Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
822 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 136 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. C5×C4⋊SL(2,ℤ/4) | C2 | semidirect |
| 4. C4×C5×SL(2,ℤ/4) | C2 | semidirect |
| 7. C2×C4×C5×A4 | C4 | semidirect |
| 12. #85482 | C5 | direct (N × H) |
| 34. C4⋊SL(2,ℤ/4) | C2×C5 | semidirect |
| 35. C4×SL(2,ℤ/4) | C2×C5 | semidirect |
| 42. C23×C4×C5 | Dic3 | semidirect |
| 70. C2×C4×A4 | C4×C5 | semidirect |
| 129. C5×A4 | #117 | semidirect |
| 182. C2×C4×C5 | SL(2,ℤ/4) | semidirect |
| 191. C23×C4 | C5×Dic3 | semidirect |
| 236. C22×C5 | #926 | semidirect |
| 291. A4 | C5×#117 | semidirect |
| 341. C2×C4 | C5×SL(2,ℤ/4) | semidirect |
| 347. C5 | #85482 | direct (N × H) |
| 364. C22 | C5×#926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×A4 | 2 |
| C5×#5432 | 2 |
| C5×C4⋊SL(2,ℤ/4) | 2 |
| C4×C5×SL(2,ℤ/4) | 2 |
| C5×#2280 | 3 |
| C5×#926 | 4 |
| #85482 | 5 |