Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
424 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C52 |
| prime radical | C52×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ 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. C52×#117 | C2 | semidirect |
| 3. C52×#107 | C2 | semidirect |
| 4. C52×#106 | C2 | semidirect |
| 5. C52×#102 | C2 | semidirect |
| 6. C52×#102 | C2 | semidirect |
| 7. C52×C22⋊C8 | C2 | semidirect |
| 19. C5×#482 | C5 | direct (N × H) |
| 35. C5×#117 | C2×C5 | semidirect |
| 36. C5×#107 | C2×C5 | semidirect |
| 37. C5×#106 | C2×C5 | semidirect |
| 38. C5×#102 | C2×C5 | semidirect |
| 39. C5×#102 | C2×C5 | semidirect |
| 40. C5×C22⋊C8 | C2×C5 | semidirect |
| 65. #482 | C52 | direct (N × H) |
| 86. #117 | C2×C52 | semidirect |
| 87. #107 | C2×C52 | semidirect |
| 88. #106 | C2×C52 | semidirect |
| 89. #102 | C2×C52 | semidirect |
| 90. #102 | C2×C52 | semidirect |
| 91. C22⋊C8 | C2×C52 | semidirect |
| 92. C52 | #482 | direct (N × H) |
| 136. C5 | C5×#482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#121 | 2 |
| C52×#117 | 2 |
| C52×#107 | 2 |
| C52×#106 | 2 |
| C52×#102 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#482 | 5 |