Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
387 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 12. C4×#1039 | C4 | semidirect |
| 13. C4×C5×Dic5 | C4 | semidirect |
| 14. Dic52 | C4 | semidirect |
| 45. C4×C52 | C4⋊C4 | semidirect |
| 46. #1039 | C4⋊C4 | semidirect |
| 47. C5×Dic5 | C4⋊C4 | semidirect |
| 48. C5×Dic5 | C4⋊C4 | semidirect |
| 69. C4×Dic5 | AGL(1,𝔽5) | semidirect |
| 108. C52 | #384 | semidirect |
| 126. C4×C5 | #683 | semidirect |
| 127. C4×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 132. Dic5 | #683 | semidirect |
| 133. Dic5 | C4⋊AGL(1,𝔽5) | semidirect |
| 170. C5 | #65265 | semidirect |
| 171. C5 | #65688 | semidirect |
| 182. C4 | #87825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1042 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×#87825 | 2 |
| C4×D5×Dic5 | 2 |
| #65688 | 5 |
| #65265 | 5 |