Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
224 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D52 |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C8 | C2×D52 |
| Fitting | C2×C52×C8 | C22 |
| socle | C22×C52 | C2×C8 |
| prime radical | C22×C5×D5 | C8 |
| cosocle | C52×C8 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#87756 | C2 | semidirect |
| 3. C2×C5×#672 | C2 | semidirect |
| 4. D5×#672 | C2 | direct (N × H) |
| 10. #87756 | C22 | semidirect |
| 11. C5×#672 | C22 | semidirect |
| 29. C2×#672 | D5 | direct (N × H) |
| 32. C2×C5×D5 | C16 | semidirect |
| 52. #672 | C2×D5 | direct (N × H) |
| 54. C2×C52 | C2×C16 | semidirect |
| 56. C5×D5 | C2×C16 | semidirect |
| 80. C52 | C22×C16 | semidirect |
| 86. C2×D5 | #672 | direct (N × H) |
| 106. C2×C5 | D5×C16 | semidirect |
| 107. C2×C5 | C2×#672 | semidirect |
| 110. D5 | C2×#672 | direct (N × H) |
| 120. C5 | C2×D5×C16 | semidirect |
| 121. C5 | C22×#672 | semidirect |
| 129. C2 | D5×#672 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×D5 | 2 |
| C2×#87756 | 2 |
| C2×C5×#672 | 2 |
| D5×#672 | 2 |
| C22×#672 | 5 |
| C2×D5×C16 | 5 |