Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽5)×GU(2,𝔽3) #14512405
Order 1920.
346 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | AGL(1,𝔽5)×S4 |
| commutator, hypocenter | C5×SL(2,𝔽3) | C42 |
| Fitting | C5×#41 | C4×D3 |
| socle | C2×C5 | C4×SL(2,ℤ/4) |
| prime radical, cosocle | D5×#41⋊C3 | C22 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. AGL(1,𝔽5)×SL(2,𝔽3) | C4 | semidirect |
| 7. #91885 | C4 | semidirect |
| 8. #91185 | C4 | semidirect |
| 9. C5×GU(2,𝔽3) | C4 | semidirect |
| 49. C5×SL(2,𝔽3) | C42 | semidirect |
| 57. GU(2,𝔽3) | AGL(1,𝔽5) | direct (N × H) |
| 149. SL(2,𝔽3) | C4×AGL(1,𝔽5) | semidirect |
| 159. AGL(1,𝔽5) | GU(2,𝔽3) | direct (N × H) |
| 228. C5 | C4×GU(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽5)×#41⋊C3 | 2 |
| D5⋊GU(2,𝔽3) | 2 |
| D5×GU(2,𝔽3) | 2 |
| AGL(1,𝔽5)×#104 | 3 |
| AGL(1,𝔽5)×C3⋊C8 | 4 |
| C4×GU(2,𝔽3) | 5 |