Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
536 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 232 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 |
| 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 |
|---|---|---|
| 1. C2×C52×D8 | C2 | semidirect |
| 2. C22×C52×C8 | C2 | semidirect |
| 3. C52×#121 | C2 | semidirect |
| 4. C52×#107 | C2 | semidirect |
| 5. C52×#102 | C2 | semidirect |
| 15. C5×#466 | C5 | direct (N × H) |
| 27. C52×C8 | D4 | semidirect |
| 28. C2×C5×D8 | C2×C5 | semidirect |
| 29. C22×C5×C8 | C2×C5 | semidirect |
| 30. C5×#121 | C2×C5 | semidirect |
| 31. C5×#107 | C2×C5 | semidirect |
| 32. C5×#102 | C2×C5 | semidirect |
| 38. C22×C52 | D8 | semidirect |
| 53. #466 | C52 | direct (N × H) |
| 70. C5×C8 | C5×D4 | semidirect |
| 71. C2×D8 | C2×C52 | semidirect |
| 72. C22×C8 | C2×C52 | semidirect |
| 73. #121 | C2×C52 | semidirect |
| 74. #107 | C2×C52 | semidirect |
| 75. #102 | C2×C52 | semidirect |
| 76. C52 | #466 | direct (N × H) |
| 82. C22×C5 | C5×D8 | semidirect |
| 113. C8 | C52×D4 | semidirect |
| 114. C5 | C5×#466 | direct (N × H) |
| 120. C22 | C52×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×D8 | 2 |
| C22×C52×C8 | 2 |
| C52×#121 | 2 |
| C52×#107 | 2 |
| C52×#102 | 2 |
| C5×#466 | 5 |