Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 190 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. #4130 | C2 | semidirect |
| 3. D5⋊M16 | C2 | semidirect |
| 4. #4007 | C2 | semidirect |
| 6. C2×C5×D4 | C4 | semidirect |
| 10. D4×D5 | C4 | semidirect |
| 12. C2×D20 | C4 | semidirect |
| 16. C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 19. D5⋊C8 | C22 | semidirect |
| 67. C2×D4 | AGL(1,𝔽5) | semidirect |
| 101. C5 | #418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D5 | 2 |
| #4130 | 2 |
| D5⋊M16 | 2 |
| #4007 | 2 |
| #418 | 5 |