Finite Group Databasebeta

← C3×D7×D285 #37561533

Subgroups — C3×D7×D285 #37561533

Order 23940.

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×C5×D7×C19C211yesmaximal, characteristic, complemented
2C3×C7×D285C211yesmaximal, characteristic, complemented
3C3×D1995C211yesmaximal, characteristic, complemented
4D7×D285C311yesmaximal, characteristic, direct product factor
5C3×D7×D95—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7C3×D7×D57—51nomaximal, Hall
8D1995C2×C311yescharacteristic, complemented
9C7×D285C2×C311yescharacteristic, complemented
10C3×D665—31no—
11C3×C7×D95—31no—
12C3×C5×D7×C19—21no—
13C3×C5×D7×C19D311yescharacteristic, complemented
14C3×C5×D7×C19C2×C311yescharacteristic, complemented
15C2×C3×D285—71nomaximal, Hall
16D7×D95—31noHall
17C3×D399—51no—
18C3×C7×D57—51no—
19C32×D7×C19D511yescharacteristic, complemented
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C22×C311yescharacteristic, complemented
23C2×C32×C5×C19—71no—
24C3×D285—71no—
25C3×D285D711yescharacteristic, direct product factor
26D7×D57—51no—
27C3×D7×D19—151no—
28D665—31no—
29C7×D95—31no—
30C5×D7×C19C3×D311yescharacteristic, complemented
31C3×D7×D15—191nomaximal, Hall
32C32×C7×C19C2×D511yescharacteristic, complemented, Hall
33C2×D285—71no—
34C2×C3×D95—211no—
35C32×C5×C19C2×D711yescharacteristic, complemented, Hall
36D399—51no—
37C7×D57—51no—
38C3×D133—151no—
39C3×D7×C19—21no—
40C3×D7×C19C3×D511yescharacteristic, complemented
41C3×D7×C19D1511yescharacteristic, complemented
42C3×C7×D19—151no—
43C2×C3×D57—351noHall
44C5×C7×C19C2×C3×D311yescharacteristic, complemented, Hall
45C3×D105—191no—
46C3×C7×D15—191no—
47C32×C5×D7D1911yescharacteristic, complemented
48C2×C3×C5×C19—71no—
49C2×C3×C5×C19—71no—
50C2×C3×C5×C19—141no—
51D285—71no—
52D285C3×D711yescharacteristic, direct product factor
53C3×D95—31no—
54C3×D95—211no—
55D7×D19—151noHall
56D7×D15—191no—
57C3×D5×D7—571no—
58C3×C7×C19—21no—
59C3×C7×C19C2×C3×D511yescharacteristic, complemented
60C3×C7×C19C2×D1511yescharacteristic, complemented
61C2×D95—211noHall
62C2×C32×C19—71no—
63C3×D57—51no—
64C3×D57—351no—
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19D3×D711yescharacteristic, complemented
68C3×C5×C19C2×C3×D711yescharacteristic, complemented
69D133—151no—
70C7×D19—151no—
71D7×C19C3×D1511yescharacteristic, complemented
72C3×D3×D7—951noHall
73C2×D57—351no—
74C2×C3×D19—1051no—
75D105—191no—
76C7×D15—191no—
77C3×D35—571no—
78C3×C7×D5—571no—
79C3×C5×D7—21no—
80C3×C5×D7C3×D1911yescharacteristic, complemented
81C3×C5×D7D5711yescharacteristic, complemented
82C2×C5×C19—71no—
83D95—31no—
84D95—211no—
85C2×C3×D15—1331noHall
86C32×C19D5×D711yescharacteristic, complemented, Hall
87D5×D7—571noHall
88C7×C19C2×C3×D1511yescharacteristic, complemented, Hall
89C3×D21—951no—
90C3×D3×C7—951no—
91C32×D7D9511yescharacteristic, complemented
92C2×C3×C19—71no—
93C2×C3×C19—71no—
94C2×C3×C19—141no—
95D57—51no—
96D57—351no—
97C3×D19—151no—
98C3×D19—1051no—
99C3×C5×C7—21no—
100C3×C5×C7C2×C3×D1911yescharacteristic, complemented
101C3×C5×C7C2×D5711yescharacteristic, complemented
102C5×C19C3×D3×D711yescharacteristic, complemented, Hall
103C2×C32×C5—71no—
104C3×D15—191no—
105C3×D15—1331no—
106C2×C3×D7—2851no—
107D3×D7—951no—
108C2×D19—1051noHall
109D35—571no—
110C5×D7C3×D5711yescharacteristic, complemented
111C7×D5—571no—
112C32×C7C2×D9511yescharacteristic, complemented, Hall
113C2×D15—1331no—
114C2×C3×D5—3991no—
115C3×C19—21no—
