Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
920 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 168 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×C4×C5⋊D5 | C2 | semidirect |
| 3. C2×C5×#685 | C2 | semidirect |
| 4. C2×C5×#683 | C2 | semidirect |
| 5. C2×#87780 | C2 | semidirect |
| 6. C2×#87779 | C2 | semidirect |
| 7. C2×#87778 | C2 | semidirect |
| 8. #11716971 | C2 | direct (N × H) |
| 14. C2×C4×C5⋊D5 | C22 | semidirect |
| 20. C5×#685 | C22 | semidirect |
| 21. C5×#683 | C22 | semidirect |
| 22. #87780 | C22 | semidirect |
| 23. #87779 | C22 | semidirect |
| 24. #87778 | C22 | semidirect |
| 59. C2×#685 | D5 | semidirect |
| 62. C2×#683 | D5 | semidirect |
| 115. #685 | C2×D5 | semidirect |
| 118. #683 | C2×D5 | semidirect |
| 120. C2×C52 | #123 | semidirect |
| 186. C52 | C2×#123 | semidirect |
| 252. C2×C5 | #4029 | semidirect |
| 253. C2×C5 | #4040 | semidirect |
| 286. C5 | C2×#4029 | semidirect |
| 287. C5 | C2×#4040 | semidirect |
| 307. C2 | #11716971 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C22×#6038 | 2 |
| C2×C5×#685 | 2 |
| C2×C5×#683 | 2 |
| C2×#87780 | 2 |
| C2×#87779 | 2 |
| C2×#87778 | 2 |
| #11716971 | 2 |
| C2×#4040 | 5 |
| C2×#4029 | 5 |