Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
122 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 46 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. C2×#704 | C2 | semidirect |
| 2. C2×#700 | C2 | semidirect |
| 4. C22⋊#170 | C2 | semidirect |
| 5. #4004 | C2 | semidirect |
| 6. #4003 | C2 | semidirect |
| 7. C4×#170 | C2 | semidirect |
| 37. #170 | D4 | semidirect |
| 55. Dic5 | M16 | semidirect |
| 92. C5 | #436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#704 | 2 |
| C2×#700 | 2 |
| #4027 | 2 |
| C22⋊#170 | 2 |
| #4004 | 2 |
| #4003 | 2 |
| C4×#170 | 2 |
| #436 | 5 |