Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
978 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 215 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 |
|---|---|---|
| 10. C4×#6034 | C4 | semidirect |
| 11. #11716763 | C4 | direct (N × H) |
| 12. C4×C5×#168 | C4 | semidirect |
| 13. #11716594 | C4 | semidirect |
| 41. #6034 | C42 | semidirect |
| 42. C5×#168 | C42 | semidirect |
| 55. C4×#168 | AGL(1,𝔽5) | semidirect |
| 61. C4×C52 | #97 | semidirect |
| 63. #1039 | #97 | semidirect |
| 113. #168 | C4×AGL(1,𝔽5) | semidirect |
| 123. C52 | C4×#97 | semidirect |
| 134. C4×C5 | #3992 | semidirect |
| 170. C5 | C4×#3992 | semidirect |
| 177. C4 | #11716763 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#87862 | 2 |
| C42×#1043 | 2 |
| C2×#11716763 | 2 |
| C4×#87767 | 2 |
| C4×#3992 | 5 |