Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×C22⋊#1042 | C2 | semidirect |
| 3. #11716854 | C2 | semidirect |
| 4. #11716842 | C2 | semidirect |
| 5. C23×C5×D5 | C4 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 9. C2×C5×C22⋊D5 | C4 | semidirect |
| 14. C2×C4×C5×D5 | C4 | semidirect |
| 16. C22⋊#1042 | C22 | semidirect |
| 20. C23×C52 | C2×C4 | semidirect |
| 26. C22×C5×D5 | C2×C4 | semidirect |
| 33. C2×C4×C52 | C2×C4 | semidirect |
| 36. C2×C5×Dic5 | C2×C4 | semidirect |
| 69. C23×D5 | Dic5 | semidirect |
| 78. C2×C5×D4 | Dic5 | semidirect |
| 79. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 81. C2×C22⋊D5 | Dic5 | semidirect |
| 87. C2×C4×D5 | Dic5 | semidirect |
| 100. C5×D5 | #99 | semidirect |
| 113. C23×C5 | C2×Dic5 | semidirect |
| 115. C23×C5 | C2×AGL(1,𝔽5) | semidirect |
| 121. C22×D5 | C2×Dic5 | semidirect |
| 137. C2×C4×C5 | C2×Dic5 | semidirect |
| 138. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 143. C2×Dic5 | C2×Dic5 | semidirect |
| 151. C52 | C2×#99 | semidirect |
| 203. C2×D4 | #1042 | semidirect |
| 227. D5 | #3966 | semidirect |
| 238. C23 | C2×#1042 | semidirect |
| 248. C2×C4 | C2×#1042 | semidirect |
| 250. C5 | C2×#3966 | semidirect |
| 251. C5 | D5⋊#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C2×C22⋊#1042 | 2 |
| #11716854 | 2 |
| #11716842 | 2 |
| D5⋊#99 | 5 |
| C2×#3966 | 5 |