Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
| 2. C2×#687 | C2 | semidirect |
| 4. #4021 | C2 | semidirect |
| 5. #3942 | C2 | semidirect |
| 6. #3941 | C2 | semidirect |
| 7. C4⋊#168 | C2 | semidirect |
| 41. C4×D4 | 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 |
|---|---|
| C4×C5×D4 | 2 |
| C2×#687 | 2 |
| C2×#686 | 2 |
| #4021 | 2 |
| #3942 | 2 |
| #3941 | 2 |
| C4⋊#168 | 2 |
| #463 | 5 |