Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1176 conjugacy classes of subgroups; only the 611 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 611 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator | C2×C52 | C23×C4 |
| Fitting, prime radical | C2×C52×#41 | C2 |
| socle, cosocle | C22×C52 | C24 |
| hypercenter | C2×#41 | C5⋊D5 |
| hypocenter | C52 | #520 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×#1039 | C2 | semidirect |
| 3. D4×#1039 | C2 | semidirect |
| 4. #11717246 | C2 | semidirect |
| 5. C2×C4⋊#1039 | C2 | semidirect |
| 6. C52×#41 | C4 | semidirect |
| 18. C52×Q8 | C2×C4 | semidirect |
| 19. C52×D4 | C2×C4 | semidirect |
| 20. C2×C4×C52 | C2×C4 | semidirect |
| 39. C5×#41 | Dic5 | semidirect |
| 55. C5×Q8 | C2×Dic5 | semidirect |
| 56. C5×D4 | C2×Dic5 | semidirect |
| 57. C2×C4×C5 | C2×Dic5 | semidirect |
| 68. C52 | #520 | semidirect |
| 77. #41 | #1039 | semidirect |
| 92. Q8 | C2×#1039 | semidirect |
| 93. D4 | C2×#1039 | semidirect |
| 97. C2×C4 | C2×#1039 | semidirect |
| 100. C5 | #66161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| Q8×#1039 | 2 |
| D4×#1039 | 2 |
| #11717246 | 2 |
| C2×C4⋊#1039 | 2 |
| #66161 | 5 |