Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
302 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. C2×#87776 | C2 | semidirect |
| 5. C5×#3942 | C2 | semidirect |
| 6. C5×#3939 | C2 | semidirect |
| 7. #11716608 | C2 | semidirect |
| 51. #3942 | D5 | semidirect |
| 52. #3939 | D5 | semidirect |
| 56. C2×C5⋊D5 | Q16 | semidirect |
| 146. C52 | #467 | semidirect |
| 219. C5 | #65102 | semidirect |
| 220. C5 | #65176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717217 | 2 |
| #11716990 | 2 |
| C2×#87776 | 2 |
| C2×#87767 | 2 |
| C5×#3942 | 2 |
| C5×#3939 | 2 |
| #11716608 | 2 |
| #65176 | 5 |
| #65102 | 5 |