Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 72 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×#87829 | C2 | semidirect |
| 3. C4×#6032 | C2 | semidirect |
| 4. C5×C4⋊#170 | C2 | semidirect |
| 5. #11716754 | C2 | semidirect |
| 26. #6032 | D4 | semidirect |
| 33. C4⋊#170 | D5 | semidirect |
| 42. C4×C52 | M16 | semidirect |
| 101. C52 | #436 | semidirect |
| 119. C4×C5 | #676 | semidirect |
| 120. C4×C5 | #700 | semidirect |
| 158. C5 | #65127 | semidirect |
| 159. C5 | #65705 | semidirect |
| 168. C4 | #87829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87829 | 2 |
| #11717013 | 2 |
| C4×#6032 | 2 |
| C5×C4⋊#170 | 2 |
| #11716754 | 2 |
| #65705 | 5 |
| #65127 | 5 |