Finite Group Databasebeta

← C3×D3×D1045 #49178694

Subgroups — C3×D3×D1045 #49178694

Order 37620.

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

normal subgroups only

This group has 176 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
1C32×D1045C211yesmaximal, characteristic, complemented
2C3×C5×D3×C11×C19C211yesmaximal, characteristic, complemented
3C3×D3135C211yesmaximal, characteristic, complemented
4C2×C3×D1045—31nomaximal
5D3×D1045C311yesmaximal, characteristic, direct product factor
6C32×C5×C11×C19C2211yescharacteristic, complemented, Hall
7C3×D3×D209—51nomaximal, Hall
8D3135C2×C311yescharacteristic, complemented
9C5×D3×C11×C19C2×C311yescharacteristic, complemented
10C3×D1045—21no—
11C3×D1045—31no—
12C3×D1045D311yescharacteristic, direct product factor
13C3×D1045C2×C311yescharacteristic, complemented
14C2×C3×C5×C11×C19—31no—
15C2×D1045—31noHall
16C3×D627—51no—
17C3×D3×C11×C19D511yescharacteristic, complemented
18C32×D209—51no—
19C3×D3×D95—111nomaximal, Hall
20C3×C5×C11×C19—21no—
21C3×C5×C11×C19C2×D311yescharacteristic, complemented
22C3×C5×C11×C19C22×C311yescharacteristic, complemented
23C2×C3×D209—151no—
24D3×D209—51no—
25D1045—31no—
26D1045C3×D311yescharacteristic, direct product factor
27C2×C5×C11×C19—31no—
28C3×D3×D55—191nomaximal, Hall
29C32×C11×C19C2×D511yescharacteristic, complemented, Hall
30C3×D285—111no—
31C3×C5×D3×C19D1111yescharacteristic, complemented
32C32×D95—111no—
33C2×C3×C11×C19—31no—
34D627—51no—
35D3×C11×C19C3×D511yescharacteristic, complemented
36C3×D209—51no—
37C3×D209—51no—
38C3×D209—101no—
39C3×D209—151no—
40C2×C3×D95—331no—
41D3×D95—111no—
42C5×C11×C19C2×C3×D311yescharacteristic, complemented, Hall
43C3×D165—191no—
44C3×C5×D3×C11D1911yescharacteristic, complemented
45C32×D55—191no—
46C32×C5×C19C2×D1111yescharacteristic, complemented, Hall
47C2×D209—151noHall
48C3×D3×D19—551noHall
49C2×C3×D55—571no—
50D3×D55—191no—
51C3×C11×C19—21no—
52C3×C11×C19D3×D511yescharacteristic, complemented
53C3×C11×C19C2×C3×D511yescharacteristic, complemented
54C2×C3×C5×C19—31no—
55D285—111no—
56C5×D3×C19C3×D1111yescharacteristic, complemented
57C3×D95—111no—
58C3×D95—111no—
59C3×D95—221no—
60C3×D95—331no—
61C32×C5×C11C2×D1911yescharacteristic, complemented, Hall
62C2×C11×C19—31no—
63D209—51no—
64D209—151no—
65C3×D3×D11—951noHall
66C2×D95—331noHall
67C3×D57—551no—
68C3×D3×C19D5511yescharacteristic, complemented
69C32×D19—551no—
70C2×C3×C5×C11—31no—
71D165—191no—
72C5×D3×C11C3×D1911yescharacteristic, complemented
73C3×D55—191no—
74C3×D55—191no—
75C3×D55—381no—
76C3×D55—571no—
77C3×C5×C19—21no—
78C3×C5×C19D3×D1111yescharacteristic, complemented
79C3×C5×C19C2×C3×D1111yescharacteristic, complemented
80C2×C3×D19—1651no—
81D3×D19—551no—
82C2×D55—571noHall
83C11×C19C3×D3×D511yescharacteristic, complemented, Hall
84C3×D33—951no—
85C3×D3×C11D9511yescharacteristic, complemented
86C32×D11—951no—
87C2×C5×C19—31no—
88D95—111no—
89D95—331no—
90C3×D3×D5—2091noHall
91C32×C19C2×D5511yescharacteristic, complemented, Hall
92C3×C5×C11—21no—
93C3×C5×C11D3×D1911yescharacteristic, complemented
94C3×C5×C11C2×C3×D1911yescharacteristic, complemented
95C2×C3×D11—2851no—
96D3×D11—951no—
97C2×C3×C19—31no—
98D57—551no—
99C3×D19—551no—
100C3×D19—551no—
101C3×D19—1101no—
102C3×D19—1651no—
103D3×C19C3×D5511yescharacteristic, complemented
104C2×C5×C11—31no—
105D55—191no—
106D55—571no—
107C32×C11C2×D9511yescharacteristic, complemented, Hall
108C5×C19C3×D3×D1111yescharacteristic, complemented, Hall
109C3×D15—2091no—
110C3×C5×D3D20911yescharacteristic, complemented
111C32×D5—2091no—
112C2×D19—1651noHall
