Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
252 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 64 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 | D5×C3⋊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×C3⋊(C3⋊(C5⋊D5)) | C2 | semidirect |
| 2. C2×C5×C3⋊D15 | C2 | semidirect |
| 3. C32×C5×Dic5 | C2 | semidirect |
| 12. C3×C5×Dic5 | D3 | semidirect |
| 13. C32×C52 | D4 | semidirect |
| 18. C2×C3⋊D15 | D5 | semidirect |
| 21. C32×Dic5 | D5 | semidirect |
| 29. C5×Dic5 | C3⋊D3 | semidirect |
| 38. C3×C52 | D12 | semidirect |
| 46. C3×Dic5 | D15 | semidirect |
| 51. C32×C5 | D20 | semidirect |
| 52. C32×C5 | C22⋊D5 | semidirect |
| 66. C52 | C4⋊(C3⋊D3) | semidirect |
| 74. Dic5 | C3⋊D15 | semidirect |
| 79. C3×C5 | #1203 | semidirect |
| 80. C3×C5 | D60 | semidirect |
| 92. C32 | #6038 | semidirect |
| 98. C5 | #67140 | semidirect |
| 99. C5 | C4⋊(C3⋊D15) | semidirect |
| 103. C3 | #10597122 | semidirect |
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 |
| C2×C5×C3⋊D15 | 2 |
| C32×C5×Dic5 | 2 |
| #10597122 | 3 |
| C4⋊(C3⋊D15) | 5 |
| #67140 | 5 |