Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 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×C4×AGL(1,𝔽5) | C2 | semidirect |
| 6. (C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 19. C5×C22⋊C4 | C4 | semidirect |
| 20. C22⋊Dic5 | C4 | semidirect |
| 21. #685 | C4 | semidirect |
| 22. #685 | C4 | semidirect |
| 98. C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 138. C5 | #388 | 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 |
| C2×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4×AGL(1,𝔽5) | 2 |
| D5×C22⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊C4 | 2 |
| #388 | 5 |