Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C5×#4076 | C2 | semidirect |
| 3. C2×#87771 | C2 | semidirect |
| 4. C5×C22⋊#168 | C2 | semidirect |
| 5. #11716605 | C2 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 14. C5×C4⋊Dic5 | C22 | semidirect |
| 15. C2×C5×#168 | C22 | semidirect |
| 30. C4⋊(C5⋊D5) | D4 | semidirect |
| 40. #4076 | D5 | semidirect |
| 43. C22⋊#168 | D5 | semidirect |
| 48. C22×C52 | D8 | semidirect |
| 78. C2×D20 | C2×D5 | semidirect |
| 84. C4⋊Dic5 | C2×D5 | semidirect |
| 85. C2×#168 | C2×D5 | semidirect |
| 142. C52 | #447 | semidirect |
| 154. C22×C5 | D40 | semidirect |
| 155. C22×C5 | #686 | semidirect |
| 226. C5 | #65021 | semidirect |
| 227. C5 | #65325 | semidirect |
| 237. C22 | #87771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C5×#4076 | 2 |
| C2×#87771 | 2 |
| C5×C22⋊#168 | 2 |
| #11716605 | 2 |
| #65325 | 5 |
| #65021 | 5 |