Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
388 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 17. Dic3⋊AGL(1,𝔽5) | C4 | semidirect |
| 19. Dic3×AGL(1,𝔽5) | C4 | semidirect |
| 20. #6712 | C4 | semidirect |
| 21. C5×Dic3⋊C4 | C4 | semidirect |
| 22. Dic3⋊Dic5 | C4 | semidirect |
| 23. #6669 | C4 | semidirect |
| 88. ΓL(1,𝔽16) | C4⋊C4 | semidirect |
| 93. Dic15 | C42 | semidirect |
| 96. C5×Dic3 | C42 | semidirect |
| 108. Dic3⋊C4 | AGL(1,𝔽5) | semidirect |
| 208. C3×C5 | C4×C4⋊C4 | semidirect |
| 225. Dic3 | C4×AGL(1,𝔽5) | semidirect |
| 265. C5 | #4649 | semidirect |
| 283. C3 | C4⋊C4×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×ΓL(1,𝔽16) | 2 |
| C2×Dic3⋊AGL(1,𝔽5) | 2 |
| C2×Dic3×AGL(1,𝔽5) | 2 |
| D5×Dic3⋊C4 | 2 |
| C3×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic3 | 2 |
| C4⋊C4×AGL(1,𝔽5) | 3 |
| #4649 | 5 |