Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
880 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 236 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×D120 | C2 | semidirect |
| 2. C22×C3×D40 | C2 | semidirect |
| 3. C22×C5×C3⋊C16 | C2 | semidirect |
| 4. C2×#90938 | C2 | direct (N × H) |
| 10. C2×D120 | C22 | semidirect |
| 12. C2×C3×D40 | C22 | semidirect |
| 13. C2×C5×C3⋊C16 | C22 | semidirect |
| 14. #90938 | C22 | direct (N × H) |
| 17. C22×D40 | D3 | semidirect |
| 30. D120 | C23 | semidirect |
| 32. C3×D40 | C23 | semidirect |
| 33. C5×C3⋊C16 | C23 | semidirect |
| 37. C22×C3⋊C16 | D5 | semidirect |
| 44. C2×D40 | C2×D3 | semidirect |
| 69. C2×C3⋊C16 | C2×D5 | semidirect |
| 82. D40 | C22×D3 | semidirect |
| 88. C22×C3×C5 | D16 | semidirect |
| 109. C3⋊C16 | C22×D5 | semidirect |
| 132. C2×C3×C5 | C2×D16 | semidirect |
| 149. C22×C5 | #826 | semidirect |
| 171. C3×C5 | C22×D16 | semidirect |
| 174. C22×C3 | D80 | semidirect |
| 180. C2×C5 | C2×#826 | semidirect |
| 198. C2×C3 | C2×D80 | semidirect |
| 201. C5 | C22×#826 | semidirect |
| 206. C22 | #90938 | direct (N × H) |
| 210. C3 | C22×D80 | semidirect |
| 213. C2 | C2×#90938 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D120 | 2 |
| C22×C3×D40 | 2 |
| C22×C5×C3⋊C16 | 2 |
| C2×#90938 | 2 |
| C22×D80 | 3 |
| C22×#826 | 5 |