Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
264 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C32×C4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C32×#700 | C2 | semidirect |
| 4. C3×#4010 | C3 | direct (N × H) |
| 6. C32×C5×Q8 | C4 | semidirect |
| 8. C32×D20 | C4 | semidirect |
| 14. C3×C4×AGL(1,𝔽5) | C2×C3 | semidirect |
| 15. C3×#700 | C2×C3 | semidirect |
| 22. #4010 | C32 | direct (N × H) |
| 27. C3×C5×Q8 | C3×C4 | semidirect |
| 29. C3×D20 | C3×C4 | semidirect |
| 38. C4×AGL(1,𝔽5) | C2×C32 | semidirect |
| 39. #700 | C2×C32 | semidirect |
| 40. C32×Q8 | AGL(1,𝔽5) | semidirect |
| 56. C32×C5 | #104 | semidirect |
| 58. C5×Q8 | C32×C4 | semidirect |
| 60. D20 | C32×C4 | semidirect |
| 74. C3×Q8 | C3×AGL(1,𝔽5) | semidirect |
| 93. C3×C5 | C3×#104 | semidirect |
| 103. C32 | #4010 | direct (N × H) |
| 104. Q8 | C32×AGL(1,𝔽5) | semidirect |
| 114. C5 | C32×#104 | semidirect |
| 121. C3 | C3×#4010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#713 | 2 |
| C32×C4×AGL(1,𝔽5) | 2 |
| C32×#700 | 2 |
| C3×#4010 | 3 |
| C32×#104 | 5 |