Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
| 5. #11716899 | C2 | semidirect |
| 8. C22×#1044 | C4 | semidirect |
| 13. C22⋊#1044 | C4 | semidirect |
| 15. C52×C22⋊C4 | C4 | semidirect |
| 16. C22⋊#1039 | C4 | semidirect |
| 17. #87808 | C4 | semidirect |
| 32. C2×#1044 | C2×C4 | semidirect |
| 34. C2×C4×C52 | C2×C4 | semidirect |
| 35. C2×#1039 | C2×C4 | semidirect |
| 45. C22×C52 | C42 | semidirect |
| 51. C2×C5⋊D5 | C42 | semidirect |
| 58. #1044 | C22⋊C4 | direct (N × H) |
| 73. C5×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 109. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 121. C52 | C4×C22⋊C4 | semidirect |
| 126. C22×C5 | C4×AGL(1,𝔽5) | semidirect |
| 163. C22⋊C4 | #1044 | direct (N × H) |
| 197. C2×C4 | C2×#1044 | semidirect |
| 199. C5 | C22⋊C4×AGL(1,𝔽5) | semidirect |
| 210. C22 | C4×#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1044 | 2 |
| C2×C22⋊#1044 | 2 |
| C2×C4×#1044 | 2 |
| C22⋊C4×C5⋊D5 | 2 |
| #11716899 | 2 |
| C22⋊C4×AGL(1,𝔽5) | 5 |