Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
183 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C25 | D4 |
| commutator | C4 | C22×C4×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C22×C5 | C2×C5×D4 |
| prime radical | C2×C5×D4 | C22×C5 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C25 ◁ C42×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Q8×C25 | C2 | semidirect |
| 4. C25×#106 | C2 | semidirect |
| 5. C25×#103 | C2 | semidirect |
| 7. C4×C8×C25 | C2 | semidirect |
| 11. SD16×C25 | C4 | direct (N × H) |
| 23. Q8×C25 | C2×C4 | semidirect |
| 34. C8×C25 | C2×C4 | semidirect |
| 50. C4×C25 | SD16 | direct (N × H) |
| 65. C4×SD16 | C25 | direct (N × H) |
| 85. C4×Q8 | C2×C25 | semidirect |
| 87. #106 | C2×C25 | semidirect |
| 88. #103 | C2×C25 | semidirect |
| 90. C4×C8 | C2×C25 | semidirect |
| 91. C25 | C4×SD16 | direct (N × H) |
| 106. SD16 | C4×C25 | direct (N × H) |
| 121. Q8 | C2×C4×C25 | semidirect |
| 132. C8 | C2×C4×C25 | semidirect |
| 142. C4 | SD16×C25 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C25 | 2 |
| C4×Q8×C25 | 2 |
| C4×D4×C25 | 2 |
| C25×#106 | 2 |
| C25×#103 | 2 |
| C25×#102 | 2 |
| C4×C8×C25 | 2 |
| C4×C5×SD16 | 5 |