Finite Group Databasebeta

← C3×C7×C3⋊(C5⋊D55) #46831671

Subgroups — C3×C7×C3⋊(C5⋊D55) #46831671

Order 34650.

288 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C3×C7×C5⋊D55—31nomaximal
3C7×C3⋊(C5⋊D55)C311yesmaximal, characteristic, direct product factor
4C3×C7×D165—56nomaximal
5C3×C52×C7×C11—21no—
6C3×C52×C7×C11D311yescharacteristic, complemented
7C3×C52×C7×C11C2×C311yescharacteristic, complemented
8C3×C3⋊(C5⋊D55)C711yesmaximal, characteristic, direct product factor, Hall
9C7×C5⋊D55—31noHall
10C32×C5×C7×C11D516yescomplemented
11C3×C7×C3⋊(C5⋊D5)—111nomaximal, Hall
12C32×C52×C11C2×C711yescharacteristic, complemented, Hall
13C7×D165—56no—
14C3×C7×D55—156no—
15C52×C7×C11C3×D311yescharacteristic, complemented, Hall
16C3⋊(C5⋊D55)C3×C711yescharacteristic, direct product factor
17C3×C5⋊D55—31no—
18C32×C52×C7D1111yescharacteristic, complemented, Hall
19C3×C7×D33—251noHall
20C3×C5×C7×C11—26no—
21C3×C5×C7×C11C3×D516yescomplemented
22C3×C5×C7×C11D1516yescomplemented
23C7×C3⋊(C5⋊D5)—111no—
24C3×C7×C5⋊D5—331no—
25C3×D165—56no—
26C3×C52×C11—21no—
27C3×C52×C11D3×C711yescharacteristic, complemented
28C3×C52×C11C2×C3×C711yescharacteristic, complemented
29C7×D55—156no—
30C32×C7×C11C5⋊D511yescharacteristic, complemented, Hall
31C3×C7×D15—556no—
32C5⋊D55—31noHall
33C3×C52×C7—21no—
34C3×C52×C7C3×D1111yescharacteristic, complemented
35C3×C52×C7D3311yescharacteristic, complemented
36C32×C5×C11C7×D516yescomplemented
37C7×D33—251no—
38C3×C7×D11—751no—
39C3×C3⋊(C5⋊D5)—111noHall
40C5×C7×C11C3×D1516yescomplemented
41C7×C5⋊D5—331noHall
42D165—56no—
43C3×D55—156no—
44C32×C5×C7D5516yescomplemented
45C52×C11C3×D3×C711yescharacteristic, complemented, Hall
46C3×C7×C11—21no—
47C3×C7×C11C3×C5⋊D511yescharacteristic, complemented
48C3×C7×C11C3⋊(C5⋊D5)11yescharacteristic, complemented
49C32×C52C7×D1111yescharacteristic, complemented, Hall
50C7×D15—556no—
51C3×C7×D5—1656no—
52C3×D33—251noHall
53C52×C7C3×D3311yescharacteristic, complemented, Hall
54C3×C5×C11—26no—
55C3×C5×C11C3×C7×D516yescomplemented
56C3×C5×C11C7×D1516yescomplemented
57C7×D11—751noHall
58C3⋊(C5⋊D5)—111no—
59C3×C5⋊D5—331no—
60C3×D3×C7—2751noHall
61D55—156no—
62C3×C5×C7—26no—
63C3×C5×C7C3×D5516yescomplemented
64C3×C5×C7D16516yescomplemented
65C32×C11C7×C5⋊D511yescharacteristic, complemented, Hall
66C3×D15—556no—
67C7×C11C3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Hall
68C3×C52—21no—
69C3×C52C3×C7×D1111yescharacteristic, complemented
70C3×C52C7×D3311yescharacteristic, complemented
71C7×D5—1656no—
72D33—251no—
73C3×D11—751no—
74C32×C7C5⋊D5511yescharacteristic, complemented, Hall
75C5×C11C3×C7×D1516yescomplemented
76C5⋊D5—331noHall
77C32×C5C7×D5516yescomplemented
78C2×C3×C7—8251no—
79D3×C7—2751no—
80C5×C7C3×D16516yescomplemented
