Finite Group Databasebeta

← D3×C7×C5⋊D55 #37528708

Subgroups — D3×C7×C5⋊D55 #37528708

Order 23100.

320 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×C7×C5⋊D55C211yesmaximal, characteristic, complemented
2C52×D3×C7×C11C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D55)C211yesmaximal, characteristic, complemented
4C2×C7×C5⋊D55—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D3×C7×D55—56nomaximal
7C7×C5⋊D55—31no—
8C7×C5⋊D55D311yescharacteristic, direct product factor
9C2×C52×C7×C11—31no—
10D3×C5⋊D55C711yesmaximal, characteristic, direct product factor, Hall
11C7×D165—56no—
12C5×D3×C7×C11D516yescomplemented
13C3×C7×D55—56no—
14D3×C7×C5⋊D5—111nomaximal, Hall
15C52×C7×C11C2×D311yescharacteristic, complemented, Hall
16C3⋊(C5⋊D55)C2×C711yescharacteristic, complemented
17C52×D3×C11C2×C711yescharacteristic, complemented
18C3×C5⋊D55C2×C711yescharacteristic, complemented
19C2×C7×D55—156no—
20C3×C5×C7×C11C2×D516yescomplemented
21C2×C5⋊D55—31noHall
22C7×C3⋊(C5⋊D5)—111no—
23C52×D3×C7D1111yescharacteristic, complemented
24C3×C7×C5⋊D5—111no—
25D3×C7×D11—251noHall
26C3×C52×C11C22×C711yescharacteristic, complemented, Hall
27C2×C5×C7×C11—36no—
28C7×D55—56no—
29C7×D55—156no—
30C2×C7×C5⋊D5—331noHall
31D3×D55—56no—
32C2×C52×C11—31no—
33C5⋊D55—31no—
34C5⋊D55D3×C711yescharacteristic, direct product factor
35C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
36C7×D33—251no—
37D3×C7×C11C5⋊D511yescharacteristic, complemented
38C3×C7×D11—251no—
39D3×C7×D5—556no—
40C5×C7×C11D3×D516yescomplemented
41C2×C52×C7—31no—
42C7×C5⋊D5—111no—
43C7×C5⋊D5—331no—
44D165—56no—
45C5×D3×C11C7×D516yescomplemented
46C3×D55—56no—
47C2×C7×D11—751noHall
48D3×C5⋊D5—111noHall
49C52×C11C2×D3×C711yescharacteristic, complemented, Hall
50C3×C7×C11C2×C5⋊D511yescharacteristic, complemented, Hall
51C2×D55—156no—
52C7×D15—556no—
53C5×D3×C7D5516yescomplemented
54C3×C7×D5—556no—
55C52×C7D3×D1111yescharacteristic, complemented, Hall
56C3×C5×C11C2×C7×D516yescomplemented
57C2×C7×C11—31no—
58C7×D11—251no—
59C7×D11—751no—
60C3⋊(C5⋊D5)—111no—
61C52×D3C7×D1111yescharacteristic, complemented
62C3×C5⋊D5—111no—
63C2×C7×D5—1656no—
64D3×D11—251noHall
65C2×C5×C11—36no—
66D55—56no—
67D55—156no—
68C3×C5×C7C2×D5516yescomplemented
69C2×C5⋊D5—331noHall
70C2×D3×C7—2751noHall
71C7×C11D3×C5⋊D511yescharacteristic, complemented, Hall
72C3×C52C2×C7×D1111yescharacteristic, complemented, Hall
73C2×C5×C7—36no—
74C7×D5—556no—
75C7×D5—1656no—
76D33—251no—
77C3×D11—251no—
78D3×C11C7×C5⋊D511yescharacteristic, complemented
79D3×D5—556no—
80C5×C11D3×C7×D516yescomplemented
