Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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. C4×C5×Q8 | C2 | semidirect |
| 4. #3967 | C2 | semidirect |
| 6. #3940 | C2 | semidirect |
| 7. C4×#168 | C2 | semidirect |
| 15. #688 | C4 | direct (N × H) |
| 23. C5×Q8 | C2×C4 | semidirect |
| 34. #168 | C2×C4 | semidirect |
| 36. C4×Q8 | D5 | semidirect |
| 49. C4×C5 | SD16 | semidirect |
| 71. Q8 | C4×D5 | semidirect |
| 83. C5 | C4×SD16 | semidirect |
| 92. C4 | #688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Q8 | 2 |
| C2×#688 | 2 |
| C4×D20 | 2 |
| #3967 | 2 |
| #3941 | 2 |
| #3940 | 2 |
| C4×#168 | 2 |
| C4×SD16 | 5 |