Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 220 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 | semidirect |
| 5. #11716962 | C2 | semidirect |
| 7. Q8×C5⋊D5 | C4 | semidirect |
| 18. C52×Q8 | C2×C4 | semidirect |
| 22. #6045 | C2×C4 | semidirect |
| 26. #6036 | Q8 | direct (N × H) |
| 30. Q8×Dic5 | D5 | semidirect |
| 42. C5×Dic5 | C2×Q8 | semidirect |
| 64. C5⋊D5 | C4×Q8 | semidirect |
| 68. C5×Q8 | C4×D5 | semidirect |
| 88. C52 | C2×C4×Q8 | semidirect |
| 104. Dic5 | Q8×D5 | semidirect |
| 125. Q8 | #6036 | direct (N × H) |
| 134. C5 | C4×Q8×D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C5×Q8×Dic5 | 2 |
| #11717018 | 2 |
| C4×#6036 | 2 |
| #11716962 | 2 |
| C4×Q8×D5 | 5 |