Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D15 |
| commutator, cosocle | C2×C3×C5 | C24 |
| Frattini | C2 | C23×D15 |
| Fitting | C22×C3×C4×C5 | C2 |
| socle | C22×C3×C5 | C23 |
| hypercenter | C22×C4 | D15 |
| hypocenter | C3×C5 | C2×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×C4×C5 | C2 | semidirect |
| 2. C2×#1220 | C2 | semidirect |
| 3. #6817 | C2 | direct (N × H) |
| 4. C2×D60 | C2 | semidirect |
| 5. C2×C4×D15 | C2 | semidirect |
| 6. C2×Dic30 | C2 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 13. #1220 | C22 | semidirect |
| 15. D60 | C22 | semidirect |
| 16. C4×D15 | C22 | semidirect |
| 17. Dic30 | C22 | semidirect |
| 19. C22×C4×C5 | D3 | semidirect |
| 33. C22×C3×C4 | D5 | semidirect |
| 43. C2×C4×C5 | C2×D3 | semidirect |
| 51. C2×C3×C5 | #41 | semidirect |
| 58. C2×C3×C4 | C2×D5 | semidirect |
| 77. C22×C4 | D15 | semidirect |
| 78. C3×C5 | C2×#41 | semidirect |
| 88. C2×C5 | #235 | semidirect |
| 100. C2×C4 | C2×D15 | semidirect |
| 102. C2×C3 | #709 | semidirect |
| 105. C5 | C2×#235 | semidirect |
| 114. C3 | C2×#709 | semidirect |
| 117. C2 | #6817 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C5 | 2 |
| C2×#1220 | 2 |
| #6817 | 2 |
| C2×D60 | 2 |
| C2×C4×D15 | 2 |
| C2×Dic30 | 2 |
| C2×#709 | 3 |
| C2×#235 | 5 |