Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
678 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C3⋊D3)⋊D5 |
| commutator, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| Fitting, socle, prime radical | C23×C32×C5 | C22 |
| hypocenter | C32×C5 | C22×Q8 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#67158 | C2 | direct (N × H) |
| 8. #67158 | C22 | direct (N × H) |
| 15. C22×C32×C5 | Q8 | semidirect |
| 31. C2×C32×C5 | C2×Q8 | semidirect |
| 42. C22×C3×C5 | Dic6 | semidirect |
| 53. C32×C5 | C22×Q8 | semidirect |
| 58. C22×C32 | Dic10 | semidirect |
| 65. C2×C3×C5 | C2×Dic6 | semidirect |
| 74. C22×C5 | #627 | semidirect |
| 78. C2×C32 | C2×Dic10 | semidirect |
| 84. C3×C5 | C22×Dic6 | semidirect |
| 87. C22×C3 | #1204 | semidirect |
| 93. C2×C5 | C2×#627 | semidirect |
| 95. C32 | C22×Dic10 | semidirect |
| 102. C2×C3 | C2×#1204 | semidirect |
| 104. C5 | C22×#627 | semidirect |
| 105. C22 | #67158 | direct (N × H) |
| 110. C3 | C22×#1204 | semidirect |
| 111. C2 | C2×#67158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C22×C3×Dic15 | 2 |
| C2×#67158 | 2 |
| C22×#1204 | 3 |
| C22×#627 | 5 |