Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
182 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 90 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. C4⋊(C3⋊#170) | C3 | direct (N × H) |
| 16. C32×C4×C5 | C8 | semidirect |
| 49. C3×C4×C5 | C3⋊C8 | semidirect |
| 50. C3×C4×C5 | C3×C8 | semidirect |
| 65. C32×C5 | C4⋊C8 | semidirect |
| 74. C32×C4 | #170 | semidirect |
| 97. C4×C5 | C3×C3⋊C8 | semidirect |
| 107. C3×C5 | C4⋊(C3⋊C8) | semidirect |
| 108. C3×C5 | C3×C4⋊C8 | semidirect |
| 122. C3×C4 | C3×#170 | semidirect |
| 123. C3×C4 | C3⋊#170 | semidirect |
| 127. C32 | C4⋊#170 | semidirect |
| 141. C5 | C3×C4⋊(C3⋊C8) | semidirect |
| 146. C4 | C3×C3⋊#170 | semidirect |
| 148. C3 | C3×C4⋊#170 | semidirect |
| 149. C3 | C4⋊(C3⋊#170) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#170 | 2 |
| C32×C4×Dic5 | 2 |
| C4⋊(C3⋊#170) | 3 |
| C3×C4⋊#170 | 3 |
| C3×C4⋊(C3⋊C8) | 5 |