Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 112 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×#1044 | C2 | semidirect |
| 4. #11716899 | C2 | semidirect |
| 7. C22×C4×C52 | C4 | semidirect |
| 8. C22×#1039 | C4 | semidirect |
| 10. C2×C4×C5⋊D5 | C4 | semidirect |
| 11. C2×C4×C5⋊D5 | C4 | semidirect |
| 14. C22⋊#1044 | C4 | direct (N × H) |
| 25. C2×#1044 | C2×C4 | semidirect |
| 43. C22×C52 | C42 | semidirect |
| 48. C2×C5⋊D5 | C42 | semidirect |
| 54. C4×C52 | C22⋊C4 | semidirect |
| 56. #1039 | C22⋊C4 | semidirect |
| 61. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 122. C52 | C4×C22⋊C4 | semidirect |
| 129. C22×C5 | C4×AGL(1,𝔽5) | semidirect |
| 149. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 162. C22×C4 | #1044 | semidirect |
| 197. C5 | C4×C22⋊AGL(1,𝔽5) | semidirect |
| 207. C22 | C4×#1044 | semidirect |
| 213. C4 | C22⋊#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C2×C22⋊#1044 | 2 |
| C2×C4×#1044 | 2 |
| #11716899 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 5 |