Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
132 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×A4 |
| commutator, socle, cosocle | C23×C5 | C22×C3 |
| Fitting | C24×C5 | C2×C3 |
| hypercenter | C22 | D5×A4 |
| hypocenter | C22×C5 | C3×D4 |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×A4 | C2 | semidirect |
| 2. C2×D5×A4 | C2 | semidirect |
| 3. A4×Dic5 | C2 | semidirect |
| 4. C22×C22⋊D5 | C3 | semidirect |
| 10. C24×C5 | C2×C3 | semidirect |
| 11. C23×D5 | C2×C3 | semidirect |
| 16. C22×Dic5 | C2×C3 | semidirect |
| 19. C5×A4 | D4 | semidirect |
| 22. C22×A4 | D5 | semidirect |
| 37. C22⋊D5 | A4 | direct (N × H) |
| 55. C22×C5 | C3×D4 | semidirect |
| 56. C22×C5 | C2×A4 | semidirect |
| 62. C2×D5 | C2×A4 | semidirect |
| 64. Dic5 | C2×A4 | semidirect |
| 66. C24 | C3×D5 | semidirect |
| 75. A4 | C22⋊D5 | direct (N × H) |
| 103. C5 | D4×A4 | semidirect |
| 117. C22 | C3×C22⋊D5 | semidirect |
| 118. C22 | D5×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×A4 | 2 |
| C2×D5×A4 | 2 |
| A4×Dic5 | 2 |
| C22×C22⋊D5 | 3 |
| C3×C22⋊D5 | 4 |
| D4×A4 | 5 |