Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 430 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 430 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. C5×Q8×Dic5 | C2 | direct (N × H) |
| 5. C2×C52×Q8 | C4 | semidirect |
| 13. C2×Q8×Dic5 | C5 | direct (N × H) |
| 15. C52×Q8 | C2×C4 | semidirect |
| 19. C2×C5×Dic5 | Q8 | direct (N × H) |
| 28. Q8×Dic5 | C2×C5 | direct (N × H) |
| 37. C5×Dic5 | C2×Q8 | direct (N × H) |
| 40. C2×C5×Q8 | Dic5 | direct (N × H) |
| 41. C2×C5×Q8 | C4×C5 | semidirect |
| 56. C2×C52 | C4×Q8 | semidirect |
| 64. C5×Q8 | C2×Dic5 | direct (N × H) |
| 65. C5×Q8 | C2×C4×C5 | semidirect |
| 77. C2×Dic5 | C5×Q8 | direct (N × H) |
| 84. C52 | C2×C4×Q8 | semidirect |
| 103. Dic5 | C2×C5×Q8 | direct (N × H) |
| 104. C2×Q8 | C5×Dic5 | direct (N × H) |
| 115. C2×C5 | Q8×Dic5 | direct (N × H) |
| 116. C2×C5 | C4×C5×Q8 | semidirect |
| 124. Q8 | C2×C5×Dic5 | direct (N × H) |
| 132. C5 | C2×Q8×Dic5 | direct (N × H) |
| 133. C5 | C2×C4×C5×Q8 | semidirect |
| 141. C2 | C5×Q8×Dic5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C5×Q8×Dic5 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C4×C5×Q8 | 5 |
| C2×Q8×Dic5 | 5 |