Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
792 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 176 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. C22×#6039 | C2 | semidirect |
| 3. C2×#87808 | C2 | semidirect |
| 4. C2×C5×#685 | C2 | semidirect |
| 5. C2×C4×C5×Dic5 | C2 | semidirect |
| 6. C2×#87779 | C2 | semidirect |
| 7. C2×#87778 | C2 | semidirect |
| 8. #11716970 | C2 | direct (N × H) |
| 17. C2×#6039 | C22 | semidirect |
| 20. #87808 | C22 | semidirect |
| 21. C5×#685 | C22 | semidirect |
| 22. C4×C5×Dic5 | C22 | semidirect |
| 23. #87779 | C22 | semidirect |
| 24. #87778 | C22 | semidirect |
| 61. C2×#685 | D5 | semidirect |
| 62. C2×C4×Dic5 | D5 | semidirect |
| 116. #685 | C2×D5 | semidirect |
| 117. C4×Dic5 | C2×D5 | semidirect |
| 119. C2×C52 | #124 | semidirect |
| 184. C52 | C2×#124 | semidirect |
| 250. C2×C5 | #4021 | semidirect |
| 251. C2×C5 | #4031 | semidirect |
| 284. C5 | C2×#4021 | semidirect |
| 285. C5 | C2×#4031 | semidirect |
| 305. C2 | #11716970 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6039 | 2 |
| C22×#6038 | 2 |
| C2×#87808 | 2 |
| C2×C5×#685 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87779 | 2 |
| C2×#87778 | 2 |
| #11716970 | 2 |
| C2×#4031 | 5 |
| C2×#4021 | 5 |