Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. C3×C4⋊Dic15 | C2 | semidirect |
| 4. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 5. #10623815 | C2 | semidirect |
| 11. C4×C3⋊D15 | C4 | semidirect |
| 22. C4⋊Dic15 | D3 | semidirect |
| 24. C5×C4⋊Dic3 | D3 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 32. C3⋊Dic15 | C2×C4 | semidirect |
| 39. C3×C4⋊Dic3 | D5 | semidirect |
| 64. C3⋊D15 | C4⋊C4 | semidirect |
| 91. C3×C4×C5 | C4×D3 | semidirect |
| 92. C3×C4×C5 | C4×D3 | semidirect |
| 107. C4⋊Dic3 | D15 | semidirect |
| 110. C32×C5 | C2×C4⋊C4 | semidirect |
| 122. C32×C4 | C4×D5 | semidirect |
| 162. C4×C5 | #624 | semidirect |
| 175. C3×C5 | D3×C4⋊C4 | semidirect |
| 176. C3×C5 | D3×C4⋊C4 | semidirect |
| 192. C3×C4 | #1200 | semidirect |
| 193. C3×C4 | C4×D15 | semidirect |
| 203. C32 | D5×C4⋊C4 | semidirect |
| 223. C5 | #63900 | semidirect |
| 231. C4 | #67149 | semidirect |
| 233. C3 | #91437 | semidirect |
| 234. C3 | C4⋊C4×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D15 | 2 |
| C2×#67149 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| #10623815 | 2 |
| C4⋊C4×D15 | 3 |
| #91437 | 3 |
| #63900 | 5 |