Finite Group Databasebeta

← C3×C5×D11×D57 #49178671

Subgroups — C3×C5×D11×D57 #49178671

Order 37620.

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

normal subgroups only

This group has 176 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
1C32×C5×C19×D11C211yesmaximal, characteristic, complemented
2C3×C5×C11×D57C211yesmaximal, characteristic, complemented
3C3×C5×D627C211yesmaximal, characteristic, complemented
4C5×D11×D57C311yesmaximal, characteristic, direct product factor
5C3×C5×D11×D19—31nomaximal
6C32×C5×C11×C19C2211yescharacteristic, complemented, Hall
7C3×D11×D57C511yesmaximal, characteristic, direct product factor, Hall
8C5×D627C2×C311yescharacteristic, complemented
9C5×C11×D57C2×C311yescharacteristic, complemented
10C3×C5×D209—31no—
11C3×C5×C19×D11—21no—
12C3×C5×C19×D11D311yescharacteristic, complemented
13C3×C5×C19×D11C2×C311yescharacteristic, complemented
14C3×C5×C11×D19—31no—
15C5×D11×D19—31noHall
16C3×D627C2×C511yescharacteristic, complemented
17C3×C11×D57C2×C511yescharacteristic, complemented
18C32×C19×D11C2×C511yescharacteristic, complemented
19C2×C3×C5×D57—111nomaximal, Hall
20C3×C5×C11×C19—21no—
21C3×C5×C11×C19C2×D311yescharacteristic, complemented
22C3×C5×C11×C19C22×C311yescharacteristic, complemented
23D11×D57C3×C511yescharacteristic, direct product factor
24C3×D11×D19—31no—
25C5×D209—31no—
26C5×C19×D11C3×D311yescharacteristic, complemented
27C5×C11×D19—31no—
28C3×C5×D3×D11—191nomaximal, Hall
29C32×C11×C19C22×C511yescharacteristic, complemented, Hall
30C2×C32×C5×C19—111no—
31C3×C5×D57—111no—
32C3×C5×D57D1111yescharacteristic, direct product factor
33D627C2×C3×C511yescharacteristic, complemented
34C11×D57C2×C3×C511yescharacteristic, complemented
35C3×D209—31no—
36C3×C19×D11—21no—
37C3×C19×D11C5×D311yescharacteristic, complemented
38C3×C19×D11C2×C3×C511yescharacteristic, complemented
39C3×C11×D19—31no—
40C2×C5×D57—111no—
41C2×C3×C5×D19—331no—
42C5×C11×C19C2×C3×D311yescharacteristic, complemented, Hall
43C3×C5×D33—191no—
44C3×C5×D3×C11—191no—
45C32×C5×D11D1911yescharacteristic, complemented
46C32×C5×C19C2×D1111yescharacteristic, complemented, Hall
47D11×D19—31noHall
48C2×C3×D57—111noHall
49C2×C3×C5×D11—571no—
50C5×D3×D11—191no—
51C3×C11×C19—21no—
52C3×C11×C19C2×C5×D311yescharacteristic, complemented
53C3×C11×C19C22×C3×C511yescharacteristic, complemented
54C2×C3×C5×C19—111no—
55C2×C3×C5×C19—111no—
56C2×C3×C5×C19—221no—
57C5×D57—111no—
58C5×D57C3×D1111yescharacteristic, direct product factor
59C3×C5×D19—31no—
60C3×C5×D19—331no—
61C32×C5×C11C2×D1911yescharacteristic, complemented, Hall
62D209—31no—
63C11×D19—31no—
64C19×D11C3×C5×D311yescharacteristic, complemented
65C3×D3×D11—191noHall
