Finite Group Databasebeta

← C2×C3×C7×D285 #37561641

Subgroups — C2×C3×C7×D285 #37561641

Order 23940.

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×C7×D285C212yesmaximal, direct product factor
2C2×C32×C5×C7×C19C211yesmaximal, characteristic, complemented
3C2×C3×C7×D95—31nomaximal
4C2×C7×D285C311yesmaximal, characteristic, direct product factor
5C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
6C2×C3×C7×D57—51nomaximal, Hall
7C7×D285C2×C312yesdirect product factor
8C3×C7×D95—32no—
9C2×C3×C5×C7×C19—21no—
10C2×C3×C5×C7×C19D311yescharacteristic, complemented
11C2×C3×C5×C7×C19C2×C311yescharacteristic, complemented
12C2×C3×D285C711yesmaximal, characteristic, direct product factor, Hall
13C2×C7×D95—31noHall
14C3×C7×D57—52no—
15C2×C32×C7×C19D511yescharacteristic, complemented
16C3×C5×C7×C19—21no—
17C3×C5×C7×C19C2×D311yescharacteristic, complemented
18C3×C5×C7×C19C22×C311yescharacteristic, complemented
19C2×C32×C5×C19C2×C711yescharacteristic, complemented
20C3×D285C2×C712yesdirect product factor
21C2×C7×D57—51no—
22C2×C3×C7×D19—151no—
23C2×C5×C7×C19C3×D311yescharacteristic, complemented
24C7×D95—32no—
25C2×C3×C7×D15—191nomaximal, Hall
26C32×C7×C19C2×D511yescharacteristic, complemented, Hall
27C2×D285C3×C711yescharacteristic, direct product factor
28C2×C3×D95—31no—
29C32×C5×C19C22×C711yescharacteristic, complemented, Hall
30C2×C3×C7×C19—21no—
31C2×C3×C7×C19C3×D511yescharacteristic, complemented
32C2×C3×C7×C19D1511yescharacteristic, complemented
33C7×D57—52no—
34C3×C7×D19—152no—
35C2×C3×D57—51noHall
36C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
37C2×C32×C5×C7D1911yescharacteristic, complemented
38C3×C7×D15—192no—
39C2×C3×C5×C19—21no—
40C2×C3×C5×C19D3×C711yescharacteristic, complemented
41C2×C3×C5×C19C2×C3×C711yescharacteristic, complemented
42D285C2×C3×C712yesdirect product factor
43C3×D95—32no—
44C2×C7×D19—151noHall
45C2×C7×D15—191no—
46C2×C3×C7×D5—571no—
47C3×C7×C19—21no—
48C3×C7×C19C2×C3×D511yescharacteristic, complemented
49C3×C7×C19C2×D1511yescharacteristic, complemented
50C2×D95—31noHall
51C2×C32×C19C7×D511yescharacteristic, complemented
52C3×D57—52no—
53C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
54C3×C5×C19—21no—
55C3×C5×C19C2×D3×C711yescharacteristic, complemented
56C3×C5×C19C22×C3×C711yescharacteristic, complemented
57C2×C7×C19C3×D1511yescharacteristic, complemented
58C7×D19—152no—
59C2×C3×D3×C7—951noHall
60C2×D57—51no—
61C2×C3×D19—151no—
62C2×C3×C5×C7—21no—
63C2×C3×C5×C7C3×D1911yescharacteristic, complemented
64C2×C3×C5×C7D5711yescharacteristic, complemented
65C7×D15—192no—
66C3×C7×D5—572no—
67C2×C5×C19C3×D3×C711yescharacteristic, complemented
68D95—32no—
69C2×C3×D15—191noHall
70C32×C19C2×C7×D511yescharacteristic, complemented, Hall
71C2×C7×D5—571noHall
72C7×C19C2×C3×D1511yescharacteristic, complemented, Hall
73C2×C32×C7D9511yescharacteristic, complemented
74C3×D3×C7—952no—
75C2×C3×C19—21no—
76C2×C3×C19C3×C7×D511yescharacteristic, complemented
77C2×C3×C19C7×D1511yescharacteristic, complemented
78D57—52no—
79C3×D19—152no—
80C3×C5×C7—21no—
81C3×C5×C7C2×C3×D1911yescharacteristic, complemented
82C3×C5×C7C2×D5711yescharacteristic, complemented
83C5×C19C2×C3×D3×C711yescharacteristic, complemented, Hall
84C2×C32×C5C7×D1911yescharacteristic, complemented
85C3×D15—192no—
86C22×C3×C7—2851no—
87C2×D3×C7—951no—
88C2×D19—151noHall
89C2×C5×C7C3×D5711yescharacteristic, complemented
90C7×D5—572no—
91C32×C7C2×D9511yescharacteristic, complemented, Hall
92C2×D15—191no—
93C2×C3×D5—571no—
94C3×C19—21no—
95C3×C19C2×C3×C7×D511yescharacteristic, complemented
96C3×C19C2×C7×D1511yescharacteristic, complemented
97C32×C5C2×C7×D1911yescharacteristic, complemented, Hall
98C2×C3×C7—21no—
99C2×C3×C7—2852no—
100C2×C3×C7C3×D9511yescharacteristic, complemented
101C2×C3×C7D28511yescharacteristic, direct product factor
102D3×C7—952no—
103C2×C19C3×C7×D1511yescharacteristic, complemented
