Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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. D4×Dic5 | C2 | semidirect |
| 3. #4039 | C2 | semidirect |
| 4. C5×#102 | C2 | semidirect |
| 5. #3953 | C2 | semidirect |
| 6. #3947 | C2 | semidirect |
| 7. #3940 | C2 | semidirect |
| 15. #686 | C4 | semidirect |
| 24. C5×D4 | C2×C4 | semidirect |
| 32. D20 | C2×C4 | semidirect |
| 35. #168 | C2×C4 | semidirect |
| 41. #102 | D5 | semidirect |
| 78. D4 | C4×D5 | semidirect |
| 88. C5 | #442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic5 | 2 |
| C2×#686 | 2 |
| #4039 | 2 |
| C5×#102 | 2 |
| #3953 | 2 |
| #3947 | 2 |
| #3940 | 2 |
| #442 | 5 |