Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1240 conjugacy classes of subgroups; only the 615 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 615 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. Q8×#1039 | C2 | semidirect |
| 3. D4×#1039 | C2 | semidirect |
| 4. #11717246 | C2 | semidirect |
| 5. C2×C4×#1039 | C2 | semidirect |
| 6. C52×#41 | C4 | semidirect |
| 18. C52×Q8 | C2×C4 | semidirect |
| 19. C52×D4 | C2×C4 | semidirect |
| 20. C2×C4×C52 | C2×C4 | semidirect |
| 37. #1039 | #41 | direct (N × H) |
| 38. C5×#41 | Dic5 | semidirect |
| 53. C5×Q8 | C2×Dic5 | semidirect |
| 54. C5×D4 | C2×Dic5 | semidirect |
| 55. C2×C4×C5 | C2×Dic5 | semidirect |
| 66. C52 | C4×#41 | semidirect |
| 74. #41 | #1039 | direct (N × H) |
| 88. Q8 | C2×#1039 | semidirect |
| 89. D4 | C2×#1039 | semidirect |
| 93. C2×C4 | C2×#1039 | semidirect |
| 96. C5 | #41×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| Q8×#1039 | 2 |
| D4×#1039 | 2 |
| #11717246 | 2 |
| C2×C4×#1039 | 2 |
| #41×Dic5 | 5 |