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 | C23×C3×C5 | C22 |
| hypercenter | C23 | D3×D5 |
| hypocenter | C3×C5 | #121 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#1220 | C2 | semidirect |
| 2. C22×C5×Dic3 | C2 | semidirect |
| 3. C2×C3×C22⋊D5 | C2 | semidirect |
| 4. C2×#1202 | C2 | semidirect |
| 5. Dic3⋊Dic5 | C2 | semidirect |
| 6. #6667 | C2 | semidirect |
| 7. #6665 | C2 | semidirect |
| 23. C2×C22⋊D5 | D3 | semidirect |
| 30. C22×C3×C5 | D4 | semidirect |
| 41. C5×Dic3 | D4 | semidirect |
| 45. C22×Dic3 | D5 | semidirect |
| 80. C22×C5 | #67 | semidirect |
| 99. C3×C5 | #121 | semidirect |
| 105. C22×C3 | D20 | semidirect |
| 113. Dic3 | C22⋊D5 | semidirect |
| 137. C5 | #939 | semidirect |
| 146. C22 | #1202 | semidirect |
| 152. C3 | #4076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1220 | 2 |
| C22×C5×Dic3 | 2 |
| C2×C3×C22⋊D5 | 2 |
| C2×#1202 | 2 |
| Dic3⋊Dic5 | 2 |
| #6667 | 2 |
| #6665 | 2 |
| #4076 | 3 |
| #939 | 5 |