Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
184 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 184 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×C3×C3⋊(C5⋊D5) | C2 | semidirect |
| 2. C2×C3×C5×D15 | C2 | semidirect |
| 3. C5×C3⋊Dic15 | C2 | semidirect |
| 11. C2×C3⋊(C5⋊D5) | D3 | semidirect |
| 12. C2×C5×D15 | D3 | semidirect |
| 18. C32×C52 | D4 | semidirect |
| 23. C2×C3×D15 | D5 | semidirect |
| 25. C3⋊Dic15 | D5 | semidirect |
| 50. C3×C52 | #67 | semidirect |
| 51. C3×C52 | #67 | semidirect |
| 57. C2×D15 | D15 | semidirect |
| 73. C32×C5 | D20 | semidirect |
| 74. C32×C5 | C22⋊D5 | semidirect |
| 99. C52 | #625 | semidirect |
| 117. C3×C5 | #1201 | semidirect |
| 118. C3×C5 | #1202 | semidirect |
| 119. C3×C5 | #1202 | semidirect |
| 120. C3×C5 | #1220 | semidirect |
| 136. C32 | #6038 | semidirect |
| 146. C5 | #67150 | semidirect |
| 147. C5 | #67157 | semidirect |
| 152. C3 | #10597123 | semidirect |
| 153. C3 | #10597127 | 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×C3×C5×D15 | 2 |
| C5×C3⋊Dic15 | 2 |
| #10597127 | 3 |
| #10597123 | 3 |
| #67157 | 5 |
| #67150 | 5 |