Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1856 conjugacy classes of subgroups; only the 600 normal subgroups are shown.
This group has 1856 conjugacy classes of subgroups — too many to draw. Only its 600 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×Q8×C5⋊D5 | C2 | semidirect |
| 2. C2×C5×Q8×D5 | C2 | semidirect |
| 3. Q8×D52 | C2 | direct (N × H) |
| 5. C2×#87872 | C2 | semidirect |
| 6. C2×D5×Dic10 | C2 | semidirect |
| 8. C2×C52×Q8 | C22 | semidirect |
| 9. Q8×C5⋊D5 | C22 | semidirect |
| 11. C2×#6045 | C22 | semidirect |
| 12. C5×Q8×D5 | C22 | semidirect |
| 14. C2×C5×Dic10 | C22 | semidirect |
| 15. C2×#6039 | C22 | semidirect |
| 19. #87872 | C22 | semidirect |
| 20. D5×Dic10 | C22 | semidirect |
| 24. C2×D52 | Q8 | direct (N × H) |
| 26. C52×Q8 | C23 | semidirect |
| 30. #6045 | C23 | semidirect |
| 33. C5×Dic10 | C23 | semidirect |
| 34. #6039 | C23 | semidirect |
| 43. C2×Q8×D5 | D5 | direct (N × H) |
| 47. C2×C5⋊D5 | C2×Q8 | semidirect |
| 49. C2×C5×D5 | C2×Q8 | semidirect |
| 51. D52 | C2×Q8 | direct (N × H) |
| 59. C2×C5×Q8 | C2×D5 | semidirect |
| 66. Q8×D5 | C2×D5 | direct (N × H) |
| 77. C2×Dic10 | C2×D5 | semidirect |
| 79. C2×C52 | C22×Q8 | semidirect |
| 81. C5⋊D5 | C22×Q8 | semidirect |
| 82. C5×D5 | C22×Q8 | semidirect |
| 91. C5×Q8 | C22×D5 | semidirect |
| 108. Dic10 | C22×D5 | semidirect |
| 115. C52 | C23×Q8 | semidirect |
| 125. C2×D5 | Q8×D5 | direct (N × H) |
| 141. C2×Q8 | D52 | direct (N × H) |
| 150. C2×C5 | C2×Q8×D5 | semidirect |
| 154. D5 | C2×Q8×D5 | direct (N × H) |
| 162. Q8 | C2×D52 | direct (N × H) |
| 171. C5 | C22×Q8×D5 | semidirect |
| 183. C2 | Q8×D52 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C2×C5×Q8×D5 | 2 |
| Q8×D52 | 2 |
| C2×C4×D52 | 2 |
| C2×#87872 | 2 |
| C2×D5×Dic10 | 2 |
| C22×Q8×D5 | 5 |