Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1360 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 156 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. C2×C5×D4×A4 | C2 | semidirect |
| 2. C42×C5×A4 | C2 | semidirect |
| 3. C22×C5×#127 | C3 | semidirect |
| 8. A4×#127 | C5 | direct (N × H) |
| 9. C23×C5×D4 | C2×C3 | semidirect |
| 13. C22×C42×C5 | C2×C3 | semidirect |
| 17. C4×C5×A4 | D4 | semidirect |
| 19. C2×D4×A4 | C2×C5 | semidirect |
| 20. C42×A4 | C2×C5 | semidirect |
| 32. C5×#127 | A4 | direct (N × H) |
| 35. C22×#127 | C3×C5 | semidirect |
| 59. C2×C5×D4 | C2×A4 | semidirect |
| 63. C22×C4×C5 | C3×D4 | semidirect |
| 66. C42×C5 | C2×A4 | semidirect |
| 67. C23×D4 | C2×C3×C5 | semidirect |
| 71. C22×C42 | C2×C3×C5 | semidirect |
| 74. C5×A4 | #127 | direct (N × H) |
| 79. C4×A4 | C5×D4 | semidirect |
| 114. #127 | C5×A4 | direct (N × H) |
| 134. C22×C5 | C3×#127 | semidirect |
| 137. C4×C5 | D4×A4 | semidirect |
| 152. C2×D4 | C2×C5×A4 | semidirect |
| 156. C22×C4 | C3×C5×D4 | semidirect |
| 159. C42 | C2×C5×A4 | semidirect |
| 163. A4 | C5×#127 | direct (N × H) |
| 194. C5 | A4×#127 | direct (N × H) |
| 205. C22 | C3×C5×#127 | semidirect |
| 208. C4 | C5×D4×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×A4 | 2 |
| C42×C5×A4 | 2 |
| C22×C5×#127 | 3 |
| C3×C5×#127 | 4 |
| A4×#127 | 5 |