Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 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. C22×C4×D5 | C2 | semidirect |
| 3. C2×C5×C4⋊C4 | C2 | semidirect |
| 4. C2×#685 | C2 | semidirect |
| 5. C2×C4×Dic5 | C2 | semidirect |
| 6. #4039 | C2 | direct (N × H) |
| 12. C2×D20 | C4 | semidirect |
| 15. C2×C4×D5 | C22 | semidirect |
| 16. C5×C4⋊C4 | C22 | semidirect |
| 17. #685 | C22 | semidirect |
| 18. C4×Dic5 | C22 | semidirect |
| 23. C22×D5 | C2×C4 | semidirect |
| 26. C2×C4×C5 | C2×C4 | semidirect |
| 30. C2×Dic5 | D4 | semidirect |
| 33. D20 | C2×C4 | semidirect |
| 38. C2×C4⋊C4 | D5 | semidirect |
| 48. C2×D5 | C22×C4 | semidirect |
| 50. C4×C5 | C22×C4 | semidirect |
| 52. Dic5 | C2×D4 | semidirect |
| 62. C4⋊C4 | C2×D5 | semidirect |
| 65. C2×C5 | C4×D4 | semidirect |
| 82. C2×C4 | C4×D5 | semidirect |
| 85. C5 | C2×C4×D4 | semidirect |
| 97. C4 | C2×C4×D5 | semidirect |
| 99. C2 | #4039 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D20 | 2 |
| C22×C4×D5 | 2 |
| C2×C5×C4⋊C4 | 2 |
| C2×#685 | 2 |
| C2×C4×Dic5 | 2 |
| #4039 | 2 |
| C2×C4×D4 | 5 |