Finite Group Databasebeta

← C52×#585 #13107901

Subgroups — C52×#585 #13107901

Order 1600.

3240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C52×2−1+4C216yesmaximal, complemented
2C52×H(5,𝔽2)C2110yesmaximal, complemented
3C2×C52×#41C2115yesmaximal, complemented
4C52×#41C22120yescomplemented
5C52×#41C22160yescomplemented
6C2×C52×Q8C22115yescomplemented
7C2×C52×D4C22145yescomplemented
8C22×C4×C52C22115yescomplemented
9C5×#585C516yesmaximal, direct product factor
10C23×C52C23115yes—
11C52×Q8C23120yes—
12C52×D4C23160yes—
13C2×C4×C52C23145yes—
14C2×C4×C52C23115yes—
15C5×2−1+4C2×C5136yescomplemented
16C5×H(5,𝔽2)C2×C5160yescomplemented
17C2×C5×#41C2×C5190yescomplemented
18C22×C52—415no—
19C22×C52C24115yes—
20C4×C52C24115yes—
21C4×C52C2411yescharacteristic
22C5×#41C22×C51120yescomplemented
23C5×#41C22×C51360yescomplemented
24C2×C5×Q8C22×C5190yescomplemented
25C2×C5×D4C22×C51270yescomplemented
26C22×C4×C5C22×C5190yescomplemented
27#585C5211yescharacteristic, direct product factor, Sylow
28C2×C52—215no—
29C2×C52C2511yescharacteristic
30C23×C5C23×C5190yes—
31C5×Q8C23×C51120yes—
32C5×D4C23×C51360yes—
33C2×C4×C5C23×C5190yes—
34C2×C4×C5C23×C51270yes—
352−1+4C2×C5216yescomplemented
36H(5,𝔽2)C2×C52110yescomplemented
37C2×#41C2×C52115yescomplemented
38C52#58511yescharacteristic, direct product factor, Sylow
39C22×C5—490no—
40C22×C5C24×C5190yes—
41C4×C5C24×C5190yes—
42C4×C5C24×C516yes—
43#41C22×C52120yescomplemented
44#41C22×C52160yescomplemented
45C2×Q8C22×C52115yescomplemented
46C2×D4C22×C52145yescomplemented
47C22×C4C22×C52115yescomplemented
48C2×C5—290no—
49C2×C5C25×C516yes—
50C23C23×C52115yes—
51Q8C23×C52120yes—
52D4C23×C52160yes—
53C2×C4C23×C52115yes—
54C2×C4C23×C52145yes—
55C5C5×#58516yesdirect product factor
56C22—415no—
57C22C24×C52115yes—
58C4C24×C5211yescharacteristic
59C4C24×C52115yes—
60C2—215no—
61C2C25×C5211yescharacteristic
subgroupG/H
centerC4×C52C24
commutator, Frattini, cosocleC2C25×C52
socleC2×C52C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C52 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C52×2−1+4C2semidirect
2. C52×H(5,𝔽2)C2semidirect
3. C2×C52×#41C2semidirect
4. C52×#41C22semidirect
5. C52×#41C22semidirect
6. C2×C52×Q8C22semidirect
7. C2×C52×D4C22semidirect
8. C22×C4×C52C22semidirect
9. C5×#585C5direct (N × H)
15. C5×2−1+4C2×C5semidirect
16. C5×H(5,𝔽2)C2×C5semidirect
17. C2×C5×#41C2×C5semidirect
22. C5×#41C22×C5semidirect
23. C5×#41C22×C5semidirect
24. C2×C5×Q8C22×C5semidirect
25. C2×C5×D4C22×C5semidirect
26. C22×C4×C5C22×C5semidirect
27. #585C52direct (N × H)
35. 2−1+4C2×C52semidirect
36. H(5,𝔽2)C2×C52semidirect
37. C2×#41C2×C52semidirect
38. C52#585direct (N × H)
43. #41C22×C52semidirect
44. #41C22×C52semidirect
45. C2×Q8C22×C52semidirect
46. C2×D4C22×C52semidirect
47. C22×C4C22×C52semidirect
55. C5C5×#585direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C52×2−1+42
C52×H(5,𝔽2)2
C2×C52×#412
C5×#5855