Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
353 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 353 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 |
|---|---|---|
| 14. C52×C4⋊C4 | C4 | semidirect |
| 15. C5×C4⋊Dic5 | C4 | semidirect |
| 16. C5×#683 | C4 | semidirect |
| 17. #65712 | C5 | direct (N × H) |
| 58. C4×C52 | C4⋊C4 | semidirect |
| 60. C5×Dic5 | C4⋊C4 | semidirect |
| 79. C5×C4⋊C4 | C4×C5 | semidirect |
| 80. C5×C4⋊C4 | AGL(1,𝔽5) | semidirect |
| 82. C4⋊Dic5 | C4×C5 | semidirect |
| 83. #683 | C4×C5 | semidirect |
| 135. C52 | #389 | semidirect |
| 163. C4×C5 | C5×C4⋊C4 | semidirect |
| 164. C4×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 166. Dic5 | C5×C4⋊C4 | semidirect |
| 176. C4⋊C4 | C5×AGL(1,𝔽5) | semidirect |
| 214. C5 | C5×#389 | semidirect |
| 215. C5 | #65712 | direct (N × H) |
| 229. C4 | C5×C4⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C5×D5×C4⋊C4 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #65712 | 5 |
| C5×#389 | 5 |