Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 2. C2×C42×C5 | C2 | semidirect |
| 3. C4×C22⋊D5 | C2 | semidirect |
| 4. #4072 | C2 | semidirect |
| 5. C4×D20 | C2 | semidirect |
| 6. #4018 | C2 | semidirect |
| 7. C42×D5 | C2 | semidirect |
| 8. C4×Dic10 | C2 | semidirect |
| 12. #709 | C4 | direct (N × H) |
| 30. C2×C4×C5 | C2×C4 | semidirect |
| 35. C22⋊D5 | C2×C4 | semidirect |
| 38. D20 | C2×C4 | semidirect |
| 40. C4×D5 | C2×C4 | semidirect |
| 41. Dic10 | C2×C4 | semidirect |
| 49. C2×C42 | D5 | semidirect |
| 58. C4×C5 | #41 | semidirect |
| 92. C2×C4 | C4×D5 | semidirect |
| 97. C5 | C4×#41 | semidirect |
| 108. C4 | #709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C2×C42×C5 | 2 |
| C4×C22⋊D5 | 2 |
| #4072 | 2 |
| C4×D20 | 2 |
| #4018 | 2 |
| C42×D5 | 2 |
| C4×Dic10 | 2 |
| C4×#41 | 5 |