Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
880 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 132 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×Q8×A4 | C2 | semidirect |
| 3. C5×A4×C22⋊C4 | C2 | semidirect |
| 4. C42×C5×A4 | C2 | semidirect |
| 5. C22×C5×#124 | C3 | semidirect |
| 13. A4×#124 | C5 | direct (N × H) |
| 14. C23×C5×Q8 | C2×C3 | semidirect |
| 21. C22×C5×C22⋊C4 | C2×C3 | semidirect |
| 22. C22×C42×C5 | C2×C3 | semidirect |
| 33. C2×Q8×A4 | C2×C5 | semidirect |
| 35. A4×C22⋊C4 | C2×C5 | semidirect |
| 36. C42×A4 | C2×C5 | semidirect |
| 59. C5×#124 | A4 | direct (N × H) |
| 67. C22×#124 | C3×C5 | semidirect |
| 100. C2×C5×Q8 | C2×A4 | semidirect |
| 127. C5×C22⋊C4 | C2×A4 | semidirect |
| 131. C42×C5 | C2×A4 | semidirect |
| 132. C23×Q8 | C2×C3×C5 | semidirect |
| 139. C22×C22⋊C4 | C2×C3×C5 | semidirect |
| 140. C22×C42 | C2×C3×C5 | semidirect |
| 144. C5×A4 | #124 | direct (N × H) |
| 225. #124 | C5×A4 | direct (N × H) |
| 262. C22×C5 | C3×#124 | semidirect |
| 286. C2×Q8 | C2×C5×A4 | semidirect |
| 313. C22⋊C4 | C2×C5×A4 | semidirect |
| 317. C42 | C2×C5×A4 | semidirect |
| 322. A4 | C5×#124 | direct (N × H) |
| 381. C5 | A4×#124 | direct (N × H) |
| 399. C22 | C3×C5×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×A4 | 2 |
| C2×C5×D4×A4 | 2 |
| C5×A4×C22⋊C4 | 2 |
| C42×C5×A4 | 2 |
| C22×C5×#124 | 3 |
| C3×C5×#124 | 4 |
| A4×#124 | 5 |