Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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. C4×C5×D4 | C2 | semidirect |
| 4. D4×Dic5 | C2 | semidirect |
| 5. C4×C22⋊D5 | C2 | semidirect |
| 6. #4039 | C2 | semidirect |
| 7. D5×C4⋊C4 | C2 | semidirect |
| 8. #4027 | C2 | semidirect |
| 9. D5×C22⋊C4 | C2 | semidirect |
| 10. C4×D20 | C2 | semidirect |
| 11. C42×D5 | C2 | semidirect |
| 14. C22×C4×C5 | C22 | semidirect |
| 16. C22×Dic5 | C22 | semidirect |
| 17. D4×D5 | C4 | direct (N × H) |
| 24. C2×C4×D5 | C22 | semidirect |
| 25. C2×C4×D5 | C22 | semidirect |
| 26. C5×C4⋊C4 | C22 | semidirect |
| 27. C5×C22⋊C4 | C22 | semidirect |
| 28. C42×C5 | C22 | semidirect |
| 29. C22⋊Dic5 | C22 | semidirect |
| 30. #685 | C22 | semidirect |
| 31. #685 | C22 | semidirect |
| 32. C4⋊Dic5 | C22 | semidirect |
| 33. #683 | C22 | semidirect |
| 34. C4×Dic5 | C22 | semidirect |
| 35. C4×Dic5 | C22 | semidirect |
| 36. C4×Dic5 | C22 | semidirect |
| 41. C22×D5 | C2×C4 | semidirect |
| 44. C5×D4 | C2×C4 | semidirect |
| 50. C22⋊D5 | C2×C4 | semidirect |
| 56. D20 | C2×C4 | semidirect |
| 61. C4×D5 | C2×C4 | semidirect |
| 62. C4×D5 | D4 | direct (N × H) |
| 70. C4×D4 | D5 | direct (N × H) |
| 76. C22×C5 | C22×C4 | semidirect |
| 82. C2×D5 | C22×C4 | semidirect |
| 87. C4×C5 | C22×C4 | semidirect |
| 88. C4×C5 | C2×D4 | semidirect |
| 91. Dic5 | C22×C4 | semidirect |
| 92. Dic5 | C2×D4 | semidirect |
| 106. C22×C4 | C2×D5 | semidirect |
| 109. C4⋊C4 | C2×D5 | semidirect |
| 113. C22⋊C4 | C2×D5 | semidirect |
| 117. C42 | C2×D5 | semidirect |
| 123. D5 | C4×D4 | direct (N × H) |
| 132. D4 | C4×D5 | direct (N × H) |
| 149. C5 | C2×C4×D4 | semidirect |
| 159. C22 | C2×C4×D5 | semidirect |
| 167. C4 | C2×C4×D5 | semidirect |
| 168. C4 | D4×D5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D5 | 2 |
| C22×C4×D5 | 2 |
| C4×C5×D4 | 2 |
| D4×Dic5 | 2 |
| C4×C22⋊D5 | 2 |
| #4039 | 2 |
| D5×C4⋊C4 | 2 |
| #4027 | 2 |
| D5×C22⋊C4 | 2 |
| C4×D20 | 2 |
| C42×D5 | 2 |
| C2×C4×D4 | 5 |