Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 2. C2×C8×C5⋊D5 | C2 | semidirect |
| 3. C5×#4047 | C2 | semidirect |
| 4. #11716936 | C2 | semidirect |
| 5. #11716933 | C2 | semidirect |
| 6. #11716923 | C2 | semidirect |
| 7. #11716921 | C2 | semidirect |
| 8. #11716909 | C2 | semidirect |
| 9. C8×D52 | C2 | semidirect |
| 19. C2×C52×C8 | C22 | semidirect |
| 20. C2×#6029 | C22 | semidirect |
| 23. C8×C5⋊D5 | C22 | semidirect |
| 24. C8×C5⋊D5 | C22 | semidirect |
| 25. C5×#681 | C22 | semidirect |
| 26. C5×#676 | C22 | semidirect |
| 27. C5×C8×D5 | C22 | semidirect |
| 28. #87769 | C22 | semidirect |
| 29. #87768 | C22 | semidirect |
| 31. D5×#168 | C22 | semidirect |
| 63. #4047 | D5 | semidirect |
| 94. C2×C5×C8 | C2×D5 | semidirect |
| 96. #681 | C2×D5 | semidirect |
| 102. #676 | C2×D5 | semidirect |
| 113. C8×D5 | C2×D5 | semidirect |
| 118. C5⋊D5 | #131 | semidirect |
| 169. C52 | C2×#131 | semidirect |
| 212. C2×C8 | D52 | semidirect |
| 246. C5 | D5×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717471 | 2 |
| C2×C8×C5⋊D5 | 2 |
| C5×#4047 | 2 |
| #11716936 | 2 |
| #11716933 | 2 |
| #11716923 | 2 |
| #11716921 | 2 |
| #11716909 | 2 |
| C8×D52 | 2 |
| D5×#131 | 5 |