Finite Group Databasebeta

← C7×D5×D165 #37528675

Subgroups — C7×D5×D165 #37528675

Order 23100.

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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×C7×D5×C11C211yesmaximal, characteristic, complemented
2C5×C7×D165C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D55)C211yesmaximal, characteristic, complemented
4C7×D5×D55—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6C2×C7×D165—51nomaximal
7C7×D5×D33—51nomaximal
8C7×C5⋊D55—31no—
9C5×C7×D55—31no—
10C5×C7×D5×C11D311yescharacteristic, complemented
11D5×D165C711yesmaximal, characteristic, direct product factor, Hall
12C7×D165—51no—
13C7×D165—51no—
14C7×D165—102no—
15C7×D165D511yescharacteristic, direct product factor
16C5×C7×D33—51no—
17C3×C7×D5×C11D511yescharacteristic, complemented
18C2×C3×C5×C7×C11—51no—
19C7×D5×D15—111nomaximal, Hall
20C52×C7×C11C2×D311yescharacteristic, complemented, Hall
21C3⋊(C5⋊D55)C2×C711yescharacteristic, complemented
22C5×D165C2×C711yescharacteristic, complemented
23C3×C5×D5×C11C2×C711yescharacteristic, complemented
24C2×C7×D55—151no—
25C7×D5×D11—151no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C2×D511yescharacteristic, complemented
29D5×D55—31noHall
30C7×C3⋊(C5⋊D5)—111no—
31C5×C7×D15—111no—
32C3×C5×C7×D5D1111yescharacteristic, complemented
33C2×C7×D33—251noHall
34C3×C52×C11C22×C711yescharacteristic, complemented, Hall
35C2×C5×C7×C11—51no—
36C7×D55—31no—
37C7×D55—151no—
38C7×D55—151no—
39C7×D55—302no—
40C7×D5×C11D1511yescharacteristic, complemented
41C5×C7×D11—151no—
42C7×D52—331noHall
43C2×D165—51no—
44D5×D33—51no—
45C5⋊D55—31no—
46C5×D55—31no—
47C5×D5×C11D3×C711yescharacteristic, complemented
48C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
49C2×C3×C7×C11—51no—
50C7×D33—51no—
51C7×D33—251no—
52C2×C7×D15—551no—
53D3×C7×D5—551no—
54C5×C7×C11—22no—
55C5×C7×C11D3×D511yescharacteristic, complemented
56C5×C7×C11C2×D1511yescharacteristic, complemented
57C7×C5⋊D5—331no—
58C5×C7×D5—331no—
59C5×C7×D5D3311yescharacteristic, complemented
60C2×C3×C5×C11—51no—
61D165—51no—
62D165—51no—
63D165—102no—
64D165C7×D511yescharacteristic, direct product factor
65C5×D33—51no—
66C3×D5×C11C7×D511yescharacteristic, complemented
67C2×C7×D11—751noHall
68D5×D15—111noHall
69C52×C11C2×D3×C711yescharacteristic, complemented, Hall
70C3×C7×C11D5211yescharacteristic, complemented, Hall
71C2×D55—151no—
72D5×D11—151no—
73C2×C3×C5×C7—51no—
74C7×D15—111no—
75C7×D15—551no—
76C7×D15—551no—
77C7×D15—1102no—
78C5×D3×C7—551no—
79C3×C7×D5D5511yescharacteristic, complemented
80C52×C7C2×D3311yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11C2×C7×D511yescharacteristic, complemented
83C3×C5×C11C2×C7×D511yescharacteristic, complemented
84C2×C7×C11—51no—
85C7×D11—151no—
86C7×D11—751no—
87C3⋊(C5⋊D5)—111no—
88C5×D15—111no—
89C3×C5×D5C7×D1111yescharacteristic, complemented
90C2×C7×D5—1651no—
91C2×C7×D5—1651no—
92C2×D33—251noHall
93C2×C5×C11—51no—
94D55—31no—
95D55—151no—
96D55—151no—
97D55—302no—
98C5×D11—151no—
99D5×C11C7×D1511yescharacteristic, complemented
100C3×C5×C7—22no—
101C3×C5×C7D5×D1111yescharacteristic, complemented
102C3×C5×C7C2×D5511yescharacteristic, complemented
103D52—331noHall
104C2×D3×C7—2751noHall
105C7×C11D5×D1511yescharacteristic, complemented, Hall
106C3×C52C2×C7×D1111yescharacteristic, complemented, Hall
107C2×C5×C7—51no—
108C2×C5×C7—1651no—
109C7×D5—331no—
110C7×D5—3302no—
111C7×D5—1651no—
112C7×D5—1651no—
