Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
399 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 399 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×D5⋊M16 | C2 | semidirect |
| 4. #11716757 | C2 | semidirect |
| 14. #87853 | C22 | semidirect |
| 17. C5×#704 | C22 | semidirect |
| 45. D5⋊M16 | D5 | semidirect |
| 84. #704 | C2×D5 | semidirect |
| 101. C5×D5 | #100 | semidirect |
| 150. C52 | C2×#100 | semidirect |
| 213. D5 | #3955 | semidirect |
| 235. C5 | C2×#3955 | semidirect |
| 236. C5 | D5⋊#100 | 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×D5⋊M16 | 2 |
| #11716757 | 2 |
| D5⋊#100 | 5 |
| C2×#3955 | 5 |