Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 3. #4130 | C2 | direct (N × H) |
| 4. C2×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. C2×C4×AGL(1,𝔽5) | C2 | semidirect |
| 8. C22×C4×C5 | C4 | semidirect |
| 9. C22×Dic5 | C4 | semidirect |
| 10. C2×C4×D5 | C4 | semidirect |
| 11. C2×C4×D5 | C4 | semidirect |
| 12. C2×C4×D5 | C4 | semidirect |
| 17. C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 18. C4×AGL(1,𝔽5) | C22 | semidirect |
| 30. C2×C4×C5 | C2×C4 | semidirect |
| 33. C2×Dic5 | C2×C4 | semidirect |
| 36. C4×D5 | C2×C4 | semidirect |
| 37. C4×D5 | C2×C4 | semidirect |
| 69. C22×C4 | AGL(1,𝔽5) | semidirect |
| 74. C2×C5 | #117 | semidirect |
| 77. D5 | #117 | semidirect |
| 98. C2×C4 | C2×AGL(1,𝔽5) | semidirect |
| 99. C5 | C2×#117 | semidirect |
| 119. C2 | #4130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D5 | 2 |
| C2×C22⋊AGL(1,𝔽5) | 2 |
| #4130 | 2 |
| C2×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4×AGL(1,𝔽5) | 2 |
| C2×#117 | 5 |