Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| 4. (C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 7. C22×C4×C5 | C4 | semidirect |
| 8. C22×Dic5 | C4 | semidirect |
| 10. C2×C4×D5 | C4 | semidirect |
| 11. C2×C4×D5 | C4 | semidirect |
| 14. C22⋊AGL(1,𝔽5) | C4 | direct (N × H) |
| 25. C2×AGL(1,𝔽5) | C2×C4 | semidirect |
| 42. C22×C5 | C42 | semidirect |
| 47. C2×D5 | C42 | semidirect |
| 53. C4×C5 | C22⋊C4 | semidirect |
| 55. Dic5 | C22⋊C4 | semidirect |
| 64. C22×C4 | AGL(1,𝔽5) | semidirect |
| 92. C5 | C4×C22⋊C4 | semidirect |
| 102. C22 | C4×AGL(1,𝔽5) | semidirect |
| 108. C4 | C22⋊AGL(1,𝔽5) | 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 |
| C2×C4×AGL(1,𝔽5) | 2 |
| (C2×AGL(1,𝔽5))⋊C4 | 2 |
| C4×C22⋊C4 | 5 |