113C7×D5D16511yescharacteristic, direct product factor
114C2×C3×C11—51no—
115D33—51no—
116D33—251no—
117C2×D15—551no—
118D3×D5—551no—
119C5×C11—22no—
120C5×C11D3×C7×D511yescharacteristic, complemented
121C5×C11C2×C7×D1511yescharacteristic, complemented
122C5⋊D5—331no—
123C5×D5—331no—
124C5×D5C7×D3311yescharacteristic, complemented
125C2×D11—751noHall
126C2×C3×C7—51no—
127D3×C7—2751no—
128D3×C7—551no—
129C5×C7—22no—
130C5×C7D5×D3311yescharacteristic, complemented
131C5×C7C2×D16511yescharacteristic, complemented
132C3×C11C7×D5211yescharacteristic, complemented, Hall
133C2×C3×C5—51no—
134D15—111no—
135D15—551no—
136D15—551no—
137D15—1102no—
138C3×D5C7×D5511yescharacteristic, complemented
139C5×D3—551no—
140C22×C7—8251noHall
141C52C2×C7×D3311yescharacteristic, complemented, Sylow
142C2×C11—51no—
143D11—151no—
144D11—751no—
145C3×C7D5×D5511yescharacteristic, complemented, Hall
146C2×D5—1651no—
147C2×D5—1651no—
148C3×C5—22no—
149C3×C5C7×D5×D1111yescharacteristic, complemented
150C3×C5C2×C7×D5511yescharacteristic, complemented
151C2×C7—51no—
152C2×C7—8251no—
153C2×C7—1651no—
154C2×D3—2751noHall
155C11C7×D5×D1511yescharacteristic, complemented, Sylow
156C2×C5—51no—
157C2×C5—1651no—
158D5—331no—
159D5—3302no—
160D5—1651no—
161D5—1651no—
162D5C7×D16511yescharacteristic, direct product factor
163C7D5×D16511yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—2751no—
166D3—551no—
167C5—22no—
168C5C7×D5×D3311yescharacteristic, complemented
169C5C2×C7×D16511yescharacteristic, complemented
170C22—8251noSylow
171C3C7×D5×D5511yescharacteristic, complemented, Sylow
172C2—51no—
173C2—8251no—
174C2—1651no—
subgroupG/H
center, hypercenterC7D5×D165
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×C5×C7×D5×C11C2semidirect
2. C5×C7×D165C2semidirect
3. C7×C3⋊(C5⋊D55)C2semidirect
5. C3×C52×C7×C11C22semidirect
10. C5×C7×D5×C11D3semidirect
11. D5×D165C7direct (N × H)
15. C7×D165D5direct (N × H)
17. C3×C7×D5×C11D5semidirect
20. C52×C7×C11C2×D3semidirect
21. C3⋊(C5⋊D55)C2×C7semidirect
22. C5×D165C2×C7semidirect
23. C3×C5×D5×C11C2×C7semidirect
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C2×D5semidirect
32. C3×C5×C7×D5D11semidirect
34. C3×C52×C11C22×C7semidirect
40. C7×D5×C11D15semidirect
47. C5×D5×C11D3×C7semidirect
48. C3×C52×C7C2×D11semidirect
55. C5×C7×C11D3×D5semidirect
56. C5×C7×C11C2×D15semidirect
59. C5×C7×D5D33semidirect
64. D165C7×D5direct (N × H)
66. C3×D5×C11C7×D5semidirect
69. C52×C11C2×D3×C7semidirect
70. C3×C7×C11D52semidirect
79. C3×C7×D5D55semidirect
80. C52×C7C2×D33semidirect
82. C3×C5×C11C2×C7×D5semidirect
83. C3×C5×C11C2×C7×D5semidirect
89. C3×C5×D5C7×D11semidirect
99. D5×C11C7×D15semidirect
101. C3×C5×C7D5×D11semidirect
102. C3×C5×C7C2×D55semidirect
105. C7×C11D5×D15semidirect
106. C3×C52C2×C7×D11semidirect
113. C7×D5D165direct (N × H)
120. C5×C11D3×C7×D5semidirect
121. C5×C11C2×C7×D15semidirect
124. C5×D5C7×D33semidirect
130. C5×C7D5×D33semidirect
131. C5×C7C2×D165semidirect
132. C3×C11C7×D52semidirect
138. C3×D5C7×D55semidirect
141. C52C2×C7×D33semidirect
145. C3×C7D5×D55semidirect
149. C3×C5C7×D5×D11semidirect
150. C3×C5C2×C7×D55semidirect
155. C11C7×D5×D15semidirect
162. D5C7×D165direct (N × H)
163. C7D5×D165direct (N × H)
168. C5C7×D5×D33semidirect
169. C5C2×C7×D165semidirect
171. C3C7×D5×D55semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C112
C5×C7×D1652
C7×C3⋊(C5⋊D55)2
C7×D5×D553
C2×C7×D1655
C7×D5×D335
D5×D1657
C7×D5×D1511