Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
806 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | A4⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×A4 | C22×C8 |
| Frattini | C2 | C22×A4⋊AGL(1,𝔽5) |
| Fitting, socle | C25×C5 | Dic3 |
| prime radical | C23×C5×A4 | C4 |
| cosocle | A4×Dic5 | C23 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×A4⋊#170 | C2 | direct (N × H) |
| 8. A4⋊#170 | C22 | direct (N × H) |
| 15. C22×C5×A4 | C8 | semidirect |
| 40. C2×C5×A4 | C2×C8 | semidirect |
| 53. C24×C5 | C3⋊C8 | semidirect |
| 84. C5×A4 | C22×C8 | semidirect |
| 87. C22×A4 | #170 | semidirect |
| 102. C23×C5 | C2×C3⋊C8 | semidirect |
| 138. C2×A4 | C2×#170 | semidirect |
| 152. C22×C5 | A4⋊C8 | semidirect |
| 153. C22×C5 | C22×C3⋊C8 | semidirect |
| 162. C24 | C3⋊#170 | semidirect |
| 189. A4 | C22×#170 | semidirect |
| 195. C2×C5 | C2×A4⋊C8 | semidirect |
| 206. C23 | C2×C3⋊#170 | semidirect |
| 226. C5 | C22×A4⋊C8 | semidirect |
| 236. C22 | A4⋊#170 | direct (N × H) |
| 237. C22 | C22×C3⋊#170 | semidirect |
| 247. C2 | C2×A4⋊#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×A4×Dic5 | 2 |
| C2×A4⋊#170 | 2 |
| C22×C22⋊#170 | 3 |
| C22×C3⋊#170 | 4 |
| C22×A4⋊C8 | 5 |