Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
710 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 170 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×C4⋊(C3⋊D15) | C2 | semidirect |
| 2. C2×C3×Dic30 | C2 | semidirect |
| 3. C2×C3×C4×C5×D3 | C2 | semidirect |
| 4. C2×#67152 | C2 | semidirect |
| 5. C2×#67149 | C2 | semidirect |
| 6. #10624197 | C2 | direct (N × H) |
| 12. C4⋊(C3⋊D15) | C22 | semidirect |
| 14. C3×Dic30 | C22 | semidirect |
| 16. C3×C4×C5×D3 | C22 | semidirect |
| 17. #67152 | C22 | semidirect |
| 18. #67149 | C22 | semidirect |
| 27. C2×Dic30 | D3 | semidirect |
| 28. C2×C4×C5×D3 | D3 | semidirect |
| 43. C2×C3×C4×D3 | D5 | semidirect |
| 64. Dic30 | C2×D3 | semidirect |
| 66. C4×C5×D3 | C2×D3 | semidirect |
| 73. C2×C32×C5 | #41 | semidirect |
| 89. C3×C4×D3 | C2×D5 | semidirect |
| 124. C2×C4×D3 | D15 | semidirect |
| 126. C32×C5 | C2×#41 | semidirect |
| 149. C2×C3×C5 | #235 | semidirect |
| 150. C2×C3×C5 | #239 | semidirect |
| 178. C4×D3 | C2×D15 | semidirect |
| 188. C2×C32 | #709 | semidirect |
| 199. C3×C5 | C2×#235 | semidirect |
| 200. C3×C5 | C2×#239 | semidirect |
| 222. C2×C5 | #3799 | semidirect |
| 225. C32 | C2×#709 | semidirect |
| 239. C2×C3 | #6769 | semidirect |
| 240. C2×C3 | #6817 | semidirect |
| 247. C5 | C2×#3799 | semidirect |
| 257. C3 | C2×#6769 | semidirect |
| 258. C3 | C2×#6817 | semidirect |
| 261. C2 | #10624197 | direct (N × H) |
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×C3×Dic30 | 2 |
| C2×C3×C4×C5×D3 | 2 |
| C2×#67152 | 2 |
| C2×#67149 | 2 |
| #10624197 | 2 |
| C2×#6817 | 3 |
| C2×#6769 | 3 |
| C2×#3799 | 5 |