Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
3310 conjugacy classes of subgroups; only the 453 normal subgroups are shown.
This group has 3310 conjugacy classes of subgroups — too many to draw. Only its 453 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C5⋊S4 |
| commutator, hypocenter | C5×A4 | C23×C4 |
| Frattini | C2 | C23×C5⋊S4 |
| Fitting, socle | C26×C5 | D3 |
| prime radical | C24×C5×A4 | C2 |
| cosocle | C2×C5×A4 | C24 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×A4⋊Dic5 | C2 | direct (N × H) |
| 4. C23×C5×A4 | C4 | semidirect |
| 7. C2×A4⋊Dic5 | C22 | direct (N × H) |
| 15. C22×C5×A4 | C2×C4 | semidirect |
| 18. A4⋊Dic5 | C23 | direct (N × H) |
| 24. C25×C5 | Dic3 | semidirect |
| 36. C2×C5×A4 | C22×C4 | semidirect |
| 39. C23×A4 | Dic5 | semidirect |
| 52. C24×C5 | C2×Dic3 | semidirect |
| 69. C5×A4 | C23×C4 | semidirect |
| 72. C22×A4 | C2×Dic5 | semidirect |
| 87. C23×C5 | SL(2,ℤ/4) | semidirect |
| 88. C23×C5 | C22×Dic3 | semidirect |
| 99. C25 | Dic15 | semidirect |
| 112. C2×A4 | C22×Dic5 | semidirect |
| 124. C22×C5 | C2×SL(2,ℤ/4) | semidirect |
| 125. C22×C5 | C23×Dic3 | semidirect |
| 138. C24 | C2×Dic15 | semidirect |
| 151. A4 | C23×Dic5 | semidirect |
| 156. C2×C5 | C22×SL(2,ℤ/4) | semidirect |
| 169. C23 | A4⋊Dic5 | direct (N × H) |
| 170. C23 | C22×Dic15 | semidirect |
| 180. C5 | C23×SL(2,ℤ/4) | semidirect |
| 190. C22 | C2×A4⋊Dic5 | direct (N × H) |
| 191. C22 | C23×Dic15 | semidirect |
| 199. C2 | C22×A4⋊Dic5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×A4 | 2 |
| C22×A4⋊Dic5 | 2 |
| C23×C22⋊Dic5 | 3 |
| C23×Dic15 | 4 |
| C23×SL(2,ℤ/4) | 5 |