Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
416 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 111 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. C52×#107 | C2 | semidirect |
| 5. #11716683 | C2 | semidirect |
| 6. #11716677 | C2 | semidirect |
| 7. #11716674 | C2 | semidirect |
| 36. C5×#107 | D5 | semidirect |
| 85. #107 | C5⋊D5 | semidirect |
| 89. C52 | #484 | semidirect |
| 130. C5 | #65173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717217 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| C52×#107 | 2 |
| #11716687 | 2 |
| #11716683 | 2 |
| #11716677 | 2 |
| #11716674 | 2 |
| #65173 | 5 |