Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽5)×C3⋊ΓL(1,𝔽16) #72230972
Order 3600.
378 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C42 |
| prime radical, cosocle | C32×D52 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C3⋊(C3⋊#1042) | C4 | semidirect |
| 7. C3⋊(C3⋊#1044) | C4 | semidirect |
| 8. C3⋊(C3⋊#1043) | C4 | semidirect |
| 9. C5×C3⋊ΓL(1,𝔽16) | C4 | semidirect |
| 10. C32×#1042 | C4 | semidirect |
| 11. C32×C5×AGL(1,𝔽5) | C4 | semidirect |
| 32. C3×#1042 | Dic3 | semidirect |
| 33. C3×C5×AGL(1,𝔽5) | Dic3 | semidirect |
| 36. C32×C52 | C42 | semidirect |
| 48. C3⋊ΓL(1,𝔽16) | AGL(1,𝔽5) | direct (N × H) |
| 50. C32×AGL(1,𝔽5) | AGL(1,𝔽5) | semidirect |
| 69. #1042 | C3⋊Dic3 | semidirect |
| 71. C5×AGL(1,𝔽5) | C3⋊Dic3 | semidirect |
| 81. C3×C52 | C4×Dic3 | semidirect |
| 95. C3×AGL(1,𝔽5) | ΓL(1,𝔽16) | semidirect |
| 105. C32×C5 | C4×AGL(1,𝔽5) | semidirect |
| 106. C32×C5 | C4×AGL(1,𝔽5) | semidirect |
| 127. C52 | C4×C3⋊Dic3 | semidirect |
| 141. AGL(1,𝔽5) | C3⋊ΓL(1,𝔽16) | direct (N × H) |
| 151. C3×C5 | Dic3×AGL(1,𝔽5) | semidirect |
| 152. C3×C5 | C4×ΓL(1,𝔽16) | semidirect |
| 167. C32 | AGL(1,𝔽5)2 | semidirect |
| 175. C5 | AGL(1,𝔽5)×C3⋊Dic3 | semidirect |
| 176. C5 | C4×C3⋊ΓL(1,𝔽16) | semidirect |
| 184. C3 | AGL(1,𝔽5)×ΓL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C3⋊ΓL(1,𝔽16) | 2 |
| D5⋊(C3⋊ΓL(1,𝔽16)) | 2 |
| C32×D5×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×ΓL(1,𝔽16) | 3 |
| C4×C3⋊ΓL(1,𝔽16) | 5 |
| AGL(1,𝔽5)×C3⋊Dic3 | 5 |