Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
1078 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C3⋊D3)⋊D5 |
| commutator, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| Fitting, socle | C23×C32×C5 | C22 |
| hypocenter | C32×C5 | C22×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C5×C3⋊D3 | C2 | semidirect |
| 2. C23×C3×D15 | C2 | semidirect |
| 3. C22×C3×Dic15 | C2 | semidirect |
| 4. C2×#67156 | C2 | direct (N × H) |
| 9. C22×C5×C3⋊D3 | C22 | semidirect |
| 11. C22×C3×D15 | C22 | semidirect |
| 12. C2×C3×Dic15 | C22 | semidirect |
| 13. #67156 | C22 | direct (N × H) |
| 15. C23×D15 | D3 | semidirect |
| 20. C22×Dic15 | D3 | semidirect |
| 24. C22×C32×C5 | D4 | semidirect |
| 27. C2×C5×C3⋊D3 | C23 | semidirect |
| 29. C2×C3×D15 | C23 | semidirect |
| 30. C3×Dic15 | C23 | semidirect |
| 32. C23×C3⋊D3 | D5 | semidirect |
| 40. C22×D15 | C2×D3 | semidirect |
| 49. C2×Dic15 | C2×D3 | semidirect |
| 55. C2×C32×C5 | C2×D4 | semidirect |
| 65. C22×C3⋊D3 | C2×D5 | semidirect |
| 72. C22×C3×C5 | D12 | semidirect |
| 73. C22×C3×C5 | #67 | semidirect |
| 77. C2×D15 | C22×D3 | semidirect |
| 86. Dic15 | C22×D3 | semidirect |
| 97. C32×C5 | C22×D4 | semidirect |
| 105. C22×C32 | C22⋊D5 | semidirect |
| 108. C2×C3⋊D3 | C22×D5 | semidirect |
| 115. C2×C3×C5 | C2×D12 | semidirect |
| 116. C2×C3×C5 | C2×#67 | semidirect |
| 143. C22×C5 | #626 | semidirect |
| 148. C2×C32 | C2×C22⋊D5 | semidirect |
| 157. C3×C5 | C22×D12 | semidirect |
| 158. C3×C5 | C22×#67 | semidirect |
| 163. C22×C3 | #1201 | semidirect |
| 164. C22×C3 | #1203 | semidirect |
| 178. C2×C5 | C2×#626 | semidirect |
| 181. C32 | C22×C22⋊D5 | semidirect |
| 192. C2×C3 | C2×#1201 | semidirect |
| 193. C2×C3 | C2×#1203 | semidirect |
| 200. C5 | C22×#626 | semidirect |
| 205. C22 | #67156 | direct (N × H) |
| 209. C3 | C22×#1201 | semidirect |
| 210. C3 | C22×#1203 | semidirect |
| 213. C2 | C2×#67156 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C3⋊D3 | 2 |
| C23×C3×D15 | 2 |
| C22×C3×Dic15 | 2 |
| C2×#67156 | 2 |
| C22×#1203 | 3 |
| C22×#1201 | 3 |
| C22×#626 | 5 |