Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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×C8×D5 | C2 | semidirect |
| 3. #4043 | C2 | semidirect |
| 5. C5×#106 | C2 | semidirect |
| 6. #3942 | C2 | semidirect |
| 7. #3941 | C2 | semidirect |
| 36. C5×C8 | D4 | semidirect |
| 42. #106 | D5 | semidirect |
| 51. C2×D5 | SD16 | semidirect |
| 91. C8 | D20 | semidirect |
| 92. C5 | #465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#677 | 2 |
| C2×C8×D5 | 2 |
| #4043 | 2 |
| #4041 | 2 |
| C5×#106 | 2 |
| #3942 | 2 |
| #3941 | 2 |
| #465 | 5 |