Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
154 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 34 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 | semidirect |
| 3. #91954 | C3 | direct (N × H) |
| 12. C5⋊#226 | C2×C3 | semidirect |
| 93. C3×C5 | #984 | semidirect |
| 115. C5 | C3×#984 | semidirect |
| 122. C3 | #91954 | 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 |
| C3×C5⋊#226 | 2 |
| #91954 | 3 |
| C3×#4097 | 3 |
| C3×Dic30 | 4 |
| C3×#984 | 5 |