Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
358 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 82 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. D4×#1039 | C2 | semidirect |
| 3. #11717017 | C2 | semidirect |
| 4. C5×#3964 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 6. #11716604 | C2 | semidirect |
| 7. #11716596 | C2 | semidirect |
| 15. C5×#686 | C4 | semidirect |
| 25. C52×D4 | C2×C4 | semidirect |
| 33. C5×D20 | C2×C4 | semidirect |
| 36. C5×#168 | C2×C4 | semidirect |
| 46. #3964 | D5 | semidirect |
| 83. #686 | Dic5 | semidirect |
| 111. C5×D4 | C4×D5 | semidirect |
| 112. C5×D4 | C2×Dic5 | semidirect |
| 132. D20 | C2×Dic5 | semidirect |
| 137. #168 | C2×Dic5 | semidirect |
| 145. C52 | #442 | semidirect |
| 212. D4 | D5×Dic5 | semidirect |
| 223. C5 | #65074 | semidirect |
| 224. C5 | #65441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1039 | 2 |
| C2×C5×#686 | 2 |
| #11717017 | 2 |
| C5×#3964 | 2 |
| #11716614 | 2 |
| #11716604 | 2 |
| #11716596 | 2 |
| #65441 | 5 |
| #65074 | 5 |