Finite Group Databasebeta

← C2×C3×C5×D561 #46778204

Subgroups — C2×C3×C5×D561 #46778204

Order 33660.

176 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 76 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×D561C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×C5×D187—31nomaximal
4C2×C5×D561C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
6C2×C3×D561C511yesmaximal, characteristic, direct product factor, Hall
7C5×D561C2×C312yesdirect product factor
8C3×C5×D187—32no—
9C2×C3×C5×C11×C17—21no—
10C2×C3×C5×C11×C17D311yescharacteristic, complemented
11C2×C3×C5×C11×C17C2×C311yescharacteristic, complemented
12C2×C5×D187—31noHall
13C3×D561C2×C512yesdirect product factor
14C2×C32×C11×C17C2×C511yescharacteristic, complemented
15C2×C3×C5×D51—111nomaximal, Hall
16C3×C5×C11×C17—21no—
17C3×C5×C11×C17C2×D311yescharacteristic, complemented
18C3×C5×C11×C17C22×C311yescharacteristic, complemented
19C2×C3×D187—31no—
20C2×D561C3×C511yescharacteristic, direct product factor
21C2×C3×C5×D33—171nomaximal, Hall
22C2×C5×C11×C17C3×D311yescharacteristic, complemented
23C5×D187—32no—
24C32×C11×C17C22×C511yescharacteristic, complemented, Hall
25C2×C32×C5×C17D1111yescharacteristic, complemented
26C3×C5×D51—112no—
27C2×C3×C11×C17—21no—
28C2×C3×C11×C17C5×D311yescharacteristic, complemented
29C2×C3×C11×C17C2×C3×C511yescharacteristic, complemented
30D561C2×C3×C512yesdirect product factor
31C3×D187—32no—
32C2×C5×D51—111no—
33C2×C3×C5×D17—331no—
34C2×C32×C5×C11D1711yescharacteristic, complemented
35C3×C5×D33—172no—
36C5×C11×C17C2×C3×D311yescharacteristic, complemented, Hall
37C32×C5×C17C2×D1111yescharacteristic, complemented, Hall
38C2×D187—31noHall
39C2×C5×D33—171no—
40C2×C3×C5×D11—511no—
41C2×C3×D51—111noHall
42C3×C11×C17—21no—
43C3×C11×C17C2×C5×D311yescharacteristic, complemented
44C3×C11×C17C22×C3×C511yescharacteristic, complemented
45C2×C3×C5×C17—21no—
46C2×C3×C5×C17C3×D1111yescharacteristic, complemented
47C2×C3×C5×C17D3311yescharacteristic, complemented
48C5×D51—112no—
49C3×C5×D17—332no—
50C32×C5×C11C2×D1711yescharacteristic, complemented, Hall
51C2×C3×D33—171noHall
52C2×C11×C17C3×C5×D311yescharacteristic, complemented
53D187—32no—
54C2×C5×D17—331noHall
55C2×C3×C5×C11—21no—
56C2×C3×C5×C11C3×D1711yescharacteristic, complemented
57C2×C3×C5×C11D5111yescharacteristic, complemented
58C5×D33—172no—
59C3×C5×D11—512no—
60C2×C32×C17C5×D1111yescharacteristic, complemented
61C3×D51—112no—
62C3×C5×C17—21no—
63C3×C5×C17C2×C3×D1111yescharacteristic, complemented
64C3×C5×C17C2×D3311yescharacteristic, complemented
65C2×C5×D11—511noHall
66C2×D51—111no—
67C2×C3×D17—331no—
68C2×C32×C11C5×D1711yescharacteristic, complemented
69C3×D33—172no—
70C11×C17C2×C3×C5×D311yescharacteristic, complemented, Hall
71C2×C3×C5×D3—1871noHall
72C2×C5×C17C3×D3311yescharacteristic, complemented
73C5×D17—332no—
74C3×C5×C11—21no—
75C3×C5×C11C2×C3×D1711yescharacteristic, complemented
76C3×C5×C11C2×D5111yescharacteristic, complemented
77C32×C17C2×C5×D1111yescharacteristic, complemented, Hall
78C2×D33—171no—
79C2×C3×D11—511no—
80C2×C5×C11C3×D5111yescharacteristic, complemented
81C5×D11—512no—
82C2×C3×C17—21no—
83C2×C3×C17C3×C5×D1111yescharacteristic, complemented
84C2×C3×C17C5×D3311yescharacteristic, complemented
85D51—112no—
86C3×D17—332no—
87C32×C11C2×C5×D1711yescharacteristic, complemented, Hall
88C2×C32×C5D18711yescharacteristic, complemented
89C3×C5×D3—1872no—
90C5×C17C2×C3×D3311yescharacteristic, complemented, Hall
91C2×D17—331noHall
92C2×C3×C11—21no—
93C2×C3×C11C3×C5×D1711yescharacteristic, complemented
94C2×C3×C11C5×D5111yescharacteristic, complemented
95D33—172no—
96C3×D11—512no—
97C22×C3×C5—5611no—
98C2×C5×D3—1871no—
99C5×C11C2×C3×D5111yescharacteristic, complemented, Hall
100C3×C17—21no—
101C3×C17C2×C3×C5×D1111yescharacteristic, complemented
102C3×C17C2×C5×D3311yescharacteristic, complemented
103C32×C5C2×D18711yescharacteristic, complemented, Hall
