Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
588 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 174 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. Q8×ΓL(1,𝔽16) | C2 | semidirect |
| 3. C3×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 4. #91921 | C2 | semidirect |
| 5. D3×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 6. AGL(1,𝔽5)×D12 | C2 | semidirect |
| 7. #91909 | C2 | semidirect |
| 10. #6821 | C4 | semidirect |
| 11. C5×#239 | C4 | semidirect |
| 15. #6769 | C4 | semidirect |
| 16. #6768 | C4 | semidirect |
| 28. Q8×AGL(1,𝔽5) | D3 | semidirect |
| 39. C3×C5×Q8 | C2×C4 | semidirect |
| 40. D60 | C2×C4 | semidirect |
| 41. C4×D15 | C2×C4 | semidirect |
| 42. C5×D12 | C2×C4 | semidirect |
| 43. C4×C5×D3 | C2×C4 | semidirect |
| 45. C3×Dic10 | C2×C4 | semidirect |
| 46. #1203 | C2×C4 | semidirect |
| 47. #1200 | C2×C4 | semidirect |
| 48. D3×Dic5 | C2×C4 | semidirect |
| 91. #239 | AGL(1,𝔽5) | semidirect |
| 109. C5×Q8 | C4×D3 | semidirect |
| 119. Dic10 | C4×D3 | semidirect |
| 134. C3×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 143. D12 | C2×AGL(1,𝔽5) | semidirect |
| 148. C4×D3 | C2×AGL(1,𝔽5) | semidirect |
| 178. C3×C5 | #520 | semidirect |
| 199. Q8 | D3×AGL(1,𝔽5) | semidirect |
| 219. C5 | #5574 | semidirect |
| 233. C3 | #66266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#239 | 2 |
| Q8×ΓL(1,𝔽16) | 2 |
| C3×Q8×AGL(1,𝔽5) | 2 |
| #91921 | 2 |
| D3×C4⋊AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×D12 | 2 |
| #91909 | 2 |
| #66266 | 3 |
| #5574 | 5 |