Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 46 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 | D15⋊D5 |
| commutator, cosocle | C2×C3×C52 | C22×C3 |
| Frattini | C2 | C3×D15⋊D5 |
| Fitting, socle | C2×C32×C52 | C22 |
| hypocenter | C3×C52 | C3×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×D15 | C2 | semidirect |
| 2. C32×#1039 | C2 | semidirect |
| 3. #10597128 | C3 | direct (N × H) |
| 8. C2×C5×D15 | C2×C3 | semidirect |
| 11. C3×#1039 | D3 | semidirect |
| 12. C3×#1039 | C2×C3 | semidirect |
| 13. C32×C52 | D4 | semidirect |
| 15. C2×C3×D15 | D5 | semidirect |
| 27. #1039 | C3×D3 | semidirect |
| 33. C3×C52 | D12 | semidirect |
| 34. C3×C52 | C3×D4 | semidirect |
| 37. C2×D15 | C3×D5 | semidirect |
| 49. C32×C5 | C22⋊D5 | semidirect |
| 63. C52 | C3×D12 | semidirect |
| 76. C3×C5 | #1203 | semidirect |
| 77. C3×C5 | C3×C22⋊D5 | semidirect |
| 87. C32 | #6037 | semidirect |
| 95. C5 | C3×#1203 | semidirect |
| 99. C3 | C3×#6037 | semidirect |
| 100. C3 | #10597128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D15 | 2 |
| C32×#1039 | 2 |
| #10597128 | 3 |
| C3×#6037 | 3 |
| C3×#1203 | 5 |