Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1432 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 1432 conjugacy classes of subgroups — too many to draw. Only its 322 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. C5×#5825 | C2 | semidirect |
| 3. C5×#5243 | C2 | semidirect |
| 4. C5×#5240 | C2 | semidirect |
| 11. C22×C5×Dic6 | C22 | semidirect |
| 14. C5×#935 | C22 | semidirect |
| 15. C5×#926 | C22 | semidirect |
| 17. C5×#834 | C22 | semidirect |
| 18. #84124 | C5 | direct (N × H) |
| 46. #5825 | C2×C5 | semidirect |
| 47. #5243 | C2×C5 | semidirect |
| 48. #5240 | C2×C5 | semidirect |
| 85. C22×Dic6 | C22×C5 | semidirect |
| 88. #935 | C22×C5 | semidirect |
| 89. #926 | C22×C5 | semidirect |
| 91. #834 | C22×C5 | semidirect |
| 233. C3×C5 | #3028 | semidirect |
| 268. C5 | #84124 | direct (N × H) |
| 279. C3 | C5×#3028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#585 | 2 |
| C5×#5825 | 2 |
| C5×#5243 | 2 |
| C5×#5240 | 2 |
| C5×#3028 | 3 |
| #84124 | 5 |