Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
186 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 2. C2×#704 | C2 | semidirect |
| 3. #4013 | C2 | direct (N × H) |
| 12. #704 | C22 | semidirect |
| 61. C2×C5 | #100 | semidirect |
| 80. C5 | C2×#100 | semidirect |
| 99. C2 | #4013 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D5 | 2 |
| C2×#704 | 2 |
| #4013 | 2 |
| C2×#100 | 5 |