Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
279 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11716847 | C2 | semidirect |
| 4. C4⋊#6032 | C2 | semidirect |
| 41. C4×C52 | M16 | semidirect |
| 44. C5×Dic5 | M16 | semidirect |
| 103. C52 | #423 | semidirect |
| 125. C4×C5 | #681 | semidirect |
| 126. C4×C5 | #704 | semidirect |
| 128. Dic5 | #681 | semidirect |
| 166. C5 | #65213 | semidirect |
| 167. C5 | #65758 | semidirect |
| 178. C4 | #87853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87853 | 2 |
| C2×C4×C5×Dic5 | 2 |
| #11716847 | 2 |
| C4⋊#6032 | 2 |
| #65758 | 5 |
| #65213 | 5 |