Finite Group DatabasebetaFinite Group Databasebeta← C2×C5×C4⋊(C3⋊Dic3) #13088108
Order 1440.
552 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 346 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×C4⋊(C3⋊Dic3) | C2 | direct (N × H) |
| 6. C2×C32×C4×C5 | C4 | semidirect |
| 10. C2×C4⋊(C3⋊Dic3) | C5 | direct (N × H) |
| 18. C32×C4×C5 | C2×C4 | semidirect |
| 23. C4⋊(C3⋊Dic3) | C2×C5 | direct (N × H) |
| 25. C2×C3×C4×C5 | Dic3 | semidirect |
| 30. C2×C32×C5 | C4⋊C4 | semidirect |
| 38. C2×C32×C4 | C4×C5 | semidirect |
| 46. C3×C4×C5 | C2×Dic3 | semidirect |
| 51. C32×C5 | C2×C4⋊C4 | semidirect |
| 55. C2×C4×C5 | C3⋊Dic3 | semidirect |
| 61. C32×C4 | C2×C4×C5 | semidirect |
| 64. C2×C3×C5 | C4⋊Dic3 | semidirect |
| 69. C2×C3×C4 | C5×Dic3 | semidirect |
| 78. C4×C5 | C2×C3⋊Dic3 | semidirect |
| 79. C2×C32 | C5×C4⋊C4 | semidirect |
| 86. C3×C5 | C2×C4⋊Dic3 | semidirect |
| 91. C3×C4 | C2×C5×Dic3 | semidirect |
| 93. C2×C5 | C4⋊(C3⋊Dic3) | direct (N × H) |
| 97. C32 | C2×C5×C4⋊C4 | semidirect |
| 101. C2×C4 | C5×C3⋊Dic3 | semidirect |
| 103. C2×C3 | C5×C4⋊Dic3 | semidirect |
| 107. C5 | C2×C4⋊(C3⋊Dic3) | direct (N × H) |
| 113. C4 | C2×C5×C3⋊Dic3 | semidirect |
| 114. C3 | C2×C5×C4⋊Dic3 | semidirect |
| 115. C2 | C5×C4⋊(C3⋊Dic3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C22×C5×C3⋊Dic3 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C2×C5×C4⋊Dic3 | 3 |
| C2×C4⋊(C3⋊Dic3) | 5 |