Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
257 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 1. C2×#87828 | C2 | semidirect |
| 3. C4⋊#6032 | C2 | semidirect |
| 4. C4×C5×#170 | C2 | semidirect |
| 5. #11716753 | C2 | semidirect |
| 27. C5×#170 | D4 | semidirect |
| 34. C4×#170 | D5 | semidirect |
| 42. C4×C52 | M16 | semidirect |
| 91. #170 | D20 | semidirect |
| 100. C52 | #436 | semidirect |
| 114. C4×C5 | #676 | semidirect |
| 115. C4×C5 | #704 | semidirect |
| 154. C5 | #64977 | semidirect |
| 155. C5 | #65774 | semidirect |
| 164. C4 | #87828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87828 | 2 |
| Dic5×D20 | 2 |
| C4⋊#6032 | 2 |
| C4×C5×#170 | 2 |
| #11716753 | 2 |
| #65774 | 5 |
| #64977 | 5 |