Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 148 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, prime radical | C23×C3×C5 | C22 |
| hypercenter | C23 | D3×D5 |
| hypocenter | C3×C5 | C22⋊Q8 |
| 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 |
|---|---|---|
| 2. C2×#1204 | C2 | semidirect |
| 5. Dic3⋊Dic5 | C2 | semidirect |
| 6. #6669 | C2 | semidirect |
| 7. #6668 | C2 | semidirect |
| 28. C22×C3×C5 | Q8 | semidirect |
| 68. C22×C5 | Dic6 | semidirect |
| 83. C3×C5 | C22⋊Q8 | semidirect |
| 86. C22×C3 | Dic10 | semidirect |
| 111. C5 | #924 | semidirect |
| 114. C22 | #1204 | semidirect |
| 122. C3 | #4024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic5 | 2 |
| C2×#1204 | 2 |
| #6719 | 2 |
| C5×#217 | 2 |
| Dic3⋊Dic5 | 2 |
| #6669 | 2 |
| #6668 | 2 |
| #4024 | 3 |
| #924 | 5 |