Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
252 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 122 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. C3×C5×C4⋊C8 | C2 | semidirect |
| 4. C5×Dic3⋊C8 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 17. #4837 | C5 | direct (N × H) |
| 22. C5×C4⋊C8 | D3 | semidirect |
| 38. C3×C4⋊C8 | C2×C5 | semidirect |
| 39. Dic3⋊C8 | C2×C5 | semidirect |
| 40. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 57. C3×C4×C5 | M16 | semidirect |
| 62. C5×Dic3 | M16 | semidirect |
| 90. C4⋊C8 | C5×D3 | semidirect |
| 116. C4×C5 | ΓL(1,𝔽25) | semidirect |
| 129. C3×C5 | #423 | semidirect |
| 135. C3×C4 | C5×M16 | semidirect |
| 140. Dic3 | C5×M16 | semidirect |
| 162. C5 | #4837 | direct (N × H) |
| 171. C4 | C5×ΓL(1,𝔽25) | semidirect |
| 174. C3 | C5×#423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×ΓL(1,𝔽25) | 2 |
| C42×C5×D3 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C5×Dic3⋊C8 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#423 | 3 |
| #4837 | 5 |