Finite Group Databasebeta

← C2×C3×C4×C5×C29 #72183153

Subgroups — C2×C3×C4×C5×C29 #72183153

Order 3480.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C29C211yesmaximal, characteristic
2C3×C4×C5×C29C212yesmaximal, direct product factor
3C2×C4×C5×C29C311yesmaximal, characteristic, direct product factor, Hall
4C2×C3×C5×C29C412yesdirect product factor
5C2×C3×C5×C29C2211yescharacteristic
6C2×C3×C4×C29C511yesmaximal, characteristic, direct product factor, Hall
7C22×C5×C29C2×C311yescharacteristic
8C4×C5×C29C2×C312yesdirect product factor
9C3×C5×C29C2×C411yescharacteristic, direct product factor, Hall
10C22×C3×C29C2×C511yescharacteristic
11C3×C4×C29C2×C512yesdirect product factor
12C2×C5×C29C3×C412yesdirect product factor
13C2×C5×C29C22×C311yescharacteristic
14C2×C4×C29C3×C511yescharacteristic, direct product factor, Hall
15C2×C3×C29C4×C512yesdirect product factor
16C2×C3×C29C22×C511yescharacteristic
17C5×C29C2×C3×C411yescharacteristic, direct product factor, Hall
18C2×C3×C4×C5C2911yesmaximal, characteristic, direct product factor, Hall
19C22×C29C2×C3×C511yescharacteristic
20C4×C29C2×C3×C512yesdirect product factor
21C3×C29C2×C4×C511yescharacteristic, direct product factor, Hall
22C22×C3×C5C2×C2911yescharacteristic
23C3×C4×C5C2×C2912yesdirect product factor
24C2×C29C3×C4×C512yesdirect product factor
25C2×C29C22×C3×C511yescharacteristic
26C2×C4×C5C3×C2911yescharacteristic, direct product factor, Hall
27C2×C3×C5C4×C2912yesdirect product factor
28C2×C3×C5C22×C2911yescharacteristic
29C29C2×C3×C4×C511yescharacteristic, direct product factor, Sylow
30C2×C3×C4C5×C2911yescharacteristic, direct product factor, Hall
31C22×C5C2×C3×C2911yescharacteristic
32C4×C5C2×C3×C2912yesdirect product factor
33C3×C5C2×C4×C2911yescharacteristic, direct product factor, Hall
34C22×C3C2×C5×C2911yescharacteristic
35C3×C4C2×C5×C2912yesdirect product factor
36C2×C5C3×C4×C2912yesdirect product factor
37C2×C5C22×C3×C2911yescharacteristic
38C2×C4C3×C5×C2911yescharacteristic, direct product factor, Sylow
39C2×C3C4×C5×C2912yesdirect product factor
40C2×C3C22×C5×C2911yescharacteristic
41C5C2×C3×C4×C2911yescharacteristic, direct product factor, Sylow
42C22C2×C3×C5×C2911yescharacteristic
43C4C2×C3×C5×C2912yesdirect product factor
44C3C2×C4×C5×C2911yescharacteristic, direct product factor, Sylow
45C2C3×C4×C5×C2912yesdirect product factor
46C2C22×C3×C5×C2911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C5×C29
socle, prime radicalC22×C3×C5×C29C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C29C2direct (N × H)
3. C2×C4×C5×C29C3direct (N × H)
4. C2×C3×C5×C29C4direct (N × H)
6. C2×C3×C4×C29C5direct (N × H)
8. C4×C5×C29C2×C3direct (N × H)
9. C3×C5×C29C2×C4direct (N × H)
11. C3×C4×C29C2×C5direct (N × H)
12. C2×C5×C29C3×C4direct (N × H)
14. C2×C4×C29C3×C5direct (N × H)
15. C2×C3×C29C4×C5direct (N × H)
17. C5×C29C2×C3×C4direct (N × H)
18. C2×C3×C4×C5C29direct (N × H)
20. C4×C29C2×C3×C5direct (N × H)
21. C3×C29C2×C4×C5direct (N × H)
23. C3×C4×C5C2×C29direct (N × H)
24. C2×C29C3×C4×C5direct (N × H)
26. C2×C4×C5C3×C29direct (N × H)
27. C2×C3×C5C4×C29direct (N × H)
29. C29C2×C3×C4×C5direct (N × H)
30. C2×C3×C4C5×C29direct (N × H)
32. C4×C5C2×C3×C29direct (N × H)
33. C3×C5C2×C4×C29direct (N × H)
35. C3×C4C2×C5×C29direct (N × H)
36. C2×C5C3×C4×C29direct (N × H)
38. C2×C4C3×C5×C29direct (N × H)
39. C2×C3C4×C5×C29direct (N × H)
41. C5C2×C3×C4×C29direct (N × H)
43. C4C2×C3×C5×C29direct (N × H)
44. C3C2×C4×C5×C29direct (N × H)
45. C2C3×C4×C5×C29direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C292
C3×C4×C5×C292
C2×C4×C5×C293
C2×C3×C4×C295
C2×C3×C4×C529