Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 162 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. #64153 | C5 | direct (N × H) |
| 21. C5×C3⋊Dic3 | Q8 | semidirect |
| 55. C32×C5 | C4⋊Q8 | semidirect |
| 66. C3⋊Dic3 | C5×Q8 | semidirect |
| 87. C3×C5 | #944 | semidirect |
| 95. C32 | C5×C4⋊Q8 | semidirect |
| 104. C5 | #64153 | direct (N × H) |
| 110. C3 | C5×#944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C2×C5×#634 | 2 |
| C5×#3750 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#944 | 3 |
| #64153 | 5 |