Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
808 conjugacy classes of subgroups; only the 392 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 392 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C52 | D4 |
| commutator | C4 | C22×C4×C52 |
| Frattini, cosocle | C2×C4 | C23×C52 |
| prime radical | C22×C52×D4 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C52 ◁ C22×C4×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C52×C8 | C2 | semidirect |
| 3. C2×C52×C4⋊C4 | C2 | semidirect |
| 4. C52×#102 | C2 | direct (N × H) |
| 8. C2×C52×D4 | C4 | semidirect |
| 13. C2×C52×C8 | C22 | semidirect |
| 15. C52×C4⋊C4 | C22 | semidirect |
| 16. C2×C5×#102 | C5 | direct (N × H) |
| 24. C52×D4 | C2×C4 | semidirect |
| 33. C22×C5×C8 | C2×C5 | semidirect |
| 34. C2×C5×C4⋊C4 | C2×C5 | semidirect |
| 35. C5×#102 | C2×C5 | direct (N × H) |
| 51. C2×C5×D4 | C4×C5 | semidirect |
| 56. C2×C5×C8 | C22×C5 | semidirect |
| 58. C5×C4⋊C4 | C22×C5 | semidirect |
| 59. C2×#102 | C52 | direct (N × H) |
| 61. C2×C52 | #102 | direct (N × H) |
| 72. C5×D4 | C2×C4×C5 | semidirect |
| 81. C22×C8 | C2×C52 | semidirect |
| 82. C2×C4⋊C4 | C2×C52 | semidirect |
| 83. #102 | C2×C52 | direct (N × H) |
| 84. C52 | C2×#102 | direct (N × H) |
| 100. C2×D4 | C4×C52 | semidirect |
| 105. C2×C8 | C22×C52 | semidirect |
| 107. C4⋊C4 | C22×C52 | semidirect |
| 109. C2×C5 | C5×#102 | direct (N × H) |
| 120. D4 | C2×C4×C52 | semidirect |
| 128. C5 | C2×C5×#102 | direct (N × H) |
| 142. C2 | C52×#102 | 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 |
| C22×C52×C8 | 2 |
| C2×C52×C4⋊C4 | 2 |
| C52×#102 | 2 |
| C2×C5×#102 | 5 |