Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
378 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11717217 | C2 | semidirect |
| 3. C2×#87776 | C2 | semidirect |
| 4. C2×#87773 | C2 | semidirect |
| 5. C5×#3942 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. #11716598 | C2 | semidirect |
| 57. #3942 | D5 | semidirect |
| 58. #3941 | D5 | semidirect |
| 167. C52 | #452 | semidirect |
| 252. C5 | #65072 | semidirect |
| 253. C5 | #65099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| #11717217 | 2 |
| C2×#87776 | 2 |
| C2×#87773 | 2 |
| C5×#3942 | 2 |
| C5×#3941 | 2 |
| #11716598 | 2 |
| #65099 | 5 |
| #65072 | 5 |