Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
210 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 2. C2×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. #4011 | C2 | semidirect |
| 4. #3999 | C2 | semidirect |
| 5. C23×D5 | C4 | semidirect |
| 8. C2×C5×D4 | C4 | semidirect |
| 9. C2×C22⋊D5 | C4 | semidirect |
| 14. C2×C4×D5 | C4 | semidirect |
| 16. C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 19. C23×C5 | C2×C4 | semidirect |
| 25. C22×D5 | C2×C4 | semidirect |
| 32. C2×C4×C5 | C2×C4 | semidirect |
| 35. C2×Dic5 | C2×C4 | semidirect |
| 69. C2×D4 | AGL(1,𝔽5) | semidirect |
| 81. D5 | #99 | semidirect |
| 92. C23 | C2×AGL(1,𝔽5) | semidirect |
| 102. C2×C4 | C2×AGL(1,𝔽5) | semidirect |
| 103. C5 | C2×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D5 | 2 |
| C2×C22⋊AGL(1,𝔽5) | 2 |
| #4011 | 2 |
| #3999 | 2 |
| C2×#99 | 5 |