Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
350 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×C5×#627 | C2 | semidirect |
| 4. C5×#3724 | C2 | semidirect |
| 5. C5×Dic3⋊Dic3 | C2 | semidirect |
| 14. #63982 | C5 | direct (N × H) |
| 25. C22×C32×C5 | Q8 | semidirect |
| 33. C2×#627 | C2×C5 | semidirect |
| 35. #3724 | C2×C5 | semidirect |
| 36. Dic3⋊Dic3 | C2×C5 | semidirect |
| 73. C22×C3×C5 | Dic6 | semidirect |
| 91. C32×C5 | C22⋊Q8 | semidirect |
| 101. C22×C32 | C5×Q8 | semidirect |
| 131. C22×C5 | #627 | semidirect |
| 147. C3×C5 | #878 | semidirect |
| 154. C22×C3 | C5×Dic6 | semidirect |
| 168. C32 | C5×C22⋊Q8 | semidirect |
| 184. C5 | #63982 | direct (N × H) |
| 187. C22 | C5×#627 | semidirect |
| 194. C3 | C5×#878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C2×C5×#627 | 2 |
| C3×C5×#217 | 2 |
| C5×#3724 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×#878 | 3 |
| #63982 | 5 |