Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 2. C2×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C5×D3×C4⋊C4 | C2 | semidirect |
| 4. C3×C5×#103 | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 6. C5×#821 | C2 | semidirect |
| 7. C5×#809 | C2 | semidirect |
| 11. C5×#239 | C4 | semidirect |
| 23. #4803 | C5 | direct (N × H) |
| 28. C5×#103 | D3 | semidirect |
| 34. C3×C5×Q8 | C2×C4 | semidirect |
| 42. C5×D12 | C2×C4 | semidirect |
| 50. C2×ΓL(1,𝔽25) | C2×C5 | semidirect |
| 51. D3×C4⋊C4 | C2×C5 | semidirect |
| 52. C3×#103 | C2×C5 | semidirect |
| 53. #835 | C2×C5 | semidirect |
| 54. #821 | C2×C5 | semidirect |
| 55. #809 | C2×C5 | semidirect |
| 86. #239 | C4×C5 | semidirect |
| 101. C5×Q8 | C4×D3 | semidirect |
| 120. #103 | C5×D3 | semidirect |
| 131. C3×Q8 | C2×C4×C5 | semidirect |
| 139. D12 | C2×C4×C5 | semidirect |
| 173. C3×C5 | #417 | semidirect |
| 195. Q8 | C4×C5×D3 | semidirect |
| 215. C5 | #4803 | direct (N × H) |
| 229. C3 | C5×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#239 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| C5×D3×C4⋊C4 | 2 |
| C3×C5×#103 | 2 |
| C5×#835 | 2 |
| C5×#821 | 2 |
| C5×#809 | 2 |
| C5×#417 | 3 |
| #4803 | 5 |