Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
744 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 328 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C52 | C22⋊C4 |
| commutator | C22 | C22×C4×C52 |
| Frattini, cosocle | C2×C4 | C23×C52 |
| prime radical | C22×C52×D4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ C22×C4×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C52×M16 | C2 | semidirect |
| 3. C52×#100 | C2 | direct (N × H) |
| 11. C52×M16 | C22 | semidirect |
| 13. C2×C5×#100 | C5 | direct (N × H) |
| 27. C2×C5×M16 | C2×C5 | semidirect |
| 28. C5×#100 | C2×C5 | direct (N × H) |
| 46. C5×M16 | C22×C5 | semidirect |
| 48. C2×#100 | C52 | direct (N × H) |
| 52. C2×C52 | #100 | direct (N × H) |
| 67. C2×M16 | C2×C52 | semidirect |
| 68. #100 | C2×C52 | direct (N × H) |
| 69. C52 | C2×#100 | direct (N × H) |
| 87. M16 | C22×C52 | semidirect |
| 92. C2×C5 | C5×#100 | direct (N × H) |
| 106. C5 | C2×C5×#100 | direct (N × H) |
| 120. C2 | C52×#100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C52×M16 | 2 |
| C52×#100 | 2 |
| C2×C5×#100 | 5 |