Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
407 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 407 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 |
|---|---|---|
| 2. D5⋊#681 | C2 | semidirect |
| 3. C5×#4130 | C2 | semidirect |
| 4. #11716734 | C2 | semidirect |
| 6. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 7. C2×C5×D20 | C4 | semidirect |
| 12. D5×D20 | C4 | semidirect |
| 16. D5⋊#168 | C22 | semidirect |
| 18. C5×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 44. #4130 | D5 | semidirect |
| 82. C2×D20 | AGL(1,𝔽5) | semidirect |
| 86. C4⋊AGL(1,𝔽5) | C2×D5 | semidirect |
| 151. C52 | #418 | semidirect |
| 238. C5 | #65290 | semidirect |
| 239. C5 | #65767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| D5⋊#681 | 2 |
| C5×#4130 | 2 |
| #11716734 | 2 |
| #65767 | 5 |
| #65290 | 5 |