116C3×C19C3×D5×D711yescharacteristic, complemented
117C3×C19D7×D1511yescharacteristic, complemented
118C32×C5D7×D1911yescharacteristic, complemented, Hall
119C2×C3×C7—2851no—
120D21—951no—
121C3×D7—21no—
122C3×D7—2851no—
123C3×D7C3×D9511yescharacteristic, complemented
124C3×D7D28511yescharacteristic, direct product factor
125D3×C7—951no—
126C2×C19—71no—
127D19—151no—
128D19—1051no—
129C2×C3×D3—6651noHall
130C5×C7C2×C3×D5711yescharacteristic, complemented, Hall
131C2×C3×C5—71no—
132C2×C3×C5—71no—
133C2×C3×C5—141no—
134D15—191no—
135D15—1331no—
136C3×D5—571no—
137C3×D5—3991no—
138C2×D7—2851noHall
139C3×C7—21no—
140C3×C7C2×C3×D9511yescharacteristic, complemented
141C3×C7C2×D28511yescharacteristic, complemented
142C2×D5—3991noHall
143C19C3×D7×D1511yescharacteristic, complemented, Sylow
144C2×C32—71no—
145C3×D3—951no—
146C3×D3—6651no—
147C3×C5—21no—
148C3×C5C3×D7×D1911yescharacteristic, complemented
149C3×C5D7×D5711yescharacteristic, complemented
150C2×C7—2851no—
151D7—2851no—
152D7C3×D28511yescharacteristic, direct product factor
153C22×C3—19951no—
154C2×D3—6651no—
155C2×C5—71no—
156D5—571no—
157D5—3991no—
158C32D7×D9511yescharacteristic, complemented, Sylow
159C7C2×C3×D28511yescharacteristic, complemented, Sylow
160C2×C3—71no—
161C2×C3—71no—
162C2×C3—141no—
163C2×C3—2851no—
164C2×C3—19951no—
165D3—951no—
166D3—6651no—
167C5C3×D7×D5711yescharacteristic, complemented, Sylow
168C22—19951noSylow
169C3—21no—
170C3C3×D7×D9511yescharacteristic, complemented
171C3D7×D28511yescharacteristic, direct product factor
172C2—71no—
173C2—2851no—
174C2—19951no—
subgroupG/H
center, hypercenterC3D7×D285
commutator, cosocle, hypocenterC3×C5×C7×C19C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C3×C5×C7×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×D7×C19C2semidirect
2. C3×C7×D285C2semidirect
3. C3×D1995C2semidirect
4. D7×D285C3direct (N × H)
6. C32×C5×C7×C19C22semidirect
8. D1995C2×C3semidirect
9. C7×D285C2×C3semidirect
13. C3×C5×D7×C19D3semidirect
14. C3×C5×D7×C19C2×C3semidirect
19. C32×D7×C19D5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C22×C3semidirect
25. C3×D285D7direct (N × H)
30. C5×D7×C19C3×D3semidirect
32. C32×C7×C19C2×D5semidirect
35. C32×C5×C19C2×D7semidirect
40. C3×D7×C19C3×D5semidirect
41. C3×D7×C19D15semidirect
44. C5×C7×C19C2×C3×D3semidirect
47. C32×C5×D7D19semidirect
52. D285C3×D7direct (N × H)
59. C3×C7×C19C2×C3×D5semidirect
60. C3×C7×C19C2×D15semidirect
65. C32×C5×C7C2×D19semidirect
67. C3×C5×C19D3×D7semidirect
68. C3×C5×C19C2×C3×D7semidirect
71. D7×C19C3×D15semidirect
80. C3×C5×D7C3×D19semidirect
81. C3×C5×D7D57semidirect
86. C32×C19D5×D7semidirect
88. C7×C19C2×C3×D15semidirect
91. C32×D7D95semidirect
100. C3×C5×C7C2×C3×D19semidirect
101. C3×C5×C7C2×D57semidirect
102. C5×C19C3×D3×D7semidirect
110. C5×D7C3×D57semidirect
112. C32×C7C2×D95semidirect
116. C3×C19C3×D5×D7semidirect
117. C3×C19D7×D15semidirect
118. C32×C5D7×D19semidirect
123. C3×D7C3×D95semidirect
124. C3×D7D285direct (N × H)
130. C5×C7C2×C3×D57semidirect
140. C3×C7C2×C3×D95semidirect
141. C3×C7C2×D285semidirect
143. C19C3×D7×D15semidirect
148. C3×C5C3×D7×D19semidirect
149. C3×C5D7×D57semidirect
152. D7C3×D285direct (N × H)
158. C32D7×D95semidirect
159. C7C2×C3×D285semidirect
167. C5C3×D7×D57semidirect
170. C3C3×D7×D95semidirect
171. C3D7×D285direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D7×C192
C3×C7×D2852
C3×D19952
D7×D2853
C3×D7×D953
C3×D7×D575
C2×C3×D2857
C3×D7×D1519