Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
276 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 157 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) | C2 | direct (N × H) |
| 17. C2×C3×C4×C5 | C8 | semidirect |
| 41. C3×C4×C5 | C2×C8 | semidirect |
| 54. C2×C4×C5 | C3⋊C8 | semidirect |
| 66. C2×C3×C5 | C4⋊C8 | semidirect |
| 77. C2×C3×C4 | #170 | semidirect |
| 84. C4×C5 | C2×C3⋊C8 | semidirect |
| 96. C3×C5 | C2×C4⋊C8 | semidirect |
| 105. C3×C4 | C2×#170 | semidirect |
| 106. C2×C5 | C4⋊(C3⋊C8) | semidirect |
| 117. C2×C4 | C3⋊#170 | semidirect |
| 120. C2×C3 | C4⋊#170 | semidirect |
| 124. C5 | C2×C4⋊(C3⋊C8) | semidirect |
| 133. C4 | C2×C3⋊#170 | semidirect |
| 134. C3 | C2×C4⋊#170 | semidirect |
| 135. C2 | 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 |
|---|---|
| C22×C3⋊#170 | 2 |
| C2×C3×C4×Dic5 | 2 |
| C4⋊(C3⋊#170) | 2 |
| C2×C4⋊#170 | 3 |
| C2×C4⋊(C3⋊C8) | 5 |