Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #127 |
| 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. C2×C3×D60 | C2 | semidirect |
| 2. C2×#67157 | C2 | semidirect |
| 3. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 11. C2×D60 | D3 | semidirect |
| 19. C32×C4×C5 | D4 | semidirect |
| 20. C5×C3⋊Dic3 | D4 | semidirect |
| 24. C4×C3⋊Dic3 | D5 | semidirect |
| 53. C3×C4×C5 | #67 | semidirect |
| 61. C32×C5 | #127 | semidirect |
| 70. C32×C4 | D20 | semidirect |
| 71. C3⋊Dic3 | D20 | semidirect |
| 92. C4×C5 | #625 | semidirect |
| 100. C3×C5 | #940 | semidirect |
| 108. C3×C4 | #1202 | semidirect |
| 114. C32 | #4020 | semidirect |
| 126. C5 | #63914 | semidirect |
| 131. C4 | #67157 | semidirect |
| 133. C3 | #91458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×#67157 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| #91458 | 3 |
| #63914 | 5 |