Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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×C5×#41 | C2 | semidirect |
| 2. C2×#688 | C2 | semidirect |
| 3. C2×#686 | C2 | semidirect |
| 4. #4076 | C2 | semidirect |
| 5. #3967 | C2 | semidirect |
| 6. #3964 | C2 | semidirect |
| 7. C22⋊#168 | C2 | semidirect |
| 28. C5×Q8 | D4 | semidirect |
| 31. C5×D4 | D4 | semidirect |
| 44. C2×#41 | D5 | semidirect |
| 91. Q8 | C22⋊D5 | semidirect |
| 97. D4 | C22⋊D5 | semidirect |
| 107. C5 | #449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| C2×#688 | 2 |
| C2×#686 | 2 |
| #4076 | 2 |
| #3967 | 2 |
| #3964 | 2 |
| C22⋊#168 | 2 |
| #449 | 5 |