Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
246 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 246 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 |
|---|---|---|
| 4. #11716743 | C2 | semidirect |
| 5. #11716742 | C2 | semidirect |
| 14. #87804 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. #87768 | C4 | semidirect |
| 31. #6029 | C2×C4 | semidirect |
| 32. C5×#168 | C2×C4 | semidirect |
| 76. #681 | AGL(1,𝔽5) | semidirect |
| 113. #168 | C2×AGL(1,𝔽5) | semidirect |
| 119. C52 | #428 | semidirect |
| 185. C5 | #65284 | semidirect |
| 186. C5 | #65727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1042 | 2 |
| C5×#4130 | 2 |
| D5×#681 | 2 |
| #11716743 | 2 |
| #11716742 | 2 |
| #65727 | 5 |
| #65284 | 5 |