Finite Group Databasebeta

← C3×C5×D3×D119 #36339458

Subgroups — C3×C5×D3×D119 #36339458

Order 21420.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×D119C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C17C211yesmaximal, characteristic, complemented
3C3×C5×D357C211yesmaximal, characteristic, complemented
4C2×C3×C5×D119—31nomaximal
5C5×D3×D119C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7C3×D3×D119C511yesmaximal, characteristic, direct product factor, Hall
8C5×D357C2×C311yescharacteristic, complemented
9C5×D3×C7×C17C2×C311yescharacteristic, complemented
10C3×C5×D119—21no—
11C3×C5×D119—31no—
12C3×C5×D119D311yescharacteristic, direct product factor
13C3×C5×D119C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C17—31no—
15C3×C5×D3×D17—71nomaximal, Hall
16C2×C5×D119—31noHall
17C3×D357C2×C511yescharacteristic, complemented
18C3×D3×C7×C17C2×C511yescharacteristic, complemented
19C32×D119C2×C511yescharacteristic, complemented
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C22×C311yescharacteristic, complemented
23C3×C5×D51—71no—
24C3×C5×D3×C17D711yescharacteristic, complemented
25C32×C5×D17—71no—
26C2×C3×D119—31no—
27D3×D119C3×C511yescharacteristic, direct product factor
28C3×C5×D3×D7—171nomaximal, Hall
29C2×C5×C7×C17—31no—
30C5×D119—31no—
31C5×D119C3×D311yescharacteristic, direct product factor
32C32×C7×C17C22×C511yescharacteristic, complemented, Hall
33C2×C3×C5×D17—211no—
34C5×D3×D17—71no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36C2×C3×C7×C17—31no—
37D357C2×C3×C511yescharacteristic, complemented
38D3×C7×C17C2×C3×C511yescharacteristic, complemented
39C3×D119—21no—
40C3×D119—31no—
41C3×D119C5×D311yescharacteristic, direct product factor
42C3×D119C2×C3×C511yescharacteristic, complemented
43C3×C5×D21—171no—
44C3×C5×D3×C7D1711yescharacteristic, complemented
45C32×C5×D7—171no—
46C3×D3×D17—71noHall
47C5×C7×C17C2×C3×D311yescharacteristic, complemented, Hall
48C2×C3×C5×C17—31no—
49C5×D51—71no—
50C5×D3×C17C3×D711yescharacteristic, complemented
51C3×C5×D17—71no—
52C3×C5×D17—71no—
53C3×C5×D17—141no—
54C3×C5×D17—211no—
55C2×D119—31noHall
56C2×C3×C5×D7—511no—
57C5×D3×D7—171no—
58C3×C7×C17—21no—
59C3×C7×C17C2×C5×D311yescharacteristic, complemented
60C3×C7×C17C22×C3×C511yescharacteristic, complemented
61C2×C5×D17—211noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C3×D51—71no—
64C3×D3×C17C5×D711yescharacteristic, complemented
65C32×D17—71no—
66C3×C5×C17—21no—
67C3×C5×C17D3×D711yescharacteristic, complemented
68C3×C5×C17C2×C3×D711yescharacteristic, complemented
69C3×D3×D7—171noHall
70C2×C7×C17—31no—
71D119—31no—
72D119C3×C5×D311yescharacteristic, direct product factor
73C2×C3×C5×C7—31no—
74C5×D21—171no—
75C5×D3×C7C3×D1711yescharacteristic, complemented
76C3×C5×D7—171no—
77C3×C5×D7—171no—
78C3×C5×D7—341no—
79C3×C5×D7—511no—
80C2×C3×D17—211no—
81D3×D17—71no—
82C2×C3×C5×D3—1191noHall
83C2×C5×C17—31no—
84C5×D17—71no—
85C5×D17—211no—
86C32×C17C2×C5×D711yescharacteristic, complemented, Hall
87C2×C5×D7—511noHall
88C3×D21—171no—
89C3×D3×C7C5×D1711yescharacteristic, complemented
90C32×D7—171no—
91C7×C17C2×C3×C5×D311yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7D3×D1711yescharacteristic, complemented
94C3×C5×C7C2×C3×D1711yescharacteristic, complemented
95C2×C3×C17—31no—
96D51—71no—
97C3×D17—71no—
98C3×D17—71no—
99C3×D17—141no—
100C3×D17—211no—
101D3×C17C3×C5×D711yescharacteristic, complemented
102C2×C32×C5—1191no—
103C3×C5×D3—1191no—
104C3×C5×D3D11911yescharacteristic, direct product factor
105C5×C17C3×D3×D711yescharacteristic, complemented, Hall
106C2×C3×D7—511no—
107D3×D7—171no—
108C2×C5×C7—31no—
109C5×D7—171no—
110C5×D7—511no—
111C2×D17—211noHall
112C32×C7C2×C5×D1711yescharacteristic, complemented, Hall
113C22×C3×C5—3571no—
114C2×C5×D3—1191no—
115C3×C17—21no—
116C3×C17C5×D3×D711yescharacteristic, complemented
