Finite Group Databasebeta

← C5×D3×C7×D55 #37528652

Subgroups — C5×D3×C7×D55 #37528652

Order 23100.

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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×D55C211yesmaximal, characteristic, complemented
2C52×D3×C7×C11C211yesmaximal, characteristic, complemented
3C5×C7×D165C211yesmaximal, characteristic, complemented
4C2×C5×C7×D55—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D3×C7×D55C511yesmaximal, characteristic, direct product factor
7C5×D3×C7×D11—51nomaximal
8C5×C7×D55—31no—
9C5×C7×D55D311yescharacteristic, direct product factor
10C2×C52×C7×C11—31no—
11C5×D3×D55C711yesmaximal, characteristic, direct product factor, Hall
12C7×D165C2×C511yescharacteristic, complemented
13C5×C7×D33—51no—
14C5×D3×C7×C11—22no—
15C5×D3×C7×C11D511yescharacteristic, complemented
16C5×D3×C7×C11C2×C511yescharacteristic, complemented
17C3×C7×D55C2×C511yescharacteristic, complemented
18C3×C5×C7×D11—51no—
19C5×D3×C7×D5—111nomaximal, Hall
20C52×C7×C11C2×D311yescharacteristic, complemented, Hall
21C5×D165C2×C711yescharacteristic, complemented
22C52×D3×C11C2×C711yescharacteristic, complemented
23C3×C5×D55C2×C711yescharacteristic, complemented
24C2×C7×D55—31no—
25C2×C5×C7×D11—151no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C22×C511yescharacteristic, complemented
29C2×C5×D55—31noHall
30C5×C7×D15—111no—
31C52×D3×C7D1111yescharacteristic, complemented
32C3×C5×C7×D5—111no—
33D3×C7×D11—51noHall
34C3×C52×C11C22×C711yescharacteristic, complemented, Hall
35C2×C5×C7×C11—31no—
36C2×C5×C7×C11—31no—
37C2×C5×C7×C11—62no—
38C7×D55—31no—
39C7×D55C5×D311yescharacteristic, direct product factor
40C5×C7×D11—51no—
41C5×C7×D11—151no—
42C2×C5×C7×D5—331noHall
43D3×D55C5×C711yescharacteristic, direct product factor
44C5×D3×D11—51no—
45C2×C52×C11—31no—
46C5×D55—31no—
47C5×D55D3×C711yescharacteristic, direct product factor
48C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
49C7×D33—51no—
50D3×C7×C11C5×D511yescharacteristic, complemented
51C3×C7×D11—51no—
52C2×C5×D3×C7—551no—
53D3×C7×D5—111no—
54C5×C7×C11—22no—
55C5×C7×C11D3×D511yescharacteristic, complemented
56C5×C7×C11C2×C5×D311yescharacteristic, complemented
57C2×C52×C7—31no—
58C5×C7×D5—111no—
59C5×C7×D5—331no—
60D165C2×C5×C711yescharacteristic, complemented
61C5×D33—51no—
62C5×D3×C11—22no—
63C5×D3×C11C7×D511yescharacteristic, complemented
64C5×D3×C11C2×C5×C711yescharacteristic, complemented
65C3×D55C2×C5×C711yescharacteristic, complemented
66C3×C5×D11—51no—
67C2×C7×D11—151noHall
68C5×D3×D5—111noHall
69C52×C11C2×D3×C711yescharacteristic, complemented, Hall
70C3×C7×C11C2×C5×D511yescharacteristic, complemented, Hall
71C2×D55—31no—
72C2×C5×D11—151no—
73C2×C3×C5×C7—551no—
74C7×D15—111no—
75C5×D3×C7—22no—
76C5×D3×C7—551no—
77C5×D3×C7C5×D1111yescharacteristic, complemented
78C5×D3×C7D5511yescharacteristic, direct product factor
79C3×C7×D5—111no—
80C52×C7D3×D1111yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11C2×C7×D511yescharacteristic, complemented
83C3×C5×C11C22×C5×C711yescharacteristic, complemented
84C2×C7×C11—31no—
85C7×D11—51no—
86C7×D11—151no—
87C5×D15—111no—
88C52×D3C7×D1111yescharacteristic, complemented
89C3×C5×D5—111no—
90C22×C5×C7—1651no—
91C2×C7×D5—331no—
92D3×D11—51noHall
93C2×C5×C11—31no—
94C2×C5×C11—31no—
95C2×C5×C11—62no—
96D55—31no—
97D55C5×D3×C711yescharacteristic, direct product factor
98C5×D11—51no—
99C5×D11—151no—
100C3×C5×C7—22no—
101C3×C5×C7C2×C5×D1111yescharacteristic, complemented
102C3×C5×C7C2×D5511yescharacteristic, complemented
103C2×C5×D5—331noHall
104C2×D3×C7—551noHall
105C7×C11C5×D3×D511yescharacteristic, complemented, Hall
106C3×C52C2×C7×D1111yescharacteristic, complemented, Hall
107C2×C5×C7—31no—
108C2×C5×C7—31no—
109C2×C5×C7—62no—
110C2×C5×C7—551no—
111C2×C5×C7—1651no—
112C7×D5—111no—
113C7×D5—331no—
114D33—51no—
115C3×D11—51no—
116D3×C11C5×C7×D511yescharacteristic, complemented
