Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
142 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 6. C22×AGL(1,𝔽5) | C4 | semidirect |
| 11. C22⋊AGL(1,𝔽5) | C4 | semidirect |
| 12. C5×C22⋊C4 | C4 | semidirect |
| 13. C22⋊Dic5 | C4 | semidirect |
| 62. C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 86. C5 | #342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊AGL(1,𝔽5) | 2 |
| D5×C22⋊C4 | 2 |
| #342 | 5 |