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×C5 | (C3⋊D3)⋊D5 |
| commutator, cosocle | C2×C32×C5 | C22×C5 |
| Frattini | C2 | C5×(C3⋊D3)⋊D5 |
| Fitting, socle | C2×C32×C52 | C22 |
| hypocenter | C32×C5 | C5×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×D15 | C2 | semidirect |
| 2. C52×C3⋊Dic3 | C2 | semidirect |
| 6. #67157 | C5 | direct (N × H) |
| 8. C2×C5×D15 | D3 | semidirect |
| 12. C32×C52 | D4 | semidirect |
| 14. C2×C3×D15 | C2×C5 | semidirect |
| 17. C5×C3⋊Dic3 | D5 | semidirect |
| 18. C5×C3⋊Dic3 | C2×C5 | semidirect |
| 33. C3×C52 | #67 | semidirect |
| 36. C2×D15 | C5×D3 | semidirect |
| 48. C32×C5 | D20 | semidirect |
| 49. C32×C5 | C5×D4 | semidirect |
| 53. C3⋊Dic3 | C5×D5 | semidirect |
| 64. C52 | #625 | semidirect |
| 77. C3×C5 | #1202 | semidirect |
| 78. C3×C5 | C5×#67 | semidirect |
| 88. C32 | C5×D20 | semidirect |
| 95. C5 | C5×#625 | semidirect |
| 96. C5 | #67157 | direct (N × H) |
| 100. C3 | C5×#1202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D15 | 2 |
| C52×C3⋊Dic3 | 2 |
| C5×#1202 | 3 |
| #67157 | 5 |
| C5×#625 | 5 |