Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
194 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 11. C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 13. C4×AGL(1,𝔽5) | C4 | semidirect |
| 14. C5×C4⋊C4 | C4 | semidirect |
| 15. C4⋊Dic5 | C4 | semidirect |
| 16. #683 | C4 | semidirect |
| 50. AGL(1,𝔽5) | C4⋊C4 | direct (N × H) |
| 52. C4×C5 | C42 | semidirect |
| 54. Dic5 | C42 | semidirect |
| 63. C4⋊C4 | AGL(1,𝔽5) | direct (N × H) |
| 91. C5 | C4×C4⋊C4 | semidirect |
| 105. C4 | C4×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4×AGL(1,𝔽5) | 2 |
| D5×C4⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊C4 | 2 |
| C4×C4⋊C4 | 5 |