66C2×C5×D19—331noHall
67C2×C32×C19—111no—
68C3×D57—111no—
69C3×D57C5×D1111yescharacteristic, direct product factor
70C2×C3×C5×C11—571no—
71C5×D33—191no—
72C5×D3×C11—191no—
73C3×C5×D11—21no—
74C3×C5×D11—571no—
75C3×C5×D11C3×D1911yescharacteristic, complemented
76C3×C5×D11D5711yescharacteristic, direct product factor
77C3×C5×C19—21no—
78C3×C5×C19D3×D1111yescharacteristic, complemented
79C3×C5×C19C2×C3×D1111yescharacteristic, complemented
80C2×D57—111no—
81C2×C3×D19—331no—
82C2×C5×D11—571noHall
83C11×C19C2×C3×C5×D311yescharacteristic, complemented, Hall
84C3×D33—191no—
85C3×D3×C11—191no—
86C32×D11C5×D1911yescharacteristic, complemented
87C2×C5×C19—111no—
88C5×D19—31no—
89C5×D19—331no—
90C2×C3×C5×D3—2091noHall
91C32×C19C2×C5×D1111yescharacteristic, complemented, Hall
92C3×C5×C11—21no—
93C3×C5×C11C2×C3×D1911yescharacteristic, complemented
94C3×C5×C11C2×D5711yescharacteristic, complemented
95C2×C3×D11—571no—
96D3×D11—191no—
97C2×C3×C19—111no—
98C2×C3×C19—111no—
99C2×C3×C19—221no—
100D57—111no—
101D57C3×C5×D1111yescharacteristic, direct product factor
102C3×D19—31no—
103C3×D19—331no—
104C2×C5×C11—571no—
105C5×D11—571no—
106C5×D11C3×D5711yescharacteristic, direct product factor
107C32×C11C2×C5×D1911yescharacteristic, complemented, Hall
108C5×C19C3×D3×D1111yescharacteristic, complemented, Hall
109C2×C32×C5—111no—
110C3×C5×D3—191no—
111C3×C5×D3—2091no—
112C2×D19—331noHall
113C2×C3×C11—571no—
114D33—191no—
115C3×D11—21no—
116C3×D11—571no—
117C3×D11C3×C5×D1911yescharacteristic, complemented
118C3×D11C5×D5711yescharacteristic, direct product factor
119D3×C11—191no—
120C22×C3×C5—6271no—
121C2×C5×D3—2091no—
122C3×C19—21no—
123C3×C19C5×D3×D1111yescharacteristic, complemented
124C3×C19C2×C3×C5×D1111yescharacteristic, complemented
125C5×C11C2×C3×D5711yescharacteristic, complemented, Hall
126C32×C5D11×D1911yescharacteristic, complemented, Hall
127C2×D11—571noHall
128C2×C19—111no—
129D19—31no—
130D19—331no—
131C2×C3×D3—2091noHall
132C3×C11—21no—
133C3×C11C2×C3×C5×D1911yescharacteristic, complemented
134C3×C11C2×C5×D5711yescharacteristic, complemented
135C2×C3×C5—111no—
136C2×C3×C5—111no—
137C2×C3×C5—221no—
138C2×C3×C5—571no—
139C2×C3×C5—6271no—
140C5×D3—191no—
141C5×D3—2091no—
142C2×C11—571no—
143D11—571no—
144D11C3×C5×D5711yescharacteristic, direct product factor
145C22×C5—6271noHall
146C19C3×C5×D3×D1111yescharacteristic, complemented, Sylow
147C2×C32—111no—
148C3×D3—191no—
149C3×D3—2091no—
150C3×C5—21no—
151C3×C5C3×D11×D1911yescharacteristic, complemented
152C3×C5D11×D5711yescharacteristic, direct product factor
153C22×C3—6271no—
154C2×D3—2091no—
155C11C2×C3×C5×D5711yescharacteristic, complemented, Sylow
156C2×C5—111no—
157C2×C5—571no—
158C2×C5—6271no—
