Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
234 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
| 43. C22×C5 | C4⋊C4 | semidirect |
| 49. C2×D5 | C4⋊C4 | semidirect |
| 56. C4×C5 | C22⋊C4 | semidirect |
| 58. Dic5 | C22⋊C4 | semidirect |
| 67. C22×C4 | AGL(1,𝔽5) | semidirect |
| 97. C5 | #380 | semidirect |
| 109. C22 | C4⋊AGL(1,𝔽5) | semidirect |
| 115. C4 | C22⋊AGL(1,𝔽5) | semidirect |
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 |
| #380 | 5 |