104C2×D11—511noHall
105C2×C3×D3—1871noHall
106C2×C17C3×C5×D3311yescharacteristic, complemented
107D17—332no—
108C3×C11—21no—
109C3×C11C2×C3×C5×D1711yescharacteristic, complemented
110C3×C11C2×C5×D5111yescharacteristic, complemented
111C2×C3×C5—21no—
112C2×C3×C5—5612no—
113C2×C3×C5C3×D18711yescharacteristic, complemented
114C2×C3×C5D56111yescharacteristic, direct product factor
115C5×D3—1872no—
116C2×C11C3×C5×D5111yescharacteristic, complemented
117D11—512no—
118C22×C5—5611noHall
119C2×C32C5×D18711yescharacteristic, complemented
120C3×D3—1872no—
121C17C2×C3×C5×D3311yescharacteristic, complemented, Sylow
122C3×C5—21no—
123C3×C5C2×D56111yescharacteristic, direct product factor
124C3×C5C2×C3×D18711yescharacteristic, complemented
125C22×C3—5611no—
126C2×D3—1871no—
127C11C2×C3×C5×D5111yescharacteristic, complemented, Sylow
128C2×C5—5612no—
129C2×C5C3×D56111yescharacteristic, direct product factor
130C32C2×C5×D18711yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—5612no—
133C2×C3C3×C5×D18711yescharacteristic, complemented
134C2×C3C5×D56111yescharacteristic, direct product factor
135D3—1872no—
136C5C2×C3×D56111yescharacteristic, direct product factor, Sylow
137C22—5611noSylow
138C3—21no—
139C3C2×C5×D56111yescharacteristic, direct product factor
140C3C2×C3×C5×D18711yescharacteristic, complemented
141C2—5612no—
142C2C3×C5×D56111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5D561
commutator, cosocle, hypocenterC3×C11×C17C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D561C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
4. C2×C5×D561C3direct (N × H)
5. C32×C5×C11×C17C22semidirect
6. C2×C3×D561C5direct (N × H)
7. C5×D561C2×C3direct (N × H)
10. C2×C3×C5×C11×C17D3semidirect
11. C2×C3×C5×C11×C17C2×C3semidirect
13. C3×D561C2×C5direct (N × H)
14. C2×C32×C11×C17C2×C5semidirect
17. C3×C5×C11×C17C2×D3semidirect
18. C3×C5×C11×C17C22×C3semidirect
20. C2×D561C3×C5direct (N × H)
22. C2×C5×C11×C17C3×D3semidirect
24. C32×C11×C17C22×C5semidirect
25. C2×C32×C5×C17D11semidirect
28. C2×C3×C11×C17C5×D3semidirect
29. C2×C3×C11×C17C2×C3×C5semidirect
30. D561C2×C3×C5direct (N × H)
34. C2×C32×C5×C11D17semidirect
36. C5×C11×C17C2×C3×D3semidirect
37. C32×C5×C17C2×D11semidirect
43. C3×C11×C17C2×C5×D3semidirect
44. C3×C11×C17C22×C3×C5semidirect
46. C2×C3×C5×C17C3×D11semidirect
47. C2×C3×C5×C17D33semidirect
50. C32×C5×C11C2×D17semidirect
52. C2×C11×C17C3×C5×D3semidirect
56. C2×C3×C5×C11C3×D17semidirect
57. C2×C3×C5×C11D51semidirect
60. C2×C32×C17C5×D11semidirect
63. C3×C5×C17C2×C3×D11semidirect
64. C3×C5×C17C2×D33semidirect
68. C2×C32×C11C5×D17semidirect
70. C11×C17C2×C3×C5×D3semidirect
72. C2×C5×C17C3×D33semidirect
75. C3×C5×C11C2×C3×D17semidirect
76. C3×C5×C11C2×D51semidirect
77. C32×C17C2×C5×D11semidirect
80. C2×C5×C11C3×D51semidirect
83. C2×C3×C17C3×C5×D11semidirect
84. C2×C3×C17C5×D33semidirect
87. C32×C11C2×C5×D17semidirect
88. C2×C32×C5D187semidirect
90. C5×C17C2×C3×D33semidirect
93. C2×C3×C11C3×C5×D17semidirect
94. C2×C3×C11C5×D51semidirect
99. C5×C11C2×C3×D51semidirect
101. C3×C17C2×C3×C5×D11semidirect
102. C3×C17C2×C5×D33semidirect
103. C32×C5C2×D187semidirect
106. C2×C17C3×C5×D33semidirect
109. C3×C11C2×C3×C5×D17semidirect
110. C3×C11C2×C5×D51semidirect
113. C2×C3×C5C3×D187semidirect
114. C2×C3×C5D561direct (N × H)
116. C2×C11C3×C5×D51semidirect
119. C2×C32C5×D187semidirect
121. C17C2×C3×C5×D33semidirect
123. C3×C5C2×D561direct (N × H)
124. C3×C5C2×C3×D187semidirect
127. C11C2×C3×C5×D51semidirect
129. C2×C5C3×D561direct (N × H)
130. C32C2×C5×D187semidirect
133. C2×C3C3×C5×D187semidirect
134. C2×C3C5×D561direct (N × H)
136. C5C2×C3×D561direct (N × H)
139. C3C2×C5×D561direct (N × H)
140. C3C2×C3×C5×D187semidirect
142. C2C3×C5×D561direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D5612
C2×C32×C5×C11×C172
C2×C3×C5×D1873
C2×C5×D5613
C2×C3×D5615
C2×C3×C5×D5111
C2×C3×C5×D3317