Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11717448 | C2 | semidirect |
| 3. #11717438 | C2 | semidirect |
| 4. #11716770 | C2 | semidirect |
| 6. C2×C5×D20 | C4 | semidirect |
| 7. C2×C5×Dic10 | C4 | semidirect |
| 12. #87871 | C4 | semidirect |
| 15. #87863 | C22 | semidirect |
| 19. C4×#1043 | C22 | semidirect |
| 75. C2×D20 | AGL(1,𝔽5) | semidirect |
| 80. C2×Dic10 | AGL(1,𝔽5) | semidirect |
| 152. C52 | #421 | semidirect |
| 235. C5 | #65769 | semidirect |
| 236. C5 | #65784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| #11717448 | 2 |
| #11717438 | 2 |
| #11716770 | 2 |
| #65784 | 5 |
| #65769 | 5 |