Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1320 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 295 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 | C22×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Frattini | C22 | C23×C5⋊D5 |
| Fitting | C2×C52×#41 | C2 |
| hypercenter | C2×#41 | C5⋊D5 |
| hypocenter | C52 | #525 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C52×#41 | C2 | semidirect |
| 2. C22×C4×C5⋊D5 | C2 | semidirect |
| 3. #11717266 | C2 | semidirect |
| 4. #11717258 | C2 | semidirect |
| 5. #11717257 | C2 | semidirect |
| 6. #11717255 | C2 | semidirect |
| 7. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 8. #11717246 | C2 | semidirect |
| 11. C2×C52×Q8 | C22 | semidirect |
| 13. C2×C52×D4 | C22 | semidirect |
| 15. C22×C4×C52 | C22 | semidirect |
| 22. C22⋊#1039 | C22 | semidirect |
| 24. C4⋊#1039 | C22 | semidirect |
| 25. #87806 | C22 | semidirect |
| 26. C4×#1039 | C22 | semidirect |
| 37. C2×C4×C52 | D4 | semidirect |
| 47. C2×C5×#41 | D5 | semidirect |
| 63. C2×C5⋊D5 | #41 | semidirect |
| 71. C2×C5×Q8 | C2×D5 | semidirect |
| 73. C2×C5×D4 | C2×D5 | semidirect |
| 75. C22×C4×C5 | C2×D5 | semidirect |
| 102. C2×C4×C5 | C22⋊D5 | semidirect |
| 112. C2×#41 | C5⋊D5 | semidirect |
| 120. C52 | #525 | semidirect |
| 137. C2×Q8 | C2×C5⋊D5 | semidirect |
| 140. C2×D4 | C2×C5⋊D5 | semidirect |
| 146. C22×C4 | C2×C5⋊D5 | semidirect |
| 173. C2×C4 | C22⋊(C5⋊D5) | semidirect |
| 177. C5 | #66162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C22×C4×C5⋊D5 | 2 |
| #11717266 | 2 |
| #11717258 | 2 |
| #11717257 | 2 |
| #11717255 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717246 | 2 |
| #66162 | 5 |