Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
772 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D52⋊C2 |
| commutator | C5⋊D5 | C23×C4 |
| Frattini | C2 | C22×D52⋊C2 |
| Fitting, socle | C23×C52 | D4 |
| prime radical | C23×C5⋊D5 | C22 |
| cosocle | C2×C5⋊D5 | C24 |
| hypocenter | C52 | C22×C4⋊C4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#87836 | C2 | direct (N × H) |
| 5. C22×#1044 | C4 | semidirect |
| 10. #87836 | C22 | direct (N × H) |
| 16. C2×#1044 | C2×C4 | semidirect |
| 23. C22×C52 | C4⋊C4 | semidirect |
| 25. C2×C5⋊D5 | C4⋊C4 | semidirect |
| 30. #1044 | C22×C4 | semidirect |
| 41. C2×C52 | C2×C4⋊C4 | semidirect |
| 43. C5⋊D5 | C2×C4⋊C4 | semidirect |
| 65. C52 | C22×C4⋊C4 | semidirect |
| 117. C22 | #87836 | direct (N × H) |
| 124. C2 | C2×#87836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1044 | 2 |
| C22×#6036 | 2 |
| C2×#87836 | 2 |
| C22×C4⋊C4 | 25 |