Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C2 | #14268437 |
| commutator, hypocenter | C32×C52 | C42 |
| Fitting, socle | C2×C32×C52 | C2×C4 |
| prime radical, cosocle | C2×C32×C5⋊D5 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C3⋊(C3⋊#1044) | C4 | semidirect |
| 8. C3×C3⋊#1043 | C4 | semidirect |
| 9. C3×C5×Dic15 | C4 | semidirect |
| 32. C3⋊#1043 | Dic3 | semidirect |
| 34. C5×Dic15 | Dic3 | semidirect |
| 38. C32×C52 | C42 | semidirect |
| 47. C3×Dic15 | AGL(1,𝔽5) | semidirect |
| 80. C3×C52 | C4×Dic3 | semidirect |
| 81. C3×C52 | C4×Dic3 | semidirect |
| 99. Dic15 | ΓL(1,𝔽16) | semidirect |
| 108. C32×C5 | C4×AGL(1,𝔽5) | semidirect |
| 135. C52 | Dic32 | semidirect |
| 158. C3×C5 | Dic3×AGL(1,𝔽5) | semidirect |
| 159. C3×C5 | C4×ΓL(1,𝔽16) | semidirect |
| 176. C32 | #87830 | semidirect |
| 190. C5 | Dic3×ΓL(1,𝔽16) | semidirect |
| 196. C3 | #11925349 | semidirect |
| 197. C3 | #11925354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊#1044) | 2 |
| C2×C3×C3⋊#1043 | 2 |
| C3×#10597126 | 2 |
| #11925354 | 3 |
| #11925349 | 3 |
| Dic3×ΓL(1,𝔽16) | 5 |