Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#677 | C2 | semidirect |
| 2. C2×#676 | C2 | semidirect |
| 3. #4043 | C2 | semidirect |
| 5. C5×#107 | C2 | semidirect |
| 6. #3942 | C2 | semidirect |
| 7. #3941 | C2 | semidirect |
| 36. C5×C8 | D4 | semidirect |
| 42. #107 | D5 | semidirect |
| 91. C8 | D20 | semidirect |
| 92. C5 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#677 | 2 |
| C2×#676 | 2 |
| #4043 | 2 |
| #4041 | 2 |
| C5×#107 | 2 |
| #3942 | 2 |
| #3941 | 2 |
| #468 | 5 |