Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 6. Q16×AGL(1,𝔽5) | C3 | direct (N × H) |
| 13. C3×C5×Q16 | C4 | semidirect |
| 14. C3×#689 | C4 | semidirect |
| 15. C3×Dic20 | C4 | semidirect |
| 45. C5×Q16 | C3×C4 | semidirect |
| 46. #689 | C3×C4 | semidirect |
| 47. Dic20 | C3×C4 | semidirect |
| 53. C3×AGL(1,𝔽5) | Q16 | direct (N × H) |
| 61. C3×Q16 | AGL(1,𝔽5) | direct (N × H) |
| 101. AGL(1,𝔽5) | C3×Q16 | direct (N × H) |
| 109. Q16 | C3×AGL(1,𝔽5) | direct (N × H) |
| 116. C3×C5 | C4×Q16 | semidirect |
| 142. C5 | C3×C4×Q16 | semidirect |
| 151. C3 | Q16×AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×AGL(1,𝔽5) | 2 |
| C3×D5×Q16 | 2 |
| C3×#4009 | 2 |
| C3×#3994 | 2 |
| C3×C8×AGL(1,𝔽5) | 2 |
| Q16×AGL(1,𝔽5) | 3 |
| C3×C4×Q16 | 5 |