81C3×C11—21no—
82C3×C11C3×C7×C5⋊D511yescharacteristic, complemented
83C3×C11C7×C3⋊(C5⋊D5)11yescharacteristic, complemented
84D15—556no—
85C3×D5—1656no—
86C52C3×C7×D3311yescharacteristic, complemented, Sylow
87D11—751noHall
88C3×C7—21no—
89C3×C7C3×C5⋊D5511yescharacteristic, complemented
90C3×C7C3⋊(C5⋊D55)11yescharacteristic, direct product factor
91C3×D3—2751noHall
92C3×C5—26no—
93C3×C5C3×C7×D5516yescomplemented
94C3×C5C7×D16516yescomplemented
95C2×C7—8251noHall
96C11C3×C7×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
97D5—1656no—
98C32C7×C5⋊D5511yescharacteristic, complemented, Sylow
99C7C3×C3⋊(C5⋊D55)11yescharacteristic, direct product factor, Sylow
100C2×C3—8251no—
101D3—2751no—
102C5C3×C7×D16516yescomplemented
103C3—21no—
104C3C7×C3⋊(C5⋊D55)11yescharacteristic, direct product factor
105C3C3×C7×C5⋊D5511yescharacteristic, complemented
106C2—8251noSylow
subgroupG/H
center, hypercenterC3×C7C3⋊(C5⋊D55)
commutator, cosocle, hypocenterC3×C52×C11C2×C3×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C52×C11
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
3. C7×C3⋊(C5⋊D55)C3direct (N × H)
6. C3×C52×C7×C11D3semidirect
7. C3×C52×C7×C11C2×C3semidirect
8. C3×C3⋊(C5⋊D55)C7direct (N × H)
10. C32×C5×C7×C11D5semidirect
12. C32×C52×C11C2×C7semidirect
15. C52×C7×C11C3×D3semidirect
16. C3⋊(C5⋊D55)C3×C7direct (N × H)
18. C32×C52×C7D11semidirect
21. C3×C5×C7×C11C3×D5semidirect
22. C3×C5×C7×C11D15semidirect
27. C3×C52×C11D3×C7semidirect
28. C3×C52×C11C2×C3×C7semidirect
30. C32×C7×C11C5⋊D5semidirect
34. C3×C52×C7C3×D11semidirect
35. C3×C52×C7D33semidirect
36. C32×C5×C11C7×D5semidirect
40. C5×C7×C11C3×D15semidirect
44. C32×C5×C7D55semidirect
45. C52×C11C3×D3×C7semidirect
47. C3×C7×C11C3×C5⋊D5semidirect
48. C3×C7×C11C3⋊(C5⋊D5)semidirect
49. C32×C52C7×D11semidirect
53. C52×C7C3×D33semidirect
55. C3×C5×C11C3×C7×D5semidirect
56. C3×C5×C11C7×D15semidirect
63. C3×C5×C7C3×D55semidirect
64. C3×C5×C7D165semidirect
65. C32×C11C7×C5⋊D5semidirect
67. C7×C11C3×C3⋊(C5⋊D5)semidirect
69. C3×C52C3×C7×D11semidirect
70. C3×C52C7×D33semidirect
74. C32×C7C5⋊D55semidirect
75. C5×C11C3×C7×D15semidirect
77. C32×C5C7×D55semidirect
80. C5×C7C3×D165semidirect
82. C3×C11C3×C7×C5⋊D5semidirect
83. C3×C11C7×C3⋊(C5⋊D5)semidirect
86. C52C3×C7×D33semidirect
89. C3×C7C3×C5⋊D55semidirect
90. C3×C7C3⋊(C5⋊D55)direct (N × H)
93. C3×C5C3×C7×D55semidirect
94. C3×C5C7×D165semidirect
96. C11C3×C7×C3⋊(C5⋊D5)semidirect
98. C32C7×C5⋊D55semidirect
99. C7C3×C3⋊(C5⋊D55)direct (N × H)
102. C5C3×C7×D165semidirect
104. C3C7×C3⋊(C5⋊D55)direct (N × H)
105. C3C3×C7×C5⋊D55semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C3×C7×C5⋊D553
C7×C3⋊(C5⋊D55)3
C3×C7×D1655
C3×C3⋊(C5⋊D55)7
C3×C7×C3⋊(C5⋊D5)11