Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1588 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 1588 conjugacy classes of subgroups — too many to draw. Only its 330 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×#935 | C2 | semidirect |
| 3. C5×#5243 | C2 | direct (N × H) |
| 4. C2×C5×#834 | C2 | semidirect |
| 11. C23×C5×Dic3 | C22 | semidirect |
| 13. C2×C5×#217 | C22 | semidirect |
| 15. C5×#935 | C22 | semidirect |
| 17. C5×#834 | C22 | semidirect |
| 18. C2×#5243 | C5 | direct (N × H) |
| 41. C22×C5×Dic3 | C23 | semidirect |
| 44. C5×#217 | C23 | semidirect |
| 47. C2×#935 | C2×C5 | semidirect |
| 48. #5243 | C2×C5 | direct (N × H) |
| 49. C2×#834 | C2×C5 | semidirect |
| 91. C23×Dic3 | C22×C5 | semidirect |
| 93. C2×#217 | C22×C5 | semidirect |
| 95. #935 | C22×C5 | semidirect |
| 97. #834 | C22×C5 | semidirect |
| 157. C22×Dic3 | C23×C5 | semidirect |
| 160. #217 | C23×C5 | semidirect |
| 200. C2×C3×C5 | #458 | semidirect |
| 262. C3×C5 | C2×#458 | semidirect |
| 280. C2×C5 | #5243 | direct (N × H) |
| 308. C2×C3 | C5×#458 | semidirect |
| 310. C5 | C2×#5243 | direct (N × H) |
| 325. C3 | C2×C5×#458 | semidirect |
| 329. C2 | C5×#5243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×H(5,𝔽2) | 2 |
| C2×C5×#935 | 2 |
| C5×#5243 | 2 |
| C2×C5×#834 | 2 |
| C2×C5×#458 | 3 |
| C2×#5243 | 5 |