Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 162 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 |
|---|---|---|
| 2. C2×#676 | C2 | semidirect |
| 3. D5×C4⋊C4 | C2 | semidirect |
| 4. C5×#103 | C2 | semidirect |
| 5. #3967 | C2 | semidirect |
| 6. #3953 | C2 | semidirect |
| 7. #3941 | C2 | semidirect |
| 10. #713 | C4 | semidirect |
| 26. C5×Q8 | C2×C4 | semidirect |
| 34. D20 | C2×C4 | semidirect |
| 45. #103 | D5 | semidirect |
| 83. Q8 | C4×D5 | semidirect |
| 98. C5 | #417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#713 | 2 |
| C2×#676 | 2 |
| D5×C4⋊C4 | 2 |
| C5×#103 | 2 |
| #3967 | 2 |
| #3953 | 2 |
| #3941 | 2 |
| #417 | 5 |