Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 130 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⋊#1043 | C2 | semidirect |
| 3. C2×C4⋊#1043 | C2 | semidirect |
| 4. C2×C4×#1043 | C2 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 9. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 12. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 29. C2×#1043 | D4 | semidirect |
| 55. C4×C52 | C22⋊C4 | semidirect |
| 56. #1039 | C22⋊C4 | semidirect |
| 60. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 100. C52 | #390 | semidirect |
| 115. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 122. C2×D4 | #1043 | semidirect |
| 155. C5 | #65780 | semidirect |
| 171. C4 | C22⋊#1043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C5⋊D5 | 2 |
| C2×C22⋊#1043 | 2 |
| C2×C4⋊#1043 | 2 |
| C2×C4×#1043 | 2 |
| #65780 | 5 |