Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
998 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 234 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 | D3×D15 |
| commutator, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C22×D3×D15 |
| 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×C3×D15 | C2 | semidirect |
| 2. C23×C3×C5×D3 | C2 | semidirect |
| 3. C22×C3⋊Dic15 | C2 | semidirect |
| 4. C2×#67150 | C2 | direct (N × H) |
| 9. C22×C3×D15 | C22 | semidirect |
| 11. C22×C3×C5×D3 | C22 | semidirect |
| 12. C2×C3⋊Dic15 | C22 | semidirect |
| 13. #67150 | C22 | direct (N × H) |
| 16. C23×D15 | D3 | semidirect |
| 17. C23×C5×D3 | D3 | semidirect |
| 24. C22×C32×C5 | D4 | semidirect |
| 27. C2×C3×D15 | C23 | semidirect |
| 29. C2×C3×C5×D3 | C23 | semidirect |
| 30. C3⋊Dic15 | C23 | semidirect |
| 33. C23×C3×D3 | D5 | semidirect |
| 42. C22×D15 | C2×D3 | semidirect |
| 44. C22×C5×D3 | C2×D3 | semidirect |
| 54. C2×C32×C5 | C2×D4 | semidirect |
| 66. C22×C3×D3 | C2×D5 | semidirect |
| 73. C22×C3×C5 | #67 | semidirect |
| 74. C22×C3×C5 | #67 | semidirect |
| 78. C2×D15 | C22×D3 | semidirect |
| 80. C2×C5×D3 | C22×D3 | semidirect |
| 89. C23×D3 | D15 | semidirect |
| 95. C32×C5 | C22×D4 | semidirect |
| 103. C22×C32 | C22⋊D5 | semidirect |
| 108. C2×C3×D3 | C22×D5 | semidirect |
| 114. C2×C3×C5 | C2×#67 | semidirect |
| 115. C2×C3×C5 | C2×#67 | semidirect |
| 131. C22×D3 | C2×D15 | semidirect |
| 139. C22×C5 | #625 | semidirect |
| 144. C2×C32 | C2×C22⋊D5 | semidirect |
| 153. C3×C5 | C22×#67 | semidirect |
| 154. C3×C5 | C22×#67 | semidirect |
| 161. C22×C3 | #1201 | semidirect |
| 162. C22×C3 | #1220 | semidirect |
| 168. C2×D3 | C22×D15 | semidirect |
| 173. C2×C5 | C2×#625 | semidirect |
| 176. C32 | C22×C22⋊D5 | semidirect |
| 188. C2×C3 | C2×#1201 | semidirect |
| 189. C2×C3 | C2×#1220 | semidirect |
| 194. C5 | C22×#625 | semidirect |
| 199. C22 | #67150 | direct (N × H) |
| 203. C3 | C22×#1201 | semidirect |
| 204. C3 | C22×#1220 | semidirect |
| 207. C2 | C2×#67150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D15 | 2 |
| C23×C3×C5×D3 | 2 |
| C22×C3⋊Dic15 | 2 |
| C2×#67150 | 2 |
| C22×#1220 | 3 |
| C22×#1201 | 3 |
| C22×#625 | 5 |