Finite Group Databasebeta

← C3×D55⋊D57 #49178697

Subgroups — C3×D55⋊D57 #49178697

Order 37620.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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×C19×D55C211yesmaximal, characteristic, complemented
2C3×C5×D627C211yesmaximal, characteristic, complemented
3C3×C11×D285C211yesmaximal, characteristic, complemented
4D55⋊D57C311yesmaximal, characteristic, direct product factor
5C3×D55⋊D19—31nomaximal
6C32×C5×C11×C19C2211yescharacteristic, complemented, Hall
7C3×D11×D57—51nomaximal, Hall
8C11×D285C2×C311yescharacteristic, complemented
9C5×D627C2×C311yescharacteristic, complemented
10C3×C19×D55—21no—
11C3×C19×D55D311yescharacteristic, complemented
12C3×C19×D55C2×C311yescharacteristic, complemented
13C3×C11×D95—31no—
14C3×C5×D209—31no—
15D55⋊D19—31noHall
16C3×D627D511yescharacteristic, complemented
17C3×C11×D57—51no—
18C32×C19×D11—51no—
19C3×D5×D57—111nomaximal, Hall
20C3×C5×C11×C19—21no—
21C3×C5×C11×C19C2×D311yescharacteristic, complemented
22C3×C5×C11×C19C22×C311yescharacteristic, complemented
23D11×D57—51no—
24C3×D11×D19—151no—
25C19×D55C3×D311yescharacteristic, complemented
26C11×D95—31no—
27C5×D209—31no—
28C3×D15⋊D11—191nomaximal, Hall
29C32×C11×C19C2×D511yescharacteristic, complemented, Hall
30C3×D285D1111yescharacteristic, complemented
31C3×C5×D57—111no—
32C32×D5×C19—111no—
33D627C3×D511yescharacteristic, complemented
34C11×D57—51no—
35C3×D209—31no—
36C3×C19×D11—51no—
37C3×C19×D11—51no—
38C3×C19×D11—101no—
39C3×C11×D19—151no—
40D5×D57—111no—
41C3×D5×D19—331no—
42C5×C11×C19C2×C3×D311yescharacteristic, complemented, Hall
43C3×C11×D15—191no—
44C3×C5×D33—191no—
45C32×D55D1911yescharacteristic, complemented
46C32×C5×C19C2×D1111yescharacteristic, complemented, Hall
47D11×D19—151noHall
48C2×C3×D57—551noHall
49D15⋊D11—191no—
50C3×D5×D11—571no—
51C3×C11×C19—21no—
52C3×C11×C19D3×D511yescharacteristic, complemented
53C3×C11×C19C2×C3×D511yescharacteristic, complemented
54D285C3×D1111yescharacteristic, complemented
55C5×D57—111no—
56C3×D95—31no—
57C3×D5×C19—111no—
58C3×D5×C19—111no—
59C3×D5×C19—221no—
60C3×C5×D19—331no—
61C32×C5×C11C2×D1911yescharacteristic, complemented, Hall
62D209—31no—
63C11×D19—151no—
64C19×D11—51no—
65C3×D3×D11—951noHall
66D5×D19—331noHall
67C2×C32×C19—551no—
68C3×D57—51no—
69C3×D57—111no—
70C11×D15—191no—
71C5×D33—191no—
72C3×D55—21no—
73C3×D55C3×D1911yescharacteristic, complemented
74C3×D55D5711yescharacteristic, complemented
75C3×D5×C11—571no—
76C3×C5×D11—571no—
77C3×C5×C19—21no—
78C3×C5×C19D3×D1111yescharacteristic, complemented
79C3×C5×C19C2×C3×D1111yescharacteristic, complemented
80C2×D57—551no—
81C2×C3×D19—1651no—
82D5×D11—571noHall
83C11×C19C3×D3×D511yescharacteristic, complemented, Hall
84C3×D33—191no—
85C3×D3×C11—951no—
86C32×D11—51no—
87D95—31no—
88C5×D19—331no—
89D5×C19—111no—
90C3×D3×D5—2091noHall
91C32×C19D5×D1111yescharacteristic, complemented, Hall
92C3×C5×C11—21no—
93C3×C5×C11C2×C3×D1911yescharacteristic, complemented
94C3×C5×C11C2×D5711yescharacteristic, complemented
95C2×C3×D11—2851no—
96D3×D11—951no—
97C2×C3×C19—551no—
98C2×C3×C19—551no—
99C2×C3×C19—1101no—
100D57—51no—
101D57—111no—
102C3×D19—151no—
103C3×D19—331no—
104D55C3×D5711yescharacteristic, complemented
105C5×D11—571no—
106D5×C11—571no—
107C32×C11D5×D1911yescharacteristic, complemented, Hall
108C5×C19C3×D3×D1111yescharacteristic, complemented, Hall
