Finite Group Databasebeta

← C32×C5⋊(C5⋊(C7⋊D7)) #36348067

Subgroups — C32×C5⋊(C5⋊(C7⋊D7)) #36348067

Order 22050.

960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C72C211yesmaximal, characteristic, complemented, Hall
2C3×C5⋊(C5⋊(C7⋊D7))C314yesmaximal, direct product factor
3C32×C5⋊(C7⋊D7)—56nomaximal
4C3×C52×C72C2×C314yescomplemented
5C32×C5⋊D35—78nomaximal
6C5⋊(C5⋊(C7⋊D7))C3211yescharacteristic, direct product factor, Hall
7C32×C5×C72D516yescomplemented
8C32×C52×C7D718yescomplemented
9C3×C5⋊(C7⋊D7)—524no—
10C52×C72C2×C3211yescharacteristic, complemented, Hall
11C3×C5⋊D35—732no—
12C32×C7⋊D7—251noHall
13C3×C5×C72C3×D5124yescomplemented
14C32×D35—3548no—
15C3×C52×C7C3×D7132yescomplemented
16C5⋊(C7⋊D7)—56no—
17C32×C5⋊D5—491noHall
18C32×C72C5⋊D511yescharacteristic, complemented, Hall
19C5⋊D35—78no—
20C32×C5×C7D35148yescomplemented
21C3×C7⋊D7—254no—
22C5×C72C32×D516yescomplemented
23C32×C52C7⋊D711yescharacteristic, complemented, Hall
24C3×D35—35192no—
25C52×C7C32×D718yescomplemented
26C3×C5⋊D5—494no—
27C3×C72C3×C5⋊D514yescomplemented
28C32×D7—1758no—
29C3×C5×C7C3×D351192yescomplemented
30C7⋊D7—251noHall
31C32×D5—2456no—
32C3×C52C3×C7⋊D714yescomplemented
33D35—3548no—
34C32×C7C5⋊D3518yescomplemented
35C5⋊D5—491noHall
36C72C32×C5⋊D511yescharacteristic, complemented, Sylow
37C32×C5C5⋊(C7⋊D7)16yescomplemented
38C3×D7—17532no—
39C5×C7C32×D35148yescomplemented
40C3×D5—24524no—
41C52C32×C7⋊D711yescharacteristic, complemented, Sylow
42C3×C7C3×C5⋊D35132yescomplemented
43C2×C32—12251noHall
44C3×C5C3×C5⋊(C7⋊D7)124yescomplemented
45D7—1758no—
46D5—2456no—
47C32C5⋊(C5⋊(C7⋊D7))11yescharacteristic, direct product factor, Sylow
48C7C32×C5⋊D3518yescomplemented
49C2×C3—12254no—
50C5C32×C5⋊(C7⋊D7)16yescomplemented
51C3C3×C5⋊(C5⋊(C7⋊D7))14yesdirect product factor
52C2—12251noSylow
subgroupG/H
center, hypercenterC32C5⋊(C5⋊(C7⋊D7))
commutator, cosocle, hypocenterC52×C72C2×C32
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C52×C72
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C52×C72C2semidirect
2. C3×C5⋊(C5⋊(C7⋊D7))C3direct (N × H)
4. C3×C52×C72C2×C3semidirect
6. C5⋊(C5⋊(C7⋊D7))C32direct (N × H)
7. C32×C5×C72D5semidirect
8. C32×C52×C7D7semidirect
10. C52×C72C2×C32semidirect
13. C3×C5×C72C3×D5semidirect
15. C3×C52×C7C3×D7semidirect
18. C32×C72C5⋊D5semidirect
20. C32×C5×C7D35semidirect
22. C5×C72C32×D5semidirect
23. C32×C52C7⋊D7semidirect
25. C52×C7C32×D7semidirect
27. C3×C72C3×C5⋊D5semidirect
29. C3×C5×C7C3×D35semidirect
32. C3×C52C3×C7⋊D7semidirect
34. C32×C7C5⋊D35semidirect
36. C72C32×C5⋊D5semidirect
37. C32×C5C5⋊(C7⋊D7)semidirect
39. C5×C7C32×D35semidirect
41. C52C32×C7⋊D7semidirect
42. C3×C7C3×C5⋊D35semidirect
44. C3×C5C3×C5⋊(C7⋊D7)semidirect
47. C32C5⋊(C5⋊(C7⋊D7))direct (N × H)
48. C7C32×C5⋊D35semidirect
50. C5C32×C5⋊(C7⋊D7)semidirect
51. C3C3×C5⋊(C5⋊(C7⋊D7))direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×C722
C3×C5⋊(C5⋊(C7⋊D7))3
C32×C5⋊(C7⋊D7)5
C32×C5⋊D357