Finite Group Databasebeta

← C3⋊(C7⋊(C7⋊#63121)) #50304425

Subgroups — C3⋊(C7⋊(C7⋊#63121)) #50304425

Order 38220.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C72×D65C211yesmaximal, characteristic
2C7⋊(C7⋊#63121)—31nomaximal, Hall
3C3×C5×C72×C13C411yescharacteristic, complemented, Hall
4C3⋊(C7⋊(C7⋊#261))—51nomaximal, Hall
5C72×D65D311yescharacteristic
6C3⋊(C7⋊#63121)—78nomaximal
7C3×C72×D13—51no—
8C5×C72×C13Dic311yescharacteristic, complemented, Hall
9C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))—131nomaximal, Hall
10C3×C7×D65D718yes—
11C7⋊(C7⋊#261)—151noHall
12C3×C72×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
13C7⋊#63121—218no—
14C3×C72×D5—131no—
15C3×C5×C7×C13Dic718yescomplemented
16C72×D13—51no—
17C3⋊(C7⋊#261)—358no—
18C7⋊(C7⋊AGL(1,𝔽5))—391noHall
19C7×D65D2118yes—
20C3⋊#63121—491noHall
21C3×C5×C72#26111yescharacteristic, complemented, Hall
22C72×C13ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
23C3⋊(C7⋊Dic7)—651noHall
24C3×C7×D13—58no—
25C72×D5—131no—
26C5×C7×C13Dic2118yescomplemented
27C3⋊(C7⋊AGL(1,𝔽5))—918no—
28C3×D65C7⋊D711yescharacteristic
29C7⋊#261—1058no—
30C2×C3×C72—651no—
31C3×C7×C13C7⋊AGL(1,𝔽5)18yescomplemented
32#63121—1471noHall
33C5×C72C3⋊#26111yescharacteristic, complemented, Hall
34C3×C7×D5—138no—
35C7⋊Dic7—1951noHall
36C3×C5×C13C7⋊Dic711yescharacteristic, complemented, Hall
37C7×D13—58no—
38C3⋊#261—2451noHall
39C3×C72#6312111yescharacteristic, complemented, Hall
40C7⋊AGL(1,𝔽5)—2738no—
41D65C3⋊(C7⋊D7)11yescharacteristic
42C3×C5×C7C7⋊#26118yescomplemented
43C2×C72—651no—
44C7×C13C3⋊(C7⋊AGL(1,𝔽5))18yescomplemented
45Dic21—4558no—
46C3×D13—51no—
47C7×D5—138no—
48C5×C13C3⋊(C7⋊Dic7)11yescharacteristic, complemented, Hall
49ΓL(1,𝔽16)—6371noHall
50#261—7351noHall
51C72C3⋊#6312111yescharacteristic, complemented, Sylow
52C2×C3×C7—658no—
53C3×C13C7⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Hall
54C5×C7C3⋊(C7⋊#261)18yescomplemented
55C3×D5—131no—
56Dic7—13658no—
57D13—51no—
58C3×C7C7⋊#6312118yescomplemented
59AGL(1,𝔽5)—19111noHall
60C3×C5C7⋊(C7⋊#261)11yescharacteristic, complemented, Hall
61C2×C7—658no—
62C13C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))11yescharacteristic, complemented, Sylow
63Dic3—31851noHall
64D5—131no—
65C7C3⋊(C7⋊#63121)18yescomplemented
66C2×C3—651no—
67C5C3⋊(C7⋊(C7⋊#261))11yescharacteristic, complemented, Sylow
68C4—95551noSylow
69C3C7⋊(C7⋊#63121)11yescharacteristic, complemented, Sylow
70C2—651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C72×C13C4
prime radical, cosocleC3×C72×D65C2
LCSG ▷ C3×C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
3. C3×C5×C72×C13C4semidirect
8. C5×C72×C13Dic3semidirect
12. C3×C72×C13AGL(1,𝔽5)semidirect
15. C3×C5×C7×C13Dic7semidirect
21. C3×C5×C72#261semidirect
22. C72×C13ΓL(1,𝔽16)semidirect
26. C5×C7×C13Dic21semidirect
31. C3×C7×C13C7⋊AGL(1,𝔽5)semidirect
33. C5×C72C3⋊#261semidirect
36. C3×C5×C13C7⋊Dic7semidirect
39. C3×C72#63121semidirect
42. C3×C5×C7C7⋊#261semidirect
44. C7×C13C3⋊(C7⋊AGL(1,𝔽5))semidirect
48. C5×C13C3⋊(C7⋊Dic7)semidirect
51. C72C3⋊#63121semidirect
53. C3×C13C7⋊(C7⋊AGL(1,𝔽5))semidirect
54. C5×C7C3⋊(C7⋊#261)semidirect
58. C3×C7C7⋊#63121semidirect
60. C3×C5C7⋊(C7⋊#261)semidirect
62. C13C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))semidirect
65. C7C3⋊(C7⋊#63121)semidirect
67. C5C3⋊(C7⋊(C7⋊#261))semidirect
69. C3C7⋊(C7⋊#63121)semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D652
C7⋊(C7⋊#63121)3
C3⋊(C7⋊(C7⋊#261))5
C3⋊(C7⋊#63121)7
C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))13