Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
112 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 112 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×Q8 | C2 | semidirect |
| 2. C2×#689 | C2 | semidirect |
| 5. #3942 | C2 | semidirect |
| 7. C4⋊#168 | C2 | semidirect |
| 40. C4×Q8 | D5 | semidirect |
| 87. C5 | #464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Q8 | 2 |
| C2×#689 | 2 |
| C2×#688 | 2 |
| #4021 | 2 |
| #3942 | 2 |
| #3941 | 2 |
| C4⋊#168 | 2 |
| #464 | 5 |