Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×C32×C5×D4 | C2 | semidirect |
| 2. C2×C3×#1220 | C2 | semidirect |
| 3. C2×C3×C4×D15 | C2 | semidirect |
| 4. C3×#6719 | C2 | semidirect |
| 5. C3×C4⋊Dic15 | C2 | semidirect |
| 6. #91827 | C3 | direct (N × H) |
| 18. C2×C3×C5×D4 | D3 | semidirect |
| 19. C2×C3×C5×D4 | C2×C3 | semidirect |
| 20. C2×#1220 | C2×C3 | semidirect |
| 21. C2×C4×D15 | C2×C3 | semidirect |
| 24. #6719 | C2×C3 | semidirect |
| 25. C4⋊Dic15 | C2×C3 | semidirect |
| 34. C2×C3×D15 | D4 | semidirect |
| 35. C32×C4×C5 | D4 | semidirect |
| 39. C2×C32×D4 | D5 | semidirect |
| 70. C2×C5×D4 | C3×D3 | semidirect |
| 97. C2×D15 | C3×D4 | semidirect |
| 102. C3×C4×C5 | #67 | semidirect |
| 103. C3×C4×C5 | C3×D4 | semidirect |
| 110. C2×C3×D4 | C3×D5 | semidirect |
| 111. C2×C3×D4 | D15 | semidirect |
| 119. C32×C5 | #121 | semidirect |
| 135. C32×C4 | C22⋊D5 | semidirect |
| 179. C4×C5 | C3×#67 | semidirect |
| 188. C2×D4 | C3×D15 | semidirect |
| 193. C3×C5 | #938 | semidirect |
| 194. C3×C5 | C3×#121 | semidirect |
| 216. C3×C4 | C3×C22⋊D5 | semidirect |
| 217. C3×C4 | #1220 | semidirect |
| 225. C32 | #4084 | semidirect |
| 248. C5 | C3×#938 | semidirect |
| 258. C4 | C3×#1220 | semidirect |
| 260. C3 | C3×#4084 | semidirect |
| 261. C3 | #91827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C3×#1220 | 2 |
| C2×C3×C4×D15 | 2 |
| C3×#6719 | 2 |
| C3×C4⋊Dic15 | 2 |
| #91827 | 3 |
| C3×#4084 | 3 |
| C3×#938 | 5 |