Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 78 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. C52×C4⋊Q8 | C2 | semidirect |
| 3. C5×#4088 | C2 | semidirect |
| 4. C5×#3968 | C2 | semidirect |
| 5. C5×#3937 | C2 | semidirect |
| 18. #65384 | C5 | direct (N × H) |
| 37. C5×C4⋊Q8 | D5 | semidirect |
| 38. C5×C4⋊Q8 | C2×C5 | semidirect |
| 39. #4088 | C2×C5 | semidirect |
| 42. #3968 | C2×C5 | semidirect |
| 43. #3937 | C2×C5 | semidirect |
| 117. C4⋊Q8 | C5×D5 | semidirect |
| 120. C52 | #456 | semidirect |
| 174. C5 | #65384 | direct (N × H) |
| 175. C5 | C5×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4147 | 2 |
| C52×C4⋊Q8 | 2 |
| C5×#4088 | 2 |
| C5×#3968 | 2 |
| C5×#3937 | 2 |
| C5×#456 | 5 |
| #65384 | 5 |