Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×D4×C25 | C2 | semidirect |
| 2. C2×#87722 | C2 | semidirect |
| 3. #11716436 | C2 | semidirect |
| 4. #11716358 | C2 | semidirect |
| 5. C4⋊#6014 | C2 | semidirect |
| 20. D4×C25 | D4 | semidirect |
| 45. C4×C25 | D8 | semidirect |
| 80. C4×D4 | D25 | semidirect |
| 83. C25 | #459 | semidirect |
| 118. D4 | D100 | semidirect |
| 135. C4 | #87722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C25 | 2 |
| C2×#87722 | 2 |
| #11716436 | 2 |
| #11716358 | 2 |
| C4⋊#6014 | 2 |
| #65304 | 5 |