Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 2. C2×C5×#827 | C2 | semidirect |
| 3. C5×#5116 | C2 | semidirect |
| 4. C5×#4562 | C2 | semidirect |
| 5. C5×#4549 | C2 | semidirect |
| 13. C2×C5×Dic12 | C22 | semidirect |
| 15. C5×#818 | C22 | semidirect |
| 17. C2×C5×C3⋊C16 | C22 | semidirect |
| 18. #72036 | C5 | direct (N × H) |
| 43. C2×#827 | C2×C5 | semidirect |
| 44. #5116 | C2×C5 | semidirect |
| 45. #4562 | C2×C5 | semidirect |
| 46. #4549 | C2×C5 | semidirect |
| 83. C2×Dic12 | C22×C5 | semidirect |
| 85. #818 | C22×C5 | semidirect |
| 87. C2×C3⋊C16 | C22×C5 | semidirect |
| 117. C22×C3×C5 | SD32 | semidirect |
| 200. C22×C5 | #827 | semidirect |
| 225. C3×C5 | #2187 | semidirect |
| 232. C22×C3 | C5×SD32 | semidirect |
| 267. C5 | #72036 | direct (N × H) |
| 274. C22 | C5×#827 | semidirect |
| 281. C3 | C5×#2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×D8 | 2 |
| C2×C5×#827 | 2 |
| C5×#5116 | 2 |
| C5×#4562 | 2 |
| C5×#4549 | 2 |
| C5×#2187 | 3 |
| #72036 | 5 |