Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
322 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 72 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×C5×C4⋊Dic5 | C2 | semidirect |
| 3. C5×C22⋊#168 | C2 | semidirect |
| 4. #11716616 | C2 | semidirect |
| 5. #11716605 | C2 | semidirect |
| 32. C2×C4⋊Dic5 | D5 | semidirect |
| 34. C22⋊#168 | D5 | semidirect |
| 114. C52 | #480 | semidirect |
| 183. C5 | #65025 | semidirect |
| 184. C5 | #65256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717250 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×C22⋊#168 | 2 |
| #11716616 | 2 |
| #11716605 | 2 |
| #65256 | 5 |
| #65025 | 5 |