159C32C5×D11×D1911yescharacteristic, complemented, Sylow
160C2×C3—111no—
161C2×C3—111no—
162C2×C3—221no—
163C2×C3—571no—
164C2×C3—6271no—
165D3—191no—
166D3—2091no—
167C5C3×D11×D5711yescharacteristic, direct product factor, Sylow
168C22—6271noSylow
169C3—21no—
170C3C3×C5×D11×D1911yescharacteristic, complemented
171C3C5×D11×D5711yescharacteristic, direct product factor
172C2—111no—
173C2—571no—
174C2—6271no—
subgroupG/H
center, hypercenterC3×C5D11×D57
commutator, cosocle, hypocenterC3×C11×C19C22×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C3×C11×C19
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×C19×D11C2semidirect
2. C3×C5×C11×D57C2semidirect
3. C3×C5×D627C2semidirect
4. C5×D11×D57C3direct (N × H)
6. C32×C5×C11×C19C22semidirect
7. C3×D11×D57C5direct (N × H)
8. C5×D627C2×C3semidirect
9. C5×C11×D57C2×C3semidirect
12. C3×C5×C19×D11D3semidirect
13. C3×C5×C19×D11C2×C3semidirect
16. C3×D627C2×C5semidirect
17. C3×C11×D57C2×C5semidirect
18. C32×C19×D11C2×C5semidirect
21. C3×C5×C11×C19C2×D3semidirect
22. C3×C5×C11×C19C22×C3semidirect
23. D11×D57C3×C5direct (N × H)
26. C5×C19×D11C3×D3semidirect
29. C32×C11×C19C22×C5semidirect
32. C3×C5×D57D11direct (N × H)
33. D627C2×C3×C5semidirect
34. C11×D57C2×C3×C5semidirect
37. C3×C19×D11C5×D3semidirect
38. C3×C19×D11C2×C3×C5semidirect
42. C5×C11×C19C2×C3×D3semidirect
45. C32×C5×D11D19semidirect
46. C32×C5×C19C2×D11semidirect
52. C3×C11×C19C2×C5×D3semidirect
53. C3×C11×C19C22×C3×C5semidirect
58. C5×D57C3×D11direct (N × H)
61. C32×C5×C11C2×D19semidirect
64. C19×D11C3×C5×D3semidirect
69. C3×D57C5×D11direct (N × H)
75. C3×C5×D11C3×D19semidirect
76. C3×C5×D11D57direct (N × H)
78. C3×C5×C19D3×D11semidirect
79. C3×C5×C19C2×C3×D11semidirect
83. C11×C19C2×C3×C5×D3semidirect
86. C32×D11C5×D19semidirect
91. C32×C19C2×C5×D11semidirect
93. C3×C5×C11C2×C3×D19semidirect
94. C3×C5×C11C2×D57semidirect
101. D57C3×C5×D11direct (N × H)
106. C5×D11C3×D57direct (N × H)
107. C32×C11C2×C5×D19semidirect
108. C5×C19C3×D3×D11semidirect
117. C3×D11C3×C5×D19semidirect
118. C3×D11C5×D57direct (N × H)
123. C3×C19C5×D3×D11semidirect
124. C3×C19C2×C3×C5×D11semidirect
125. C5×C11C2×C3×D57semidirect
126. C32×C5D11×D19semidirect
133. C3×C11C2×C3×C5×D19semidirect
134. C3×C11C2×C5×D57semidirect
144. D11C3×C5×D57direct (N × H)
146. C19C3×C5×D3×D11semidirect
151. C3×C5C3×D11×D19semidirect
152. C3×C5D11×D57direct (N × H)
155. C11C2×C3×C5×D57semidirect
159. C32C5×D11×D19semidirect
167. C5C3×D11×D57direct (N × H)
170. C3C3×C5×D11×D19semidirect
171. C3C5×D11×D57direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C19×D112
C3×C5×C11×D572
C3×C5×D6272
C5×D11×D573
C3×C5×D11×D193
C3×D11×D575
C2×C3×C5×D5711
C3×C5×D3×D1119