Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 1. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×C5×#625 | C2 | semidirect |
| 4. C5×#3724 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 15. #63980 | C5 | direct (N × H) |
| 18. C2×C5×#67 | D3 | semidirect |
| 26. C22×C32×C5 | D4 | semidirect |
| 32. C5×C3⋊Dic3 | D4 | semidirect |
| 35. C22×C3⋊Dic3 | C2×C5 | semidirect |
| 36. C2×C3×#67 | C2×C5 | semidirect |
| 37. C2×#625 | C2×C5 | semidirect |
| 38. #3724 | C2×C5 | semidirect |
| 39. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 83. C22×C3×C5 | #67 | semidirect |
| 96. C2×#67 | C5×D3 | semidirect |
| 102. C32×C5 | #121 | semidirect |
| 113. C22×C32 | C5×D4 | semidirect |
| 119. C3⋊Dic3 | C5×D4 | semidirect |
| 152. C22×C5 | #625 | semidirect |
| 168. C3×C5 | #939 | semidirect |
| 178. C22×C3 | C5×#67 | semidirect |
| 194. C32 | C5×#121 | semidirect |
| 213. C5 | #63980 | direct (N × H) |
| 219. C22 | C5×#625 | semidirect |
| 225. C3 | C5×#939 | 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×C3×C5×#67 | 2 |
| C2×C5×#625 | 2 |
| C5×#3724 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#939 | 3 |
| #63980 | 5 |