117C3×C17C2×C3×C5×D711yescharacteristic, complemented
118C32×C5C2×D11911yescharacteristic, complemented, Hall
119C2×C3×C7—31no—
120D21—171no—
121C3×D7—171no—
122C3×D7—171no—
123C3×D7—341no—
124C3×D7—511no—
125D3×C7C3×C5×D1711yescharacteristic, complemented
126C2×C3×D3—1191noHall
127C5×C7C3×D3×D1711yescharacteristic, complemented, Hall
128C2×C17—31no—
129D17—71no—
130D17—211no—
131C2×C3×C5—31no—
132C2×C3×C5—3571no—
133C2×C3×C5—1191no—
134C2×C3×C5—1191no—
135C2×C3×C5—2381no—
136C5×D3—1191no—
137C5×D3C3×D11911yescharacteristic, direct product factor
138C2×D7—511noHall
139C3×C7—21no—
140C3×C7C5×D3×D1711yescharacteristic, complemented
141C3×C7C2×C3×C5×D1711yescharacteristic, complemented
142C22×C5—3571noHall
143C2×C32—1191no—
144C3×D3—1191no—
145C3×D3C5×D11911yescharacteristic, direct product factor
146C17C3×C5×D3×D711yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5D3×D11911yescharacteristic, direct product factor
149C3×C5C2×C3×D11911yescharacteristic, complemented
150C2×C7—31no—
151D7—171no—
152D7—511no—
153C22×C3—3571no—
154C2×D3—1191no—
155C2×C5—31no—
156C2×C5—3571no—
157C2×C5—1191no—
158C32C2×C5×D11911yescharacteristic, complemented, Sylow
159C7C3×C5×D3×D1711yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—3571no—
162C2×C3—1191no—
163C2×C3—1191no—
164C2×C3—2381no—
165D3—1191no—
166D3C3×C5×D11911yescharacteristic, direct product factor
167C5C3×D3×D11911yescharacteristic, direct product factor, Sylow
168C22—3571noSylow
169C3—21no—
170C3C5×D3×D11911yescharacteristic, direct product factor
171C3C2×C3×C5×D11911yescharacteristic, complemented
172C2—31no—
173C2—3571no—
174C2—1191no—
subgroupG/H
center, hypercenterC3×C5D3×D119
commutator, cosocle, hypocenterC3×C7×C17C22×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C3×C7×C17
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D119C2semidirect
2. C3×C5×D3×C7×C17C2semidirect
3. C3×C5×D357C2semidirect
5. C5×D3×D119C3direct (N × H)
6. C32×C5×C7×C17C22semidirect
7. C3×D3×D119C5direct (N × H)
8. C5×D357C2×C3semidirect
9. C5×D3×C7×C17C2×C3semidirect
12. C3×C5×D119D3direct (N × H)
13. C3×C5×D119C2×C3semidirect
17. C3×D357C2×C5semidirect
18. C3×D3×C7×C17C2×C5semidirect
19. C32×D119C2×C5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C22×C3semidirect
24. C3×C5×D3×C17D7semidirect
27. D3×D119C3×C5direct (N × H)
31. C5×D119C3×D3direct (N × H)
32. C32×C7×C17C22×C5semidirect
35. C32×C5×C17C2×D7semidirect
37. D357C2×C3×C5semidirect
38. D3×C7×C17C2×C3×C5semidirect
41. C3×D119C5×D3direct (N × H)
42. C3×D119C2×C3×C5semidirect
44. C3×C5×D3×C7D17semidirect
47. C5×C7×C17C2×C3×D3semidirect
50. C5×D3×C17C3×D7semidirect
59. C3×C7×C17C2×C5×D3semidirect
60. C3×C7×C17C22×C3×C5semidirect
62. C32×C5×C7C2×D17semidirect
64. C3×D3×C17C5×D7semidirect
67. C3×C5×C17D3×D7semidirect
68. C3×C5×C17C2×C3×D7semidirect
72. D119C3×C5×D3direct (N × H)
75. C5×D3×C7C3×D17semidirect
86. C32×C17C2×C5×D7semidirect
89. C3×D3×C7C5×D17semidirect
91. C7×C17C2×C3×C5×D3semidirect
93. C3×C5×C7D3×D17semidirect
94. C3×C5×C7C2×C3×D17semidirect
101. D3×C17C3×C5×D7semidirect
104. C3×C5×D3D119direct (N × H)
105. C5×C17C3×D3×D7semidirect
112. C32×C7C2×C5×D17semidirect
116. C3×C17C5×D3×D7semidirect
117. C3×C17C2×C3×C5×D7semidirect
118. C32×C5C2×D119semidirect
125. D3×C7C3×C5×D17semidirect
127. C5×C7C3×D3×D17semidirect
137. C5×D3C3×D119direct (N × H)
140. C3×C7C5×D3×D17semidirect
141. C3×C7C2×C3×C5×D17semidirect
145. C3×D3C5×D119direct (N × H)
146. C17C3×C5×D3×D7semidirect
148. C3×C5D3×D119direct (N × H)
149. C3×C5C2×C3×D119semidirect
158. C32C2×C5×D119semidirect
159. C7C3×C5×D3×D17semidirect
166. D3C3×C5×D119direct (N × H)
167. C5C3×D3×D119direct (N × H)
170. C3C5×D3×D119direct (N × H)
171. C3C2×C3×C5×D119semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1192
C3×C5×D3×C7×C172
C3×C5×D3572
C2×C3×C5×D1193
C5×D3×D1193
C3×D3×D1195
C3×C5×D3×D177
C3×C5×D3×D717