Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
286 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 7. C3⋊(C3⋊#1042) | C4 | semidirect |
| 8. C5×C3⋊ΓL(1,𝔽16) | C4 | semidirect |
| 9. C3×C3⋊#1042 | C4 | semidirect |
| 10. C3×C3⋊#1044 | C4 | semidirect |
| 11. C3×C3⋊#1043 | C4 | semidirect |
| 12. C3×C5×ΓL(1,𝔽16) | C4 | semidirect |
| 35. C3⋊#1044 | Dic3 | semidirect |
| 36. C3⋊#1043 | Dic3 | semidirect |
| 40. C3⋊#1042 | Dic3 | semidirect |
| 44. C5×ΓL(1,𝔽16) | Dic3 | semidirect |
| 53. C32×C52 | C42 | semidirect |
| 60. C3⋊ΓL(1,𝔽16) | AGL(1,𝔽5) | semidirect |
| 67. C3×ΓL(1,𝔽16) | AGL(1,𝔽5) | semidirect |
| 113. C3×C52 | C4×Dic3 | semidirect |
| 114. C3×C52 | C4×Dic3 | semidirect |
| 136. ΓL(1,𝔽16) | ΓL(1,𝔽16) | semidirect |
| 160. C32×C5 | C4×AGL(1,𝔽5) | semidirect |
| 161. C32×C5 | C4×AGL(1,𝔽5) | semidirect |
| 196. C52 | Dic32 | semidirect |
| 228. C3×C5 | Dic3×AGL(1,𝔽5) | semidirect |
| 229. C3×C5 | Dic3×AGL(1,𝔽5) | semidirect |
| 230. C3×C5 | Dic3×AGL(1,𝔽5) | semidirect |
| 231. C3×C5 | C4×ΓL(1,𝔽16) | semidirect |
| 256. C32 | AGL(1,𝔽5)2 | semidirect |
| 270. C5 | Dic3×ΓL(1,𝔽16) | semidirect |
| 271. C5 | ΓL(1,𝔽16)⋊Dic3 | semidirect |
| 280. C3 | AGL(1,𝔽5)×ΓL(1,𝔽16) | semidirect |
| 281. C3 | ΓL(1,𝔽16)⋊AGL(1,𝔽5) | 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 |
| C3×D5×ΓL(1,𝔽16) | 2 |
| C3×D5⋊ΓL(1,𝔽16) | 2 |
| ΓL(1,𝔽16)⋊AGL(1,𝔽5) | 3 |
| AGL(1,𝔽5)×ΓL(1,𝔽16) | 3 |
| ΓL(1,𝔽16)⋊Dic3 | 5 |
| Dic3×ΓL(1,𝔽16) | 5 |