Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
190 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 190 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. #4038 | C2 | semidirect |
| 4. C5×#102 | C2 | semidirect |
| 5. #3964 | C2 | semidirect |
| 6. #3953 | C2 | semidirect |
| 7. #3941 | C2 | semidirect |
| 12. D4×D5 | C4 | semidirect |
| 15. C2×C5×C8 | C22 | semidirect |
| 16. C5×C4⋊C4 | C22 | semidirect |
| 18. C4⋊Dic5 | C22 | semidirect |
| 20. C2×#168 | C22 | semidirect |
| 48. #102 | D5 | semidirect |
| 74. C2×C8 | C2×D5 | semidirect |
| 76. C4⋊C4 | C2×D5 | semidirect |
| 104. C5 | #418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D5 | 2 |
| C2×#676 | 2 |
| #4038 | 2 |
| C5×#102 | 2 |
| #3964 | 2 |
| #3953 | 2 |
| #3941 | 2 |
| #418 | 5 |