Finite Group Databasebeta

← C3×C7×D5×D69 #44394576

Subgroups — C3×C7×D5×D69 #44394576

Order 28980.

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×C7×D5×C23C211yesmaximal, characteristic, complemented
2C3×C5×C7×D69C211yesmaximal, characteristic, complemented
3C3×C7×D345C211yesmaximal, characteristic, complemented
4C7×D5×D69C311yesmaximal, characteristic, direct product factor
5C3×C7×D5×D23—31nomaximal
6C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
7C2×C3×C7×D69—51nomaximal, Hall
8C7×D345C2×C311yescharacteristic, complemented
9C5×C7×D69C2×C311yescharacteristic, complemented
10C3×C7×D115—31no—
11C3×C7×D5×C23—21no—
12C3×C7×D5×C23D311yescharacteristic, complemented
13C3×C7×D5×C23C2×C311yescharacteristic, complemented
14C3×C5×C7×D23—31no—
15C3×D5×D69C711yesmaximal, characteristic, direct product factor, Hall
16C7×D5×D23—31noHall
17C3×C7×D69—51no—
18C3×C7×D69D511yescharacteristic, direct product factor
19C2×C32×C7×C23—51no—
20C3×C5×C7×C23—21no—
21C3×C5×C7×C23C2×D311yescharacteristic, complemented
22C3×C5×C7×C23C22×C311yescharacteristic, complemented
23C3×D345C2×C711yescharacteristic, complemented
24C3×C5×D69C2×C711yescharacteristic, complemented
25C32×D5×C23C2×C711yescharacteristic, complemented
26C2×C7×D69—51no—
27C2×C3×C7×D23—151no—
28C7×D115—31no—
29C7×D5×C23C3×D311yescharacteristic, complemented
30C5×C7×D23—31no—
31C32×C7×C23C2×D511yescharacteristic, complemented, Hall
32D5×D69C3×C711yescharacteristic, direct product factor
33C3×D5×D23—31no—
34C3×D3×C7×D5—231nomaximal, Hall
35C32×C5×C23C22×C711yescharacteristic, complemented, Hall
36C2×C3×C7×C23—51no—
37C2×C3×C7×C23—51no—
38C2×C3×C7×C23—101no—
39C7×D69—51no—
40C7×D69C3×D511yescharacteristic, direct product factor
41C3×C7×D23—31no—
42C3×C7×D23—151no—
43C2×C3×D69—51noHall
44C5×C7×C23C2×C3×D311yescharacteristic, complemented, Hall
45D345C2×C3×C711yescharacteristic, complemented
46C5×D69C2×C3×C711yescharacteristic, complemented
47C3×D115—31no—
48C3×D5×C23—21no—
49C3×D5×C23D3×C711yescharacteristic, complemented
50C3×D5×C23C2×C3×C711yescharacteristic, complemented
51C3×C5×D23—31no—
52C2×C7×D23—151noHall
53C3×C7×D15—231no—
54C3×C5×D3×C7—231no—
55C32×C7×D5D2311yescharacteristic, complemented
56C3×C7×C23—21no—
57C3×C7×C23D3×D511yescharacteristic, complemented
58C3×C7×C23C2×C3×D511yescharacteristic, complemented
59D5×D23—31noHall
60C2×C3×C7×D5—691no—
61D3×C7×D5—231no—
62C2×C32×C23—51no—
63C3×D69—51no—
64C3×D69C7×D511yescharacteristic, direct product factor
65C3×C5×C23—21no—
66C3×C5×C23C2×D3×C711yescharacteristic, complemented
67C3×C5×C23C22×C3×C711yescharacteristic, complemented
68C2×C7×C23—51no—
69C7×D23—31no—
70C7×D23—151no—
71C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
72C2×D69—51no—
73C2×C3×D23—151no—
74C2×C3×D3×C7—1151noHall
75D115—31no—
76C5×D23—31no—
77D5×C23C3×D3×C711yescharacteristic, complemented
78C2×C3×C5×C7—691no—
79C7×D15—231no—
80C5×D3×C7—231no—
81C3×C7×D5—21no—
82C3×C7×D5—691no—
83C3×C7×D5C3×D2311yescharacteristic, complemented
84C3×C7×D5D6911yescharacteristic, direct product factor
85C32×C23C2×C7×D511yescharacteristic, complemented, Hall
86C3×D3×D5—231noHall
87C7×C23C3×D3×D511yescharacteristic, complemented, Hall
88C2×C7×D5—691noHall
89C2×C3×C23—51no—
90C2×C3×C23—51no—
91C2×C3×C23—101no—
92D69—51no—
93D69C3×C7×D511yescharacteristic, direct product factor
94C3×D23—31no—
95C3×D23—151no—
96C2×C32×C7—51no—
97C3×D3×C7—231no—
98C3×D3×C7—1151no—
99C5×C23C2×C3×D3×C711yescharacteristic, complemented, Hall
100C3×C5×C7—21no—
101C3×C5×C7C2×C3×D2311yescharacteristic, complemented
102C3×C5×C7C2×D6911yescharacteristic, complemented
103C2×D23—151noHall
104C3×D15—231no—
105C3×C5×D3—231no—
106C32×D5C7×D2311yescharacteristic, complemented
107C22×C3×C7—3451no—
108C2×D3×C7—1151no—
109C2×C5×C7—691no—
110C7×D5—691no—
111C7×D5C3×D6911yescharacteristic, direct product factor
112C3×C23—21no—
113C3×C23D3×C7×D511yescharacteristic, complemented
