Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 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×#700 | C2 | semidirect |
| 3. C22⋊#170 | C2 | semidirect |
| 4. #4003 | C2 | semidirect |
| 13. C2×#170 | C22 | semidirect |
| 39. C22×C5 | M16 | semidirect |
| 47. C2×D5 | M16 | semidirect |
| 85. C5 | #407 | semidirect |
| 95. C22 | #700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D5 | 2 |
| C2×#700 | 2 |
| C22⋊#170 | 2 |
| #4003 | 2 |
| #407 | 5 |