Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
170 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 42 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. C3×C5⋊#226 | C2 | direct (N × H) |
| 3. C2×C5⋊#226 | C3 | direct (N × H) |
| 12. C5⋊#226 | C2×C3 | direct (N × H) |
| 72. C2×C3×C5 | #226 | semidirect |
| 97. C3×C5 | C2×#226 | semidirect |
| 105. C2×C5 | C3×#226 | semidirect |
| 119. C2×C3 | C5⋊#226 | direct (N × H) |
| 121. C5 | C2×C3×#226 | semidirect |
| 128. C3 | C2×C5⋊#226 | direct (N × H) |
| 129. C2 | C3×C5⋊#226 | direct (N × H) |
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 |
| C3×C5⋊#226 | 2 |
| C2×C5⋊#226 | 3 |
| C2×C3×#689 | 3 |
| C2×C3×Dic15 | 4 |
| C2×C3×#226 | 5 |