Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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. C22×#170 | C2 | semidirect |
| 2. C2×#700 | C2 | semidirect |
| 4. C22⋊#170 | C2 | semidirect |
| 5. #4003 | C2 | semidirect |
| 6. #4002 | C2 | semidirect |
| 7. C4⋊#170 | C2 | semidirect |
| 37. #170 | D4 | semidirect |
| 47. C22×C5 | M16 | semidirect |
| 92. C5 | #435 | semidirect |
| 98. C22 | #700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#170 | 2 |
| C2×#700 | 2 |
| #4027 | 2 |
| C22⋊#170 | 2 |
| #4003 | 2 |
| #4002 | 2 |
| C4⋊#170 | 2 |
| #435 | 5 |