117C2×C5×D3—551no—
118D3×D5—111no—
119C5×C11—22no—
120C5×C11D3×C7×D511yescharacteristic, complemented
121C5×C11C2×C5×D3×C711yescharacteristic, complemented
122C2×C52—31no—
123C5×D5—111no—
124C5×D5—331no—
125C2×D11—151noHall
126C2×C3×C7—551no—
127D3×C7—551no—
128D3×C7C5×D5511yescharacteristic, direct product factor
129C5×C7—22no—
130C5×C7C5×D3×D1111yescharacteristic, complemented
131C5×C7D3×D5511yescharacteristic, direct product factor
132C3×C11C2×C5×C7×D511yescharacteristic, complemented, Hall
133C2×C3×C5—551no—
134D15—111no—
135C3×D5—111no—
136C5×D3—22no—
137C5×D3—551no—
138C5×D3C5×C7×D1111yescharacteristic, complemented
139C5×D3C7×D5511yescharacteristic, direct product factor
140C22×C7—1651noHall
141C52D3×C7×D1111yescharacteristic, complemented, Sylow
142C2×C11—31no—
143D11—51no—
144D11—151no—
145C3×C7C2×C5×D5511yescharacteristic, complemented, Hall
146C22×C5—1651no—
147C2×D5—331no—
148C3×C5—22no—
149C3×C5C2×C5×C7×D1111yescharacteristic, complemented
150C3×C5C2×C7×D5511yescharacteristic, complemented
151C2×C7—31no—
152C2×C7—551no—
153C2×C7—1651no—
154C2×D3—551noHall
155C11C5×D3×C7×D511yescharacteristic, complemented, Sylow
156C2×C5—31no—
157C2×C5—31no—
158C2×C5—62no—
159C2×C5—551no—
160C2×C5—1651no—
161D5—111no—
162D5—331no—
163C7C5×D3×D5511yescharacteristic, direct product factor, Sylow
164C2×C3—551no—
165D3—551no—
166D3C5×C7×D5511yescharacteristic, direct product factor
167C5—22no—
168C5C5×D3×C7×D1111yescharacteristic, complemented
169C5D3×C7×D5511yescharacteristic, direct product factor
170C22—1651noSylow
171C3C2×C5×C7×D5511yescharacteristic, complemented, Sylow
172C2—31no—
173C2—551no—
174C2—1651no—
subgroupG/H
center, hypercenterC5×C7D3×D55
commutator, cosocle, hypocenterC3×C5×C11C22×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C5×C11
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D55C2semidirect
2. C52×D3×C7×C11C2semidirect
3. C5×C7×D165C2semidirect
5. C3×C52×C7×C11C22semidirect
6. D3×C7×D55C5direct (N × H)
9. C5×C7×D55D3direct (N × H)
11. C5×D3×D55C7direct (N × H)
12. C7×D165C2×C5semidirect
15. C5×D3×C7×C11D5semidirect
16. C5×D3×C7×C11C2×C5semidirect
17. C3×C7×D55C2×C5semidirect
20. C52×C7×C11C2×D3semidirect
21. C5×D165C2×C7semidirect
22. C52×D3×C11C2×C7semidirect
23. C3×C5×D55C2×C7semidirect
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C22×C5semidirect
31. C52×D3×C7D11semidirect
34. C3×C52×C11C22×C7semidirect
39. C7×D55C5×D3direct (N × H)
43. D3×D55C5×C7direct (N × H)
47. C5×D55D3×C7direct (N × H)
48. C3×C52×C7C2×D11semidirect
50. D3×C7×C11C5×D5semidirect
55. C5×C7×C11D3×D5semidirect
56. C5×C7×C11C2×C5×D3semidirect
60. D165C2×C5×C7semidirect
63. C5×D3×C11C7×D5semidirect
64. C5×D3×C11C2×C5×C7semidirect
65. C3×D55C2×C5×C7semidirect
69. C52×C11C2×D3×C7semidirect
70. C3×C7×C11C2×C5×D5semidirect
77. C5×D3×C7C5×D11semidirect
78. C5×D3×C7D55direct (N × H)
80. C52×C7D3×D11semidirect
82. C3×C5×C11C2×C7×D5semidirect
83. C3×C5×C11C22×C5×C7semidirect
88. C52×D3C7×D11semidirect
97. D55C5×D3×C7direct (N × H)
101. C3×C5×C7C2×C5×D11semidirect
102. C3×C5×C7C2×D55semidirect
105. C7×C11C5×D3×D5semidirect
106. C3×C52C2×C7×D11semidirect
116. D3×C11C5×C7×D5semidirect
120. C5×C11D3×C7×D5semidirect
121. C5×C11C2×C5×D3×C7semidirect
128. D3×C7C5×D55direct (N × H)
130. C5×C7C5×D3×D11semidirect
131. C5×C7D3×D55direct (N × H)
132. C3×C11C2×C5×C7×D5semidirect
138. C5×D3C5×C7×D11semidirect
139. C5×D3C7×D55direct (N × H)
141. C52D3×C7×D11semidirect
145. C3×C7C2×C5×D55semidirect
149. C3×C5C2×C5×C7×D11semidirect
150. C3×C5C2×C7×D55semidirect
155. C11C5×D3×C7×D5semidirect
163. C7C5×D3×D55direct (N × H)
166. D3C5×C7×D55direct (N × H)
168. C5C5×D3×C7×D11semidirect
169. C5D3×C7×D55direct (N × H)
171. C3C2×C5×C7×D55semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D552
C52×D3×C7×C112
C5×C7×D1652
C2×C5×C7×D553
D3×C7×D555
C5×D3×C7×D115
C5×D3×D557
C5×D3×C7×D511