Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
106 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 32 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. C5×GU(2,𝔽3) | C3 | direct (N × H) |
| 4. C3×C5×SL(2,𝔽3) | C4 | semidirect |
| 6. C3×GU(2,𝔽3) | C5 | direct (N × H) |
| 20. C5×SL(2,𝔽3) | C3×C4 | semidirect |
| 23. GU(2,𝔽3) | C3×C5 | direct (N × H) |
| 29. C3×SL(2,𝔽3) | C4×C5 | semidirect |
| 59. SL(2,𝔽3) | C3×C4×C5 | semidirect |
| 72. C3×C5 | GU(2,𝔽3) | direct (N × H) |
| 91. C5 | C3×GU(2,𝔽3) | direct (N × H) |
| 98. C3 | C5×GU(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41⋊C3 | 2 |
| C5×GU(2,𝔽3) | 3 |
| C3×C5×#104 | 3 |
| C3×C5×C3⋊C8 | 4 |
| C3×GU(2,𝔽3) | 5 |