114C3×C23C2×C3×C7×D511yescharacteristic, complemented
115C32×C7D5×D2311yescharacteristic, complemented, Hall
116C2×C3×D5—691no—
117D3×D5—231no—
118C2×C23—51no—
119D23—31no—
120D23—151no—
121C32×C5C2×C7×D2311yescharacteristic, complemented, Hall
122C2×C3×C7—51no—
123C2×C3×C7—51no—
124C2×C3×C7—101no—
125C2×C3×C7—691no—
126C2×C3×C7—3451no—
127D3×C7—231no—
128D3×C7—1151no—
129C2×C3×D3—1151noHall
130C5×C7C2×C3×D6911yescharacteristic, complemented, Hall
131C2×C3×C5—691no—
132D15—231no—
133C3×D5—21no—
134C3×D5—691no—
135C3×D5C3×C7×D2311yescharacteristic, complemented
136C3×D5C7×D6911yescharacteristic, direct product factor
137C5×D3—231no—
138C22×C7—3451noHall
139C23C3×D3×C7×D511yescharacteristic, complemented, Sylow
140C3×C7—21no—
141C3×C7C3×D5×D2311yescharacteristic, complemented
142C3×C7D5×D6911yescharacteristic, direct product factor
143C2×D5—691noHall
144C2×C32—51no—
145C3×D3—231no—
146C3×D3—1151no—
147C3×C5—21no—
148C3×C5C2×C3×C7×D2311yescharacteristic, complemented
149C3×C5C2×C7×D6911yescharacteristic, complemented
150C2×C7—51no—
151C2×C7—691no—
152C2×C7—3451no—
153C22×C3—3451no—
154C2×D3—1151no—
155C2×C5—691no—
156D5—691no—
157D5C3×C7×D6911yescharacteristic, direct product factor
158C32C7×D5×D2311yescharacteristic, complemented, Sylow
159C7C3×D5×D6911yescharacteristic, direct product factor, Sylow
160C2×C3—51no—
161C2×C3—51no—
162C2×C3—101no—
163C2×C3—691no—
164C2×C3—3451no—
165D3—231no—
166D3—1151no—
167C5C2×C3×C7×D6911yescharacteristic, complemented, Sylow
168C22—3451noSylow
169C3—21no—
170C3C3×C7×D5×D2311yescharacteristic, complemented
171C3C7×D5×D6911yescharacteristic, direct product factor
172C2—51no—
173C2—691no—
174C2—3451no—
subgroupG/H
center, hypercenterC3×C7D5×D69
commutator, cosocle, hypocenterC3×C5×C23C22×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C3×C5×C23
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C23C2semidirect
2. C3×C5×C7×D69C2semidirect
3. C3×C7×D345C2semidirect
4. C7×D5×D69C3direct (N × H)
6. C32×C5×C7×C23C22semidirect
8. C7×D345C2×C3semidirect
9. C5×C7×D69C2×C3semidirect
12. C3×C7×D5×C23D3semidirect
13. C3×C7×D5×C23C2×C3semidirect
15. C3×D5×D69C7direct (N × H)
18. C3×C7×D69D5direct (N × H)
21. C3×C5×C7×C23C2×D3semidirect
22. C3×C5×C7×C23C22×C3semidirect
23. C3×D345C2×C7semidirect
24. C3×C5×D69C2×C7semidirect
25. C32×D5×C23C2×C7semidirect
29. C7×D5×C23C3×D3semidirect
31. C32×C7×C23C2×D5semidirect
32. D5×D69C3×C7direct (N × H)
35. C32×C5×C23C22×C7semidirect
40. C7×D69C3×D5direct (N × H)
44. C5×C7×C23C2×C3×D3semidirect
45. D345C2×C3×C7semidirect
46. C5×D69C2×C3×C7semidirect
49. C3×D5×C23D3×C7semidirect
50. C3×D5×C23C2×C3×C7semidirect
55. C32×C7×D5D23semidirect
57. C3×C7×C23D3×D5semidirect
58. C3×C7×C23C2×C3×D5semidirect
64. C3×D69C7×D5direct (N × H)
66. C3×C5×C23C2×D3×C7semidirect
67. C3×C5×C23C22×C3×C7semidirect
71. C32×C5×C7C2×D23semidirect
77. D5×C23C3×D3×C7semidirect
83. C3×C7×D5C3×D23semidirect
84. C3×C7×D5D69direct (N × H)
85. C32×C23C2×C7×D5semidirect
87. C7×C23C3×D3×D5semidirect
93. D69C3×C7×D5direct (N × H)
99. C5×C23C2×C3×D3×C7semidirect
101. C3×C5×C7C2×C3×D23semidirect
102. C3×C5×C7C2×D69semidirect
106. C32×D5C7×D23semidirect
111. C7×D5C3×D69direct (N × H)
113. C3×C23D3×C7×D5semidirect
114. C3×C23C2×C3×C7×D5semidirect
115. C32×C7D5×D23semidirect
121. C32×C5C2×C7×D23semidirect
130. C5×C7C2×C3×D69semidirect
135. C3×D5C3×C7×D23semidirect
136. C3×D5C7×D69direct (N × H)
139. C23C3×D3×C7×D5semidirect
141. C3×C7C3×D5×D23semidirect
142. C3×C7D5×D69direct (N × H)
148. C3×C5C2×C3×C7×D23semidirect
149. C3×C5C2×C7×D69semidirect
157. D5C3×C7×D69direct (N × H)
158. C32C7×D5×D23semidirect
159. C7C3×D5×D69direct (N × H)
167. C5C2×C3×C7×D69semidirect
170. C3C3×C7×D5×D23semidirect
171. C3C7×D5×D69direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D5×C232
C3×C5×C7×D692
C3×C7×D3452
C7×D5×D693
C3×C7×D5×D233
C2×C3×C7×D695
C3×D5×D697
C3×D3×C7×D523