Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 54 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 | #120 |
| 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. C22×D3×D5 | C2 | semidirect |
| 2. C2×#1220 | C2 | semidirect |
| 3. C2×C5×#67 | C2 | semidirect |
| 4. C2×C3×C22⋊D5 | C2 | semidirect |
| 5. #6667 | C2 | semidirect |
| 6. (C2×D3)⋊Dic5 | C2 | semidirect |
| 7. #6665 | C2 | semidirect |
| 9. C23×C3×C5 | C22 | semidirect |
| 17. C2×Dic15 | C22 | semidirect |
| 19. C2×C5×Dic3 | C22 | semidirect |
| 21. C2×C3×Dic5 | C22 | semidirect |
| 26. C2×C22⋊D5 | D3 | semidirect |
| 36. C2×D15 | D4 | semidirect |
| 39. C2×C5×D3 | D4 | semidirect |
| 42. C2×C3×D5 | D4 | semidirect |
| 50. C2×#67 | D5 | semidirect |
| 55. C23×C5 | C2×D3 | semidirect |
| 66. C2×Dic5 | C2×D3 | semidirect |
| 76. C23×C3 | C2×D5 | semidirect |
| 87. C2×Dic3 | C2×D5 | semidirect |
| 101. C2×D5 | #67 | semidirect |
| 112. C3×C5 | #120 | semidirect |
| 126. C2×D3 | C22⋊D5 | semidirect |
| 143. C23 | D3×D5 | semidirect |
| 157. C5 | #937 | semidirect |
| 175. C3 | #4083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D5 | 2 |
| C2×#1220 | 2 |
| C2×C5×#67 | 2 |
| C2×C3×C22⋊D5 | 2 |
| #6667 | 2 |
| (C2×D3)⋊Dic5 | 2 |
| #6665 | 2 |
| #4083 | 3 |
| #937 | 5 |