Finite Group DatabasebetaFinite Group DatabasebetaOrder 3645.
446 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 446 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, socle | C3×C5 | C32⋊H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C5 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C5 ◁ C33×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×3−1+4 | C3 | semidirect |
| 2. C5×#6912 | C3 | semidirect |
| 3. C5×#6911 | C3 | semidirect |
| 4. C5×#6910 | C3 | semidirect |
| 5. C5×#6909 | C3 | semidirect |
| 6. C5×#6909 | C3 | semidirect |
| 7. C3×C5×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×C5×AΣL(1,𝔽27) | C3 | semidirect |
| 9. C3×C5×AΣL(1,𝔽27) | C3 | semidirect |
| 10. #10624762 | C5 | direct (N × H) |
| 31. 3−1+4 | C3×C5 | semidirect |
| 32. #6912 | C3×C5 | semidirect |
| 33. #6911 | C3×C5 | semidirect |
| 34. #6910 | C3×C5 | semidirect |
| 35. #6909 | C3×C5 | semidirect |
| 36. #6909 | C3×C5 | semidirect |
| 37. C3×AΣL(1,𝔽27) | C3×C5 | semidirect |
| 38. C3×AΣL(1,𝔽27) | C3×C5 | semidirect |
| 39. C3×AΣL(1,𝔽27) | C3×C5 | semidirect |
| 176. C5 | #10624762 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×3−1+4 | 3 |
| C5×#6912 | 3 |
| C5×#6911 | 3 |
| C5×#6910 | 3 |
| C5×#6909 | 3 |
| C3×C5×AΣL(1,𝔽27) | 3 |
| #10624762 | 5 |