Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
152 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C23 | D3×D5 |
| commutator | C2×C3×C5 | C42 |
| Fitting, socle, prime radical, cosocle | C23×C3×C5 | C22 |
| hypocenter | C3×C5 | #95 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C2×Dic15 | C4 | semidirect |
| 11. C2×C5×Dic3 | C4 | semidirect |
| 14. C2×C3×Dic5 | C4 | semidirect |
| 41. C2×Dic5 | Dic3 | semidirect |
| 59. C2×Dic3 | Dic5 | semidirect |
| 73. C3×C5 | #95 | semidirect |
| 108. C5 | C3⋊#95 | semidirect |
| 119. C3 | #3963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic15 | 2 |
| C22×C5×Dic3 | 2 |
| C22×C3×Dic5 | 2 |
| #3963 | 3 |
| C3⋊#95 | 5 |