Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 56 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×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C23 |
| Fitting | C2×C3×C4×C5 | C22 |
| hypercenter | C2×C4 | D3×D5 |
| hypocenter | C3×C5 | #121 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D60 | C2 | semidirect |
| 2. C2×C3×C4×D5 | C2 | semidirect |
| 3. C2×#1202 | C2 | semidirect |
| 4. C5×C4⋊Dic3 | C2 | semidirect |
| 5. #6667 | C2 | semidirect |
| 18. C2×C4×D5 | D3 | semidirect |
| 27. C2×C3×D5 | D4 | semidirect |
| 28. C3×C4×C5 | D4 | semidirect |
| 35. C4⋊Dic3 | D5 | semidirect |
| 64. C2×D5 | D12 | semidirect |
| 66. C4×C5 | #67 | semidirect |
| 73. C3×C5 | #121 | semidirect |
| 82. C3×C4 | D20 | semidirect |
| 102. C5 | #930 | semidirect |
| 112. C4 | #1202 | semidirect |
| 113. C3 | #4041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D60 | 2 |
| C2×C3×C4×D5 | 2 |
| C2×#1202 | 2 |
| C5×C4⋊Dic3 | 2 |
| #6667 | 2 |
| #4041 | 3 |
| #930 | 5 |