Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×C4×AGL(1,𝔽5) | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 8. C22×AGL(1,𝔽5) | C4 | semidirect |
| 13. C22⋊AGL(1,𝔽5) | C4 | semidirect |
| 15. C5×C22⋊C4 | C4 | semidirect |
| 16. C22⋊Dic5 | C4 | semidirect |
| 17. #685 | C4 | semidirect |
| 32. C2×AGL(1,𝔽5) | C2×C4 | semidirect |
| 34. C2×C4×C5 | C2×C4 | semidirect |
| 35. C2×Dic5 | C2×C4 | semidirect |
| 44. C22×C5 | C42 | semidirect |
| 50. C2×D5 | C42 | semidirect |
| 57. AGL(1,𝔽5) | C22⋊C4 | direct (N × H) |
| 70. C22⋊C4 | AGL(1,𝔽5) | direct (N × H) |
| 97. C2×C4 | C2×AGL(1,𝔽5) | semidirect |
| 98. C5 | C4×C22⋊C4 | semidirect |
| 109. C22 | C4×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,𝔽5) | 2 |
| C2×C22⋊AGL(1,𝔽5) | 2 |
| C2×C4×AGL(1,𝔽5) | 2 |
| D5×C22⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊C4 | 2 |
| C4×C22⋊C4 | 5 |