113C2×C3×C11—31no—
114D33—951no—
115C3×D11—2851no—
116C3×D11—951no—
117C3×D11—951no—
118C3×D11—1901no—
119D3×C11C3×D9511yescharacteristic, complemented
120C2×C3×D5—6271no—
121D3×D5—2091no—
122C3×C19—21no—
123C3×C19D3×D5511yescharacteristic, complemented
124C3×C19C2×C3×D5511yescharacteristic, complemented
125C5×C11C3×D3×D1911yescharacteristic, complemented, Hall
126C32×C5C2×D20911yescharacteristic, complemented, Hall
127C2×D11—2851noHall
128C2×C19—31no—
129D19—551no—
130D19—1651no—
131C2×C3×D3—10451noHall
132C3×C11—21no—
133C3×C11D3×D9511yescharacteristic, complemented
134C3×C11C2×C3×D9511yescharacteristic, complemented
135C2×C3×C5—31no—
136D15—2091no—
137C3×D5—6271no—
138C3×D5—4181no—
139C3×D5—2091no—
140C3×D5—2091no—
141C5×D3C3×D20911yescharacteristic, complemented
142C2×C11—31no—
143D11—2851no—
144D11—951no—
145C2×D5—6271noHall
146C19C3×D3×D5511yescharacteristic, complemented, Sylow
147C2×C32—10451no—
148C3×D3—10451no—
149C3×D3D104511yescharacteristic, direct product factor
150C3×C5—21no—
151C3×C5D3×D20911yescharacteristic, complemented
152C3×C5C2×C3×D20911yescharacteristic, complemented
153C22×C3—31351no—
154C2×D3—10451no—
155C11C3×D3×D9511yescharacteristic, complemented, Sylow
156C2×C5—31no—
157D5—6271no—
158D5—2091no—
159C32C2×D104511yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—10451no—
162C2×C3—10451no—
163C2×C3—20901no—
164C2×C3—31351no—
165D3—10451no—
166D3C3×D104511yescharacteristic, direct product factor
167C5C3×D3×D20911yescharacteristic, complemented, Sylow
168C22—31351noSylow
169C3—21no—
170C3D3×D104511yescharacteristic, direct product factor
171C3C2×C3×D104511yescharacteristic, complemented
172C2—31no—
173C2—10451no—
174C2—31351no—
subgroupG/H
center, hypercenterC3D3×D1045
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×D1045C2semidirect
2. C3×C5×D3×C11×C19C2semidirect
3. C3×D3135C2semidirect
5. D3×D1045C3direct (N × H)
6. C32×C5×C11×C19C22semidirect
8. D3135C2×C3semidirect
9. C5×D3×C11×C19C2×C3semidirect
12. C3×D1045D3direct (N × H)
13. C3×D1045C2×C3semidirect
17. C3×D3×C11×C19D5semidirect
21. C3×C5×C11×C19C2×D3semidirect
22. C3×C5×C11×C19C22×C3semidirect
26. D1045C3×D3direct (N × H)
29. C32×C11×C19C2×D5semidirect
31. C3×C5×D3×C19D11semidirect
35. D3×C11×C19C3×D5semidirect
42. C5×C11×C19C2×C3×D3semidirect
44. C3×C5×D3×C11D19semidirect
46. C32×C5×C19C2×D11semidirect
52. C3×C11×C19D3×D5semidirect
53. C3×C11×C19C2×C3×D5semidirect
56. C5×D3×C19C3×D11semidirect
61. C32×C5×C11C2×D19semidirect
68. C3×D3×C19D55semidirect
72. C5×D3×C11C3×D19semidirect
78. C3×C5×C19D3×D11semidirect
79. C3×C5×C19C2×C3×D11semidirect
83. C11×C19C3×D3×D5semidirect
85. C3×D3×C11D95semidirect
91. C32×C19C2×D55semidirect
93. C3×C5×C11D3×D19semidirect
94. C3×C5×C11C2×C3×D19semidirect
103. D3×C19C3×D55semidirect
107. C32×C11C2×D95semidirect
108. C5×C19C3×D3×D11semidirect
110. C3×C5×D3D209semidirect
119. D3×C11C3×D95semidirect
123. C3×C19D3×D55semidirect
124. C3×C19C2×C3×D55semidirect
125. C5×C11C3×D3×D19semidirect
126. C32×C5C2×D209semidirect
133. C3×C11D3×D95semidirect
134. C3×C11C2×C3×D95semidirect
141. C5×D3C3×D209semidirect
146. C19C3×D3×D55semidirect
149. C3×D3D1045direct (N × H)
151. C3×C5D3×D209semidirect
152. C3×C5C2×C3×D209semidirect
155. C11C3×D3×D95semidirect
159. C32C2×D1045semidirect
166. D3C3×D1045direct (N × H)
167. C5C3×D3×D209semidirect
170. C3D3×D1045direct (N × H)
171. C3C2×C3×D1045semidirect

Maximal subgroups

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

subgroupindex
C32×D10452
C3×C5×D3×C11×C192
C3×D31352
C2×C3×D10453
D3×D10453
C3×D3×D2095
C3×D3×D9511
C3×D3×D5519