Finite Group Databasebeta

← D21⋊(C5⋊D55) #37528720

Subgroups — D21⋊(C5⋊D55) #37528720

Order 23100.

320 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 85 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×C5⋊D385C211yesmaximal, characteristic, complemented
2C52×C11×D21C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D55)C211yesmaximal, characteristic, complemented
4D7×C5⋊D55—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D21⋊D55—56nomaximal
7C5⋊D385D311yescharacteristic, complemented
8C7×C5⋊D55—31no—
9C52×C11×D7—31no—
10D3×C5⋊D55—71nomaximal, Hall
11C7×D165—56no—
12C5×C11×D21D516yescomplemented
13C3×D385—56no—
14D21⋊(C5⋊D5)—111nomaximal, Hall
15C52×C7×C11C2×D311yescharacteristic, complemented, Hall
16C3⋊(C5⋊D55)D711yescharacteristic, complemented
17C52×D3×C11—71no—
18C3×C5⋊D55—71no—
19D7×D55—156no—
20C3×C5×C7×C11C2×D516yescomplemented
21C2×C5⋊D55—211noHall
22C7×C3⋊(C5⋊D5)—111no—
23C52×D21D1111yescharacteristic, complemented
24C3×C5⋊D35—111no—
25D21⋊D11—251noHall
26C3×C52×C11C2×D711yescharacteristic, complemented, Hall
27D385—56no—
28C7×D55—156no—
29C5×C11×D7—36no—
30D7×C5⋊D5—331noHall
31D3×D55—356no—
32C2×C52×C11—211no—
33C5⋊D55—31no—
34C5⋊D55—71no—
35C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
36C11×D21C5⋊D511yescharacteristic, complemented
37C7×D33—251no—
38C3×D77—251no—
39D15⋊D7—556no—
40C5×C7×C11D3×D516yescomplemented
41C5⋊D35—111no—
42C7×C5⋊D5—331no—
43C52×D7—31no—
44D165—56no—
45C5×D3×C11—76no—
46C3×D55—356no—
47D7×D11—751noHall
48D3×C5⋊D5—771noHall
49C52×C11D3×D711yescharacteristic, complemented, Hall
50C3×C7×C11C2×C5⋊D511yescharacteristic, complemented, Hall
51C2×D55—1056no—
52C7×D15—556no—
53C5×D21D5516yescomplemented
54C3×D35—556no—
55C52×C7D3×D1111yescharacteristic, complemented, Hall
56C3×C5×C11D5×D716yescomplemented
57D77—251no—
58C7×D11—751no—
59C11×D7—31no—
60C3⋊(C5⋊D5)—111no—
61C52×D3—71no—
62C3×C5⋊D5—771no—
63D5×D7—1656no—
64D3×D11—1751noHall
65C2×C5×C11—216no—
66D55—156no—
67D55—356no—
68C3×C5×C7C2×D5516yescomplemented
69C2×C5⋊D5—2311noHall
70D3×D7—2751noHall
71C7×C11D3×C5⋊D511yescharacteristic, complemented, Hall
72C3×C52D7×D1111yescharacteristic, complemented, Hall
73D35—556no—
74C5×D7—36no—
75C7×D5—1656no—
76D33—251no—
77C3×D11—1751no—
78D3×C11—71no—
79D3×D5—3856no—
80C5×C11D15⋊D716yescomplemented
81C2×C52—211no—
82C5⋊D5—331no—
83C5⋊D5—771no—
84C2×D11—5251noHall
85D21C5⋊D5511yescharacteristic, complemented
86C3×D7—2751no—
87D3×C7—2751no—
88C5×C7D3×D5516yescomplemented
89C3×C11D7×C5⋊D511yescharacteristic, complemented, Hall
90D15—556no—
91C3×D5—3856no—
92C5×D3—76no—
93C2×D7—8251noHall
94C52D21⋊D1111yescharacteristic, complemented, Sylow
95C2×C11—211no—
96D11—751no—
97D11—1751no—
98C3×C7C2×C5⋊D5511yescharacteristic, complemented, Hall
99C2×D5—11556no—
100C3×C5D7×D5516yescomplemented
101C2×C7—8251no—
102D7—31no—
103D7—2751no—
104C2×D3—19251noHall
105C11D21⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
106C2×C5—216no—
107D5—3856no—
108D5—1656no—
109C7D3×C5⋊D5511yescharacteristic, complemented, Sylow
110C2×C3—19251no—
111D3—71no—
112D3—2751no—
113C5D21⋊D5516yescomplemented
114C22—57751noSylow
115C3D7×C5⋊D5511yescharacteristic, complemented, Sylow
116C2—211no—
117C2—8251no—
118C2—19251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊D385C2semidirect
2. C52×C11×D21C2semidirect
3. C7×C3⋊(C5⋊D55)C2semidirect
5. C3×C52×C7×C11C22semidirect
7. C5⋊D385D3semidirect
12. C5×C11×D21D5semidirect
15. C52×C7×C11C2×D3semidirect
16. C3⋊(C5⋊D55)D7semidirect
20. C3×C5×C7×C11C2×D5semidirect
23. C52×D21D11semidirect
26. C3×C52×C11C2×D7semidirect
35. C3×C52×C7C2×D11semidirect
36. C11×D21C5⋊D5semidirect
40. C5×C7×C11D3×D5semidirect
49. C52×C11D3×D7semidirect
50. C3×C7×C11C2×C5⋊D5semidirect
53. C5×D21D55semidirect
55. C52×C7D3×D11semidirect
56. C3×C5×C11D5×D7semidirect
68. C3×C5×C7C2×D55semidirect
71. C7×C11D3×C5⋊D5semidirect
72. C3×C52D7×D11semidirect
80. C5×C11D15⋊D7semidirect
85. D21C5⋊D55semidirect
88. C5×C7D3×D55semidirect
89. C3×C11D7×C5⋊D5semidirect
94. C52D21⋊D11semidirect
98. C3×C7C2×C5⋊D55semidirect
100. C3×C5D7×D55semidirect
105. C11D21⋊(C5⋊D5)semidirect
109. C7D3×C5⋊D55semidirect
113. C5D21⋊D55semidirect
115. C3D7×C5⋊D55semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊D3852
C52×C11×D212
C7×C3⋊(C5⋊D55)2
D7×C5⋊D553
D21⋊D555
D3×C5⋊D557
D21⋊(C5⋊D5)11