Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
388 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 12. C4⋊ΓL(1,𝔽16) | C4 | semidirect |
| 14. C4×ΓL(1,𝔽16) | C4 | semidirect |
| 15. C3×C5×C4⋊C4 | C4 | semidirect |
| 16. C3×C4⋊Dic5 | C4 | semidirect |
| 17. C3×#683 | C4 | semidirect |
| 55. C5×C4⋊C4 | Dic3 | semidirect |
| 56. C4⋊Dic5 | Dic3 | semidirect |
| 57. #683 | Dic3 | semidirect |
| 68. ΓL(1,𝔽16) | C4⋊C4 | direct (N × H) |
| 70. C3×C4×C5 | C42 | semidirect |
| 72. C3×Dic5 | C42 | semidirect |
| 80. C3×C4⋊C4 | AGL(1,𝔽5) | semidirect |
| 143. C4×C5 | C4×Dic3 | semidirect |
| 145. Dic5 | C4×Dic3 | semidirect |
| 154. C4⋊C4 | ΓL(1,𝔽16) | direct (N × H) |
| 157. C3×C5 | C4×C4⋊C4 | semidirect |
| 168. C3×C4 | C4×AGL(1,𝔽5) | semidirect |
| 204. C5 | Dic3×C4⋊C4 | semidirect |
| 218. C4 | C4×ΓL(1,𝔽16) | semidirect |
| 219. 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×C4×ΓL(1,𝔽16) | 2 |
| C3×D5×C4⋊C4 | 2 |
| #91235 | 2 |
| C4⋊C4×AGL(1,𝔽5) | 3 |
| Dic3×C4⋊C4 | 5 |