Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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. C5×#124 | C2 | semidirect |
| 2. C2×#688 | C2 | semidirect |
| 4. C4×D20 | C2 | semidirect |
| 5. #3967 | C2 | semidirect |
| 6. #3964 | C2 | semidirect |
| 7. C4⋊#168 | C2 | semidirect |
| 40. #124 | D5 | semidirect |
| 92. C5 | #463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#124 | 2 |
| C2×#688 | 2 |
| C2×#686 | 2 |
| C4×D20 | 2 |
| #3967 | 2 |
| #3964 | 2 |
| C4⋊#168 | 2 |
| #463 | 5 |