81C2×C52—31no—
82C5⋊D5—111no—
83C5⋊D5—331no—
84C2×D11—751noHall
85C2×C3×C7—2751no—
86D3×C7—2751no—
87D3×C7C5⋊D5511yescharacteristic, direct product factor
88C5×C7D3×D5516yescomplemented
89C3×C11C2×C7×C5⋊D511yescharacteristic, complemented, Hall
90D15—556no—
91C3×D5—556no—
92C5×D3C7×D5516yescomplemented
93C22×C7—8251noHall
94C52D3×C7×D1111yescharacteristic, complemented, Sylow
95C2×C11—31no—
96D11—251no—
97D11—751no—
98C3×C7C2×C5⋊D5511yescharacteristic, complemented, Hall
99C2×D5—1656no—
100C3×C5C2×C7×D5516yescomplemented
101C2×C7—31no—
102C2×C7—2751no—
103C2×C7—8251no—
104C2×D3—2751noHall
105C11D3×C7×C5⋊D511yescharacteristic, complemented, Sylow
106C2×C5—36no—
107D5—556no—
108D5—1656no—
109C7D3×C5⋊D5511yescharacteristic, direct product factor, Sylow
110C2×C3—2751no—
111D3—2751no—
112D3C7×C5⋊D5511yescharacteristic, direct product factor
113C5D3×C7×D5516yescomplemented
114C22—8251noSylow
115C3C2×C7×C5⋊D5511yescharacteristic, complemented, Sylow
116C2—31no—
117C2—2751no—
118C2—8251no—
subgroupG/H
center, hypercenterC7D3×C5⋊D55
commutator, cosocle, hypocenterC3×C52×C11C22×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52×C11
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C5⋊D55C2semidirect
2. C52×D3×C7×C11C2semidirect
3. C7×C3⋊(C5⋊D55)C2semidirect
5. C3×C52×C7×C11C22semidirect
8. C7×C5⋊D55D3direct (N × H)
10. D3×C5⋊D55C7direct (N × H)
12. C5×D3×C7×C11D5semidirect
15. C52×C7×C11C2×D3semidirect
16. C3⋊(C5⋊D55)C2×C7semidirect
17. C52×D3×C11C2×C7semidirect
18. C3×C5⋊D55C2×C7semidirect
20. C3×C5×C7×C11C2×D5semidirect
23. C52×D3×C7D11semidirect
26. C3×C52×C11C22×C7semidirect
34. C5⋊D55D3×C7direct (N × H)
35. C3×C52×C7C2×D11semidirect
37. D3×C7×C11C5⋊D5semidirect
40. C5×C7×C11D3×D5semidirect
45. C5×D3×C11C7×D5semidirect
49. C52×C11C2×D3×C7semidirect
50. C3×C7×C11C2×C5⋊D5semidirect
53. C5×D3×C7D55semidirect
55. C52×C7D3×D11semidirect
56. C3×C5×C11C2×C7×D5semidirect
61. C52×D3C7×D11semidirect
68. C3×C5×C7C2×D55semidirect
71. C7×C11D3×C5⋊D5semidirect
72. C3×C52C2×C7×D11semidirect
78. D3×C11C7×C5⋊D5semidirect
80. C5×C11D3×C7×D5semidirect
87. D3×C7C5⋊D55direct (N × H)
88. C5×C7D3×D55semidirect
89. C3×C11C2×C7×C5⋊D5semidirect
92. C5×D3C7×D55semidirect
94. C52D3×C7×D11semidirect
98. C3×C7C2×C5⋊D55semidirect
100. C3×C5C2×C7×D55semidirect
105. C11D3×C7×C5⋊D5semidirect
109. C7D3×C5⋊D55direct (N × H)
112. D3C7×C5⋊D55direct (N × H)
113. C5D3×C7×D55semidirect
115. C3C2×C7×C5⋊D55semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C5⋊D552
C52×D3×C7×C112
C7×C3⋊(C5⋊D55)2
C2×C7×C5⋊D553
D3×C7×D555
D3×C5⋊D557
D3×C7×C5⋊D511