Finite Group DatabasebetaFinite Group DatabasebetaOrder 1500.
46 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C3×C52 | C4×C5 |
| Frattini | C5 | C5×ΓL(1,𝔽16) |
| Fitting | C3×H(3,𝔽5) | C4 |
| socle | C3×C5 | C5×AGL(1,𝔽5) |
| prime radical | C3×(C5⋊D5)⋊C5 | C2 |
| cosocle | C3×C5⋊D5 | C2×C5 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×H(3,𝔽5) | C4 | semidirect |
| 4. C3⋊#1043 | C5 | semidirect |
| 9. H(3,𝔽5) | Dic3 | semidirect |
| 13. C3×C52 | C4×C5 | semidirect |
| 14. C3×C52 | AGL(1,𝔽5) | semidirect |
| 24. C52 | C5×Dic3 | semidirect |
| 25. C52 | ΓL(1,𝔽16) | semidirect |
| 43. C3 | #1043⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C5⋊D5)⋊C5 | 2 |
| #1043⋊C5 | 3 |
| C3⋊#1043 | 5 |
| C5×ΓL(1,𝔽16) | 5 |