Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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, prime radical, cosocle | C22×C3×C5 | C23 |
| Fitting | C2×C3×C4×C5 | C22 |
| hypercenter | C2×C4 | D3×D5 |
| hypocenter | C3×C5 | C4⋊Q8 |
| 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 |
|---|---|---|
| 31. C3×Dic5 | Q8 | semidirect |
| 33. C5×Dic3 | Q8 | semidirect |
| 70. Dic5 | Dic6 | semidirect |
| 78. C3×C5 | C4⋊Q8 | semidirect |
| 86. Dic3 | Dic10 | semidirect |
| 102. C5 | #888 | semidirect |
| 111. C3 | #4034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic30 | 2 |
| C2×#1204 | 2 |
| C5×Dic3⋊C4 | 2 |
| C3×#683 | 2 |
| Dic3⋊Dic5 | 2 |
| #6668 | 2 |
| Dic3×Dic5 | 2 |
| #4034 | 3 |
| #888 | 5 |