Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 91 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. #67158 | C4 | semidirect |
| 25. C5×C3⋊Dic3 | Q8 | semidirect |
| 80. C32×C5 | C4×Q8 | semidirect |
| 89. C3⋊Dic3 | Dic10 | semidirect |
| 126. C3×C5 | #887 | semidirect |
| 142. C32 | C4×Dic10 | semidirect |
| 155. C5 | #63838 | semidirect |
| 163. C3 | #91324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67158 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×#6712 | 2 |
| #10623832 | 2 |
| #10623828 | 2 |
| #91324 | 3 |
| #63838 | 5 |