Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 9. C4⋊#1044 | C4 | direct (N × H) |
| 11. C42×C52 | C4 | semidirect |
| 12. C4×#1039 | C4 | semidirect |
| 13. C4×#1039 | C4 | semidirect |
| 14. C4×#1039 | C4 | semidirect |
| 42. C4×C52 | C42 | semidirect |
| 43. C4×C52 | C4⋊C4 | semidirect |
| 45. #1039 | C42 | semidirect |
| 46. #1039 | C4⋊C4 | semidirect |
| 57. C42×C5 | AGL(1,𝔽5) | semidirect |
| 99. C52 | C4×C4⋊C4 | semidirect |
| 115. C4×C5 | C4×AGL(1,𝔽5) | semidirect |
| 116. C4×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 132. C42 | #1044 | semidirect |
| 158. C5 | C4×C4⋊AGL(1,𝔽5) | semidirect |
| 169. C4 | C4×#1044 | semidirect |
| 170. C4 | C4⋊#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1044 | 2 |
| C2×C4×#1044 | 2 |
| C42×C5⋊D5 | 2 |
| #11716899 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 5 |