Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
448 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 1. C5×#4144 | C2 | semidirect |
| 2. C5×#4083 | C2 | semidirect |
| 3. C5×#4028 | C2 | semidirect |
| 4. C52×#99 | C2 | semidirect |
| 5. C5×#3938 | C2 | semidirect |
| 6. C23×C5×D5 | C22 | semidirect |
| 15. C52×C22⋊C4 | C22 | semidirect |
| 16. C5×C22⋊Dic5 | C22 | semidirect |
| 20. #65030 | C5 | direct (N × H) |
| 21. C23×C52 | D4 | semidirect |
| 27. C22×C5×D5 | D4 | semidirect |
| 30. C2×C4×C52 | D4 | semidirect |
| 37. C2×C5×Dic5 | D4 | semidirect |
| 43. #4144 | C2×C5 | semidirect |
| 46. #4083 | C2×C5 | semidirect |
| 47. #4028 | C2×C5 | semidirect |
| 50. C5×#99 | D5 | semidirect |
| 51. C5×#99 | C2×C5 | semidirect |
| 52. #3938 | C2×C5 | semidirect |
| 71. C23×D5 | C22×C5 | semidirect |
| 93. C5×C22⋊C4 | C2×D5 | semidirect |
| 94. C5×C22⋊C4 | C22×C5 | semidirect |
| 95. C22⋊Dic5 | C22×C5 | semidirect |
| 112. C23×C5 | D20 | semidirect |
| 113. C23×C5 | C5×D4 | semidirect |
| 120. C22×D5 | C5×D4 | semidirect |
| 139. C2×C4×C5 | D20 | semidirect |
| 140. C2×C4×C5 | C5×D4 | semidirect |
| 147. C2×Dic5 | C5×D4 | semidirect |
| 156. #99 | C5×D5 | semidirect |
| 157. C52 | B(4,𝔽2) | semidirect |
| 211. C22⋊C4 | C2×C5×D5 | semidirect |
| 233. C23 | C5×D20 | semidirect |
| 248. C2×C4 | C5×D20 | semidirect |
| 250. C5 | #65030 | direct (N × H) |
| 251. C5 | C5×B(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4144 | 2 |
| C5×#4083 | 2 |
| C5×#4028 | 2 |
| C52×#99 | 2 |
| C5×#3938 | 2 |
| C5×B(4,𝔽2) | 5 |
| #65030 | 5 |