Finite Group DatabasebetaFinite Group DatabasebetaOrder 3645.
456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 456 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×H(5,𝔽3) | C3 | semidirect |
| 2. C5×#6911 | C3 | semidirect |
| 3. C5×#6909 | C3 | semidirect |
| 4. C3×C5×#732 | C3 | semidirect |
| 5. C3×C5×#731 | C3 | semidirect |
| 6. #10624760 | C5 | direct (N × H) |
| 7. C3×C5×3−1+2 | C32 | semidirect |
| 12. C3×C5×H(3,𝔽3) | C32 | semidirect |
| 13. C32×C5×C9 | C32 | semidirect |
| 18. H(5,𝔽3) | C3×C5 | semidirect |
| 19. #6911 | C3×C5 | semidirect |
| 20. #6909 | C3×C5 | semidirect |
| 21. C3×#732 | C3×C5 | semidirect |
| 22. C3×#731 | C3×C5 | semidirect |
| 40. C3×3−1+2 | C32×C5 | semidirect |
| 45. C3×H(3,𝔽3) | C32×C5 | semidirect |
| 46. C32×C9 | C32×C5 | semidirect |
| 98. C5 | #10624760 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×H(5,𝔽3) | 3 |
| C5×#6911 | 3 |
| C5×#6909 | 3 |
| C3×C5×#732 | 3 |
| C3×C5×#731 | 3 |
| #10624760 | 5 |