Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
400 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 16. #5570 | C5 | direct (N × H) |
| 22. C3×C5×Q8 | Q8 | semidirect |
| 60. C5×Q8 | Dic6 | semidirect |
| 74. C3×Q8 | C5×Q8 | semidirect |
| 96. C3×C5 | #557 | semidirect |
| 107. Q8 | C5×Dic6 | semidirect |
| 116. C5 | #5570 | direct (N × H) |
| 123. C3 | C5×#557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C5×Q8×Dic3 | 2 |
| C5×#890 | 2 |
| C5×#869 | 2 |
| C4×C5×Dic6 | 2 |
| C5×#557 | 3 |
| #5570 | 5 |