Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
252 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×C52 | C2 | semidirect |
| 2. C2×C5×C3⋊D15 | C2 | semidirect |
| 3. C5×C3⋊Dic15 | C2 | semidirect |
| 8. #67184 | C5 | direct (N × H) |
| 10. C22×C3×C52 | D3 | semidirect |
| 13. C32×C52 | D4 | semidirect |
| 16. C22×C32×C5 | D5 | semidirect |
| 17. C22×C32×C5 | C2×C5 | semidirect |
| 18. C2×C3⋊D15 | C2×C5 | semidirect |
| 20. C3⋊Dic15 | C2×C5 | semidirect |
| 27. C22×C52 | C3⋊D3 | semidirect |
| 38. C3×C52 | #67 | semidirect |
| 41. C22×C3×C5 | C5×D3 | semidirect |
| 42. C22×C3×C5 | D15 | semidirect |
| 51. C32×C5 | C22⋊D5 | semidirect |
| 52. C32×C5 | C5×D4 | semidirect |
| 55. C22×C32 | C5×D5 | semidirect |
| 66. C52 | #638 | semidirect |
| 70. C22×C5 | C5×C3⋊D3 | semidirect |
| 71. C22×C5 | C3⋊D15 | semidirect |
| 79. C3×C5 | C5×#67 | semidirect |
| 80. C3×C5 | #1220 | semidirect |
| 81. C22×C3 | C5×D15 | semidirect |
| 92. C32 | C5×C22⋊D5 | semidirect |
| 98. C5 | C5×#638 | semidirect |
| 99. C5 | #67184 | direct (N × H) |
| 101. C22 | C5×C3⋊D15 | semidirect |
| 103. C3 | C5×#1220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C52 | 2 |
| C2×C5×C3⋊D15 | 2 |
| C5×C3⋊Dic15 | 2 |
| C5×#1220 | 3 |
| #67184 | 5 |
| C5×#638 | 5 |