Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
574 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×(C3⋊D3)⋊D5 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | #120 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×(C3⋊D3)⋊D5 | C2 | semidirect |
| 2. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×#67156 | C2 | semidirect |
| 4. C3×#6714 | C2 | semidirect |
| 5. #10623830 | C2 | semidirect |
| 8. C22×C5×C3⋊D3 | C22 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 14. C2×C3×Dic15 | C22 | semidirect |
| 22. #6714 | D3 | semidirect |
| 29. C2×C5×C3⋊D3 | D4 | semidirect |
| 32. C2×C3×D15 | D4 | semidirect |
| 38. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 52. C2×C3×C4×C5 | C2×D3 | semidirect |
| 53. C2×Dic15 | C2×D3 | semidirect |
| 71. C22×C3⋊D3 | C2×D5 | semidirect |
| 75. C2×C32×C4 | C2×D5 | semidirect |
| 83. C2×D15 | D12 | semidirect |
| 110. C32×C5 | #120 | semidirect |
| 117. C2×C4×C5 | D32 | semidirect |
| 124. C2×C3⋊D3 | C22⋊D5 | semidirect |
| 154. C2×C3×C4 | D3×D5 | semidirect |
| 182. C3×C5 | #882 | semidirect |
| 211. C32 | #4083 | semidirect |
| 220. C2×C4 | (C3⋊D3)⋊D5 | semidirect |
| 232. C5 | #63923 | semidirect |
| 245. C3 | #91475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊D3)⋊D5 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×#67156 | 2 |
| C3×#6714 | 2 |
| #10623830 | 2 |
| #91475 | 3 |
| #63923 | 5 |