Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
397 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 397 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C2×C4×#1042 | C2 | semidirect |
| 2. C2×#87825 | C2 | semidirect |
| 6. C5×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽5))⋊Dic5 | C2 | semidirect |
| 19. #87808 | C4 | semidirect |
| 20. C5×#685 | C4 | semidirect |
| 21. #87779 | C4 | semidirect |
| 22. #87778 | C4 | semidirect |
| 65. (C2×AGL(1,𝔽5))⋊C4 | D5 | semidirect |
| 121. #685 | AGL(1,𝔽5) | semidirect |
| 202. C52 | #388 | semidirect |
| 326. C5 | #64958 | semidirect |
| 327. C5 | #65700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1042 | 2 |
| C2×#87825 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| D5×#685 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| #65700 | 5 |
| #64958 | 5 |