Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2608 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 2608 conjugacy classes of subgroups — too many to draw. Only its 315 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 |
|---|---|---|
| 3. C2×A4×Dic10 | C2 | direct (N × H) |
| 4. C24×Dic10 | C3 | semidirect |
| 9. A4×Dic10 | C22 | direct (N × H) |
| 17. C23×Dic10 | C2×C3 | semidirect |
| 18. C22×C5×A4 | Q8 | semidirect |
| 48. C22×Dic10 | A4 | direct (N × H) |
| 49. C22×Dic10 | C22×C3 | semidirect |
| 52. C2×C5×A4 | C2×Q8 | semidirect |
| 65. C24×C5 | C3×Q8 | semidirect |
| 94. C2×Dic10 | C2×A4 | direct (N × H) |
| 104. C5×A4 | C22×Q8 | semidirect |
| 107. C22×A4 | Dic10 | direct (N × H) |
| 123. C23×C5 | C2×C3×Q8 | semidirect |
| 141. Dic10 | C22×A4 | direct (N × H) |
| 167. C2×A4 | C2×Dic10 | direct (N × H) |
| 181. C22×C5 | Q8×A4 | semidirect |
| 182. C22×C5 | C22×C3×Q8 | semidirect |
| 191. C24 | C3×Dic10 | semidirect |
| 224. A4 | C22×Dic10 | direct (N × H) |
| 230. C2×C5 | C2×Q8×A4 | semidirect |
| 241. C23 | C2×C3×Dic10 | semidirect |
| 262. C5 | C22×Q8×A4 | semidirect |
| 272. C22 | A4×Dic10 | direct (N × H) |
| 273. C22 | C22×C3×Dic10 | semidirect |
| 283. C2 | C2×A4×Dic10 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×A4 | 2 |
| C22×A4×Dic5 | 2 |
| C2×A4×Dic10 | 2 |
| C24×Dic10 | 3 |
| C22×C3×Dic10 | 4 |
| C22×Q8×A4 | 5 |