Finite Group DatabasebetaFinite Group Databasebeta← C4×C5⋊((C3⋊D3)⋊C3) #11761864
Order 1080.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C5×H(3,𝔽3) | C2 | semidirect |
| 3. (C3⋊Dic15)⋊C3 | C2 | semidirect |
| 4. C4×C3⋊D15 | C3 | semidirect |
| 7. C5⋊((C3⋊D3)⋊C3) | C4 | direct (N × H) |
| 12. C32×C4×C5 | D3 | semidirect |
| 13. C32×C4×C5 | C2×C3 | semidirect |
| 14. C3⋊Dic15 | C2×C3 | semidirect |
| 16. C5×H(3,𝔽3) | C2×C4 | semidirect |
| 21. C4×H(3,𝔽3) | D5 | semidirect |
| 26. C3⋊D15 | C3×C4 | semidirect |
| 43. C32×C5 | C4×D3 | semidirect |
| 44. C32×C5 | C2×C3×C4 | semidirect |
| 49. C32×C4 | C3×D5 | semidirect |
| 50. C32×C4 | D15 | semidirect |
| 60. H(3,𝔽3) | C4×D5 | semidirect |
| 65. C4×C5 | (C3⋊D3)⋊C3 | semidirect |
| 89. C32 | C3×C4×D5 | semidirect |
| 90. C32 | C4×D15 | semidirect |
| 99. C5 | C4×(C3⋊D3)⋊C3 | semidirect |
| 102. C4 | C5⋊((C3⋊D3)⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5⋊((C3⋊D3)⋊C3) | 2 |
| C4×C5×H(3,𝔽3) | 2 |
| (C3⋊Dic15)⋊C3 | 2 |
| C4×C3⋊D15 | 3 |
| C3×C4×D15 | 3 |
| C4×(C3⋊D3)⋊C3 | 5 |