Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
366 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C52×#103 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3948 | C2 | semidirect |
| 7. C5×#3942 | C2 | semidirect |
| 10. C5×Q8×D5 | C4 | semidirect |
| 23. D5×#103 | C5 | direct (N × H) |
| 26. C52×Q8 | C2×C4 | semidirect |
| 39. C5×Dic10 | C2×C4 | semidirect |
| 52. C5×#103 | D5 | direct (N × H) |
| 53. C5×#103 | C2×C5 | semidirect |
| 54. #3967 | C2×C5 | semidirect |
| 55. #3948 | C2×C5 | semidirect |
| 56. #3942 | C2×C5 | semidirect |
| 79. Q8×D5 | C4×C5 | semidirect |
| 103. C5×D5 | #103 | direct (N × H) |
| 113. C5×Q8 | C4×D5 | semidirect |
| 114. C5×Q8 | C2×C4×C5 | semidirect |
| 140. Dic10 | C2×C4×C5 | semidirect |
| 152. #103 | C5×D5 | direct (N × H) |
| 153. C52 | C2×#103 | semidirect |
| 205. D5 | C5×#103 | direct (N × H) |
| 211. Q8 | C4×C5×D5 | semidirect |
| 225. C5 | D5×#103 | direct (N × H) |
| 226. C5 | C2×C5×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C5×C8×D5 | 2 |
| C5×D5×C4⋊C4 | 2 |
| C52×#103 | 2 |
| C5×#3967 | 2 |
| C5×#3948 | 2 |
| C5×#3942 | 2 |
| C2×C5×#103 | 5 |
| D5×#103 | 5 |