 18. C32×C52 | D4 | semidirect |
| 20. C2×C3⋊D15 | D5 | semidirect |
| 25. C3×Dic15 | D5 | semidirect |
| 51. C3×C52 | D12 | semidirect |
| 52. C3×C52 | #67 | semidirect |
| 67. Dic15 | D15 | semidirect |
| 74. C32×C5 | D20 | semidirect |
| 75. C32×C5 | C22⋊D5 | semidirect |
| 102. C52 | #626 | semidirect |
| 120. C3×C5 | #1201 | semidirect |
| 121. C3×C5 | #1202 | semidirect |
| 122. C3×C5 | #1203 | semidirect |
| 123. C3×C5 | D60 | semidirect |
| 139. C32 | #6038 | semidirect |
| 150. C5 | #67151 | semidirect |
| 151. C5 | #67156 | semidirect |
| 156. C3 | #10597122 | semidirect |
| 157. C3 | #10597127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C3⋊D15 | 2 |
| C2×C3×C3⋊(C5⋊D5) | 2 |
| C3×C5×Dic15 | 2 |
| #10597127 | 3 |
| #10597122 | 3 |
| #67156 | 5 |
| #67151 | 5 |