Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
403 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 403 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 13. #87825 | C4 | direct (N × H) |
| 14. C4×#1039 | C4 | semidirect |
| 15. C4×C5×Dic5 | C4 | semidirect |
| 16. Dic52 | C4 | semidirect |
| 17. Dic52 | C4 | semidirect |
| 54. C4×C52 | C4⋊C4 | semidirect |
| 56. #1039 | C42 | semidirect |
| 58. C5×Dic5 | C42 | semidirect |
| 59. C5×Dic5 | C4⋊C4 | semidirect |
| 84. C4×Dic5 | AGL(1,𝔽5) | semidirect |
| 133. C52 | C4×C4⋊C4 | semidirect |
| 152. C4×C5 | #683 | semidirect |
| 153. C4×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 162. Dic5 | #683 | semidirect |
| 163. Dic5 | C4×AGL(1,𝔽5) | semidirect |
| 207. C5 | C4×#683 | semidirect |
| 208. C5 | C4×C4⋊AGL(1,𝔽5) | semidirect |
| 221. C4 | #87825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1042 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×#87825 | 2 |
| C4×D5×Dic5 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 5 |
| C4×#683 | 5 |