Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
472 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 70 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×D5×D20 | C2 | semidirect |
| 2. C2×#87809 | C2 | semidirect |
| 3. C5×#4084 | C2 | semidirect |
| 4. C2×C5×#686 | C2 | semidirect |
| 5. #11716605 | C2 | semidirect |
| 6. #11716603 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 9. C2×C52×D4 | C22 | semidirect |
| 18. C2×#6029 | C22 | semidirect |
| 21. C5×C4⋊Dic5 | C22 | semidirect |
| 22. C2×C5×#168 | C22 | semidirect |
| 36. C4⋊(C5⋊D5) | D4 | semidirect |
| 41. C5×D20 | D4 | semidirect |
| 51. #4084 | D5 | semidirect |
| 55. C2×#686 | D5 | semidirect |
| 74. C2×C5×D5 | D8 | semidirect |
| 85. C2×C5×D4 | C2×D5 | semidirect |
| 86. C2×C5×D4 | C2×D5 | semidirect |
| 109. C4⋊Dic5 | C2×D5 | semidirect |
| 113. C2×#168 | C2×D5 | semidirect |
| 166. D20 | C22⋊D5 | semidirect |
| 181. C52 | #447 | semidirect |
| 216. C2×D5 | #686 | semidirect |
| 234. C2×D4 | D52 | semidirect |
| 284. C5 | #65325 | semidirect |
| 285. C5 | #65445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| C2×#87809 | 2 |
| C5×#4084 | 2 |
| C2×C5×#686 | 2 |
| #11716605 | 2 |
| #11716603 | 2 |
| #11716597 | 2 |
| #65445 | 5 |
| #65325 | 5 |