Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
184 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. Dic3⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 11. C2×Dic15 | C4 | semidirect |
| 12. C2×C5×Dic3 | C4 | semidirect |
| 13. D5×Dic3 | C4 | semidirect |
| 27. Dic15 | C2×C4 | semidirect |
| 28. C5×Dic3 | C2×C4 | semidirect |
| 43. C2×C3×C5 | C4⋊C4 | semidirect |
| 45. C3×D5 | C4⋊C4 | semidirect |
| 56. C2×Dic3 | AGL(1,𝔽5) | semidirect |
| 70. C3×C5 | C2×C4⋊C4 | semidirect |
| 79. Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 80. C2×C5 | Dic3⋊C4 | semidirect |
| 82. D5 | Dic3⋊C4 | semidirect |
| 97. C2×C3 | C4⋊AGL(1,𝔽5) | semidirect |
| 99. C5 | C2×Dic3⋊C4 | semidirect |
| 109. C3 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 113. C2 | Dic3⋊AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽16) | 2 |
| C22×C3×AGL(1,𝔽5) | 2 |
| C2×D5×Dic3 | 2 |
| Dic3⋊AGL(1,𝔽5) | 2 |
| C2×C4⋊AGL(1,𝔽5) | 3 |
| C2×Dic3⋊C4 | 5 |