109C3×D15—191no—
110C3×C5×D3—2091no—
111C32×D5—111no—
112C2×D19—1651noHall
113C2×C3×C11—2851no—
114D33—191no—
115C3×D11—51no—
116C3×D11—51no—
117C3×D11—101no—
118C3×D11—571no—
119D3×C11—951no—
120C2×C3×D5—6271no—
121D3×D5—2091no—
122C3×C19—21no—
123C3×C19C3×D5×D1111yescharacteristic, complemented
124C3×C19D15⋊D1111yescharacteristic, complemented
125C5×C11C2×C3×D5711yescharacteristic, complemented, Hall
126C32×C5D11×D1911yescharacteristic, complemented, Hall
127C2×D11—2851noHall
128C2×C19—551no—
129D19—151no—
130D19—331no—
131C2×C3×D3—10451noHall
132C3×C11—21no—
133C3×C11C3×D5×D1911yescharacteristic, complemented
134C3×C11D5×D5711yescharacteristic, complemented
135C2×C3×C5—6271no—
136D15—191no—
137C3×D5—111no—
138C3×D5—111no—
139C3×D5—221no—
140C3×D5—571no—
141C5×D3—2091no—
142C2×C11—2851no—
143D11—51no—
144D11—571no—
145C2×D5—6271noHall
146C19C3×D15⋊D1111yescharacteristic, complemented, Sylow
147C2×C32—551no—
148C3×D3—951no—
149C3×D3—2091no—
150C3×C5—21no—
151C3×C5C3×D11×D1911yescharacteristic, complemented
152C3×C5D11×D5711yescharacteristic, complemented
153C22×C3—31351no—
154C2×D3—10451no—
155C11C3×D5×D5711yescharacteristic, complemented, Sylow
156C2×C5—6271no—
157D5—111no—
158D5—571no—
159C32D55⋊D1911yescharacteristic, complemented, Sylow
160C2×C3—2851no—
161C2×C3—551no—
162C2×C3—551no—
163C2×C3—1101no—
164C2×C3—6271no—
165D3—951no—
166D3—2091no—
167C5C3×D11×D5711yescharacteristic, complemented, Sylow
168C22—31351noSylow
169C3—21no—
170C3C3×D55⋊D1911yescharacteristic, complemented
171C3D55⋊D5711yescharacteristic, direct product factor
172C2—2851no—
173C2—551no—
174C2—6271no—
subgroupG/H
center, hypercenterC3D55⋊D57
commutator, cosocle, hypocenterC3×C5×C11×C19C22×C3
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C3×C5×C11×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C19×D55C2semidirect
2. C3×C5×D627C2semidirect
3. C3×C11×D285C2semidirect
4. D55⋊D57C3direct (N × H)
6. C32×C5×C11×C19C22semidirect
8. C11×D285C2×C3semidirect
9. C5×D627C2×C3semidirect
11. C3×C19×D55D3semidirect
12. C3×C19×D55C2×C3semidirect
16. C3×D627D5semidirect
21. C3×C5×C11×C19C2×D3semidirect
22. C3×C5×C11×C19C22×C3semidirect
25. C19×D55C3×D3semidirect
29. C32×C11×C19C2×D5semidirect
30. C3×D285D11semidirect
33. D627C3×D5semidirect
42. C5×C11×C19C2×C3×D3semidirect
45. C32×D55D19semidirect
46. C32×C5×C19C2×D11semidirect
52. C3×C11×C19D3×D5semidirect
53. C3×C11×C19C2×C3×D5semidirect
54. D285C3×D11semidirect
61. C32×C5×C11C2×D19semidirect
73. C3×D55C3×D19semidirect
74. C3×D55D57semidirect
78. C3×C5×C19D3×D11semidirect
79. C3×C5×C19C2×C3×D11semidirect
83. C11×C19C3×D3×D5semidirect
91. C32×C19D5×D11semidirect
93. C3×C5×C11C2×C3×D19semidirect
94. C3×C5×C11C2×D57semidirect
104. D55C3×D57semidirect
107. C32×C11D5×D19semidirect
108. C5×C19C3×D3×D11semidirect
123. C3×C19C3×D5×D11semidirect
124. C3×C19D15⋊D11semidirect
125. C5×C11C2×C3×D57semidirect
126. C32×C5D11×D19semidirect
133. C3×C11C3×D5×D19semidirect
134. C3×C11D5×D57semidirect
146. C19C3×D15⋊D11semidirect
151. C3×C5C3×D11×D19semidirect
152. C3×C5D11×D57semidirect
155. C11C3×D5×D57semidirect
159. C32D55⋊D19semidirect
167. C5C3×D11×D57semidirect
170. C3C3×D55⋊D19semidirect
171. C3D55⋊D57direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C19×D552
C3×C5×D6272
C3×C11×D2852
D55⋊D573
C3×D55⋊D193
C3×D11×D575
C3×D5×D5711
C3×D15⋊D1119