Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
262 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. C5×#3718 | C2 | direct (N × H) |
| 10. C2×#3718 | C5 | direct (N × H) |
| 23. #3718 | C2×C5 | direct (N × H) |
| 35. C2×C32×C5 | Q16 | semidirect |
| 58. C32×C5 | C2×Q16 | semidirect |
| 71. C2×C3×C5 | #216 | semidirect |
| 87. C2×C32 | C5×Q16 | semidirect |
| 93. C3×C5 | C2×#216 | semidirect |
| 102. C2×C5 | #3718 | direct (N × H) |
| 104. C32 | C2×C5×Q16 | semidirect |
| 112. C2×C3 | C5×#216 | semidirect |
| 114. C5 | C2×#3718 | direct (N × H) |
| 120. C3 | C2×C5×#216 | semidirect |
| 121. C2 | C5×#3718 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Dic6 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| C5×#3718 | 2 |
| C2×C5×#216 | 3 |
| C2×#3718 | 5 |