104D19—152no—
105C2×C3×D3—951noHall
106C5×C7C2×C3×D5711yescharacteristic, complemented, Hall
107C2×C3×C5—21no—
108C2×C3×C5C3×C7×D1911yescharacteristic, complemented
109C2×C3×C5C7×D5711yescharacteristic, complemented
110D15—192no—
111C3×D5—572no—
112C22×C7—2851noHall
113C3×C7—21no—
114C3×C7C2×C3×D9511yescharacteristic, complemented
115C3×C7C2×D28511yescharacteristic, direct product factor
116C2×D5—571noHall
117C19C2×C3×C7×D1511yescharacteristic, complemented, Sylow
118C2×C32C7×D9511yescharacteristic, complemented
119C3×D3—952no—
120C3×C5—21no—
121C3×C5C2×C3×C7×D1911yescharacteristic, complemented
122C3×C5C2×C7×D5711yescharacteristic, complemented
123C2×C7—2852no—
124C2×C7C3×D28511yescharacteristic, direct product factor
125C22×C3—2851no—
126C2×D3—951no—
127C2×C5C3×C7×D5711yescharacteristic, complemented
128D5—572no—
129C32C2×C7×D9511yescharacteristic, complemented, Sylow
130C7C2×C3×D28511yescharacteristic, direct product factor, Sylow
131C2×C3—21no—
132C2×C3—2852no—
133C2×C3C3×C7×D9511yescharacteristic, complemented
134C2×C3C7×D28511yescharacteristic, direct product factor
135D3—952no—
136C5C2×C3×C7×D5711yescharacteristic, complemented, Sylow
137C22—2851noSylow
138C3—21no—
139C3C2×C7×D28511yescharacteristic, direct product factor
140C3C2×C3×C7×D9511yescharacteristic, complemented
141C2—2852no—
142C2C3×C7×D28511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7D285
commutator, cosocle, hypocenterC3×C5×C19C22×C3×C7
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C19C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×D285C2direct (N × H)
2. C2×C32×C5×C7×C19C2semidirect
4. C2×C7×D285C3direct (N × H)
5. C32×C5×C7×C19C22semidirect
7. C7×D285C2×C3direct (N × H)
10. C2×C3×C5×C7×C19D3semidirect
11. C2×C3×C5×C7×C19C2×C3semidirect
12. C2×C3×D285C7direct (N × H)
15. C2×C32×C7×C19D5semidirect
17. C3×C5×C7×C19C2×D3semidirect
18. C3×C5×C7×C19C22×C3semidirect
19. C2×C32×C5×C19C2×C7semidirect
20. C3×D285C2×C7direct (N × H)
23. C2×C5×C7×C19C3×D3semidirect
26. C32×C7×C19C2×D5semidirect
27. C2×D285C3×C7direct (N × H)
29. C32×C5×C19C22×C7semidirect
31. C2×C3×C7×C19C3×D5semidirect
32. C2×C3×C7×C19D15semidirect
36. C5×C7×C19C2×C3×D3semidirect
37. C2×C32×C5×C7D19semidirect
40. C2×C3×C5×C19D3×C7semidirect
41. C2×C3×C5×C19C2×C3×C7semidirect
42. D285C2×C3×C7direct (N × H)
48. C3×C7×C19C2×C3×D5semidirect
49. C3×C7×C19C2×D15semidirect
51. C2×C32×C19C7×D5semidirect
53. C32×C5×C7C2×D19semidirect
55. C3×C5×C19C2×D3×C7semidirect
56. C3×C5×C19C22×C3×C7semidirect
57. C2×C7×C19C3×D15semidirect
63. C2×C3×C5×C7C3×D19semidirect
64. C2×C3×C5×C7D57semidirect
67. C2×C5×C19C3×D3×C7semidirect
70. C32×C19C2×C7×D5semidirect
72. C7×C19C2×C3×D15semidirect
73. C2×C32×C7D95semidirect
76. C2×C3×C19C3×C7×D5semidirect
77. C2×C3×C19C7×D15semidirect
81. C3×C5×C7C2×C3×D19semidirect
82. C3×C5×C7C2×D57semidirect
83. C5×C19C2×C3×D3×C7semidirect
84. C2×C32×C5C7×D19semidirect
89. C2×C5×C7C3×D57semidirect
91. C32×C7C2×D95semidirect
95. C3×C19C2×C3×C7×D5semidirect
96. C3×C19C2×C7×D15semidirect
97. C32×C5C2×C7×D19semidirect
100. C2×C3×C7C3×D95semidirect
101. C2×C3×C7D285direct (N × H)
103. C2×C19C3×C7×D15semidirect
106. C5×C7C2×C3×D57semidirect
108. C2×C3×C5C3×C7×D19semidirect
109. C2×C3×C5C7×D57semidirect
114. C3×C7C2×C3×D95semidirect
115. C3×C7C2×D285direct (N × H)
117. C19C2×C3×C7×D15semidirect
118. C2×C32C7×D95semidirect
121. C3×C5C2×C3×C7×D19semidirect
122. C3×C5C2×C7×D57semidirect
124. C2×C7C3×D285direct (N × H)
127. C2×C5C3×C7×D57semidirect
129. C32C2×C7×D95semidirect
130. C7C2×C3×D285direct (N × H)
133. C2×C3C3×C7×D95semidirect
134. C2×C3C7×D285direct (N × H)
136. C5C2×C3×C7×D57semidirect
139. C3C2×C7×D285direct (N × H)
140. C3C2×C3×C7×D95semidirect
142. C2C3×C7×D285direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×D2852
C2×C32×C5×C7×C192
C2×C3×C7×D953
C2×C7×D2853
C2×C3×C7×D575
C2×C3×D2857
C2×C3×C7×D1519