Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
156 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 5. C3×C5×SL(2,𝔽3) | C4 | semidirect |
| 6. C3⋊#859 | C5 | direct (N × H) |
| 16. C3×C5×Q8 | Dic3 | semidirect |
| 20. C5×SL(2,𝔽3) | Dic3 | semidirect |
| 31. C3×SL(2,𝔽3) | C4×C5 | semidirect |
| 44. C5×Q8 | C3⋊Dic3 | semidirect |
| 58. C3×Q8 | C5×Dic3 | semidirect |
| 62. SL(2,𝔽3) | C5×Dic3 | semidirect |
| 75. C3×C5 | #859 | semidirect |
| 87. Q8 | C5×C3⋊Dic3 | semidirect |
| 97. C5 | C3⋊#859 | direct (N × H) |
| 103. C3 | C5×#859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SL(2,𝔽3) | 2 |
| C5×#859 | 3 |
| C5×#835 | 3 |
| C2×C5×C3⋊Dic3 | 4 |
| C3⋊#859 | 5 |