Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. C4×C5×D4 | C2 | semidirect |
| 3. C4×D20 | C2 | semidirect |
| 4. #3964 | C2 | semidirect |
| 5. #3941 | C2 | semidirect |
| 6. #3939 | C2 | semidirect |
| 7. C4×#168 | C2 | semidirect |
| 15. #686 | C4 | direct (N × H) |
| 24. C5×D4 | C2×C4 | semidirect |
| 32. D20 | C2×C4 | semidirect |
| 35. #168 | C2×C4 | semidirect |
| 38. C4×D4 | D5 | semidirect |
| 52. C4×C5 | D8 | semidirect |
| 78. D4 | C4×D5 | semidirect |
| 88. C5 | C4×D8 | semidirect |
| 99. C4 | #686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D4 | 2 |
| C2×#686 | 2 |
| C4×D20 | 2 |
| #3964 | 2 |
| #3941 | 2 |
| #3939 | 2 |
| C4×#168 | 2 |
| C4×D8 | 5 |