Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 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×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. D4×AGL(1,𝔽5) | C2 | semidirect |
| 4. #4130 | C2 | semidirect |
| 6. C22×AGL(1,𝔽5) | C22 | semidirect |
| 7. C2×C5×D4 | C4 | semidirect |
| 8. C2×C22⋊D5 | C4 | semidirect |
| 9. D4×D5 | C4 | semidirect |
| 11. C2×D20 | C4 | semidirect |
| 14. C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 15. C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 16. C4×AGL(1,𝔽5) | C22 | semidirect |
| 18. C23×C5 | C2×C4 | semidirect |
| 20. C22×D5 | C2×C4 | semidirect |
| 21. C22×D5 | C2×C4 | semidirect |
| 26. C5×D4 | C2×C4 | semidirect |
| 27. C2×C4×C5 | C2×C4 | semidirect |
| 28. C22⋊D5 | C2×C4 | semidirect |
| 29. C2×Dic5 | C2×C4 | semidirect |
| 30. D20 | C2×C4 | semidirect |
| 31. C4×D5 | C2×C4 | semidirect |
| 55. C2×D4 | AGL(1,𝔽5) | semidirect |
| 73. C23 | C2×AGL(1,𝔽5) | semidirect |
| 76. D4 | C2×AGL(1,𝔽5) | semidirect |
| 82. C2×C4 | C2×AGL(1,𝔽5) | semidirect |
| 83. C5 | #518 | 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×C22⋊AGL(1,𝔽5) | 2 |
| D4×AGL(1,𝔽5) | 2 |
| #4130 | 2 |
| #518 | 5 |