Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
463 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 463 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11716849 | C2 | semidirect |
| 4. C5×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊Dic5 | C2 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 10. C2×C4×C5×D5 | C4 | semidirect |
| 12. C2×#6036 | C4 | semidirect |
| 13. C2×D5×Dic5 | C4 | semidirect |
| 48. (C2×AGL(1,𝔽5))⋊C4 | D5 | semidirect |
| 90. C2×C4×D5 | AGL(1,𝔽5) | semidirect |
| 157. C52 | #381 | semidirect |
| 255. C5 | #64953 | semidirect |
| 256. C5 | #65764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| #11716849 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| #65764 | 5 |
| #64953 | 5 |