Finite Group Databasebeta

← C3×C7×D5×D87 #49141579

Subgroups — C3×C7×D5×D87 #49141579

Order 36540.

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×C29C211yesmaximal, characteristic, complemented
2C3×C5×C7×D87C211yesmaximal, characteristic, complemented
3C3×C7×D435C211yesmaximal, characteristic, complemented
4C7×D5×D87C311yesmaximal, characteristic, direct product factor
5C3×C7×D5×D29—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C2×C3×C7×D87—51nomaximal, Hall
8C7×D435C2×C311yescharacteristic, complemented
9C5×C7×D87C2×C311yescharacteristic, complemented
10C3×C7×D145—31no—
11C3×C7×D5×C29—21no—
12C3×C7×D5×C29D311yescharacteristic, complemented
13C3×C7×D5×C29C2×C311yescharacteristic, complemented
14C3×C5×C7×D29—31no—
15C3×D5×D87C711yesmaximal, characteristic, direct product factor, Hall
16C7×D5×D29—31noHall
17C3×C7×D87—51no—
18C3×C7×D87D511yescharacteristic, direct product factor
19C2×C32×C7×C29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×D435C2×C711yescharacteristic, complemented
24C3×C5×D87C2×C711yescharacteristic, complemented
25C32×D5×C29C2×C711yescharacteristic, complemented
26C2×C7×D87—51no—
27C2×C3×C7×D29—151no—
28C7×D145—31no—
29C7×D5×C29C3×D311yescharacteristic, complemented
30C5×C7×D29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32D5×D87C3×C711yescharacteristic, direct product factor
33C3×D5×D29—31no—
34C32×C5×C29C22×C711yescharacteristic, complemented, Hall
35C3×D3×C7×D5—291nomaximal, Hall
36C2×C3×C7×C29—51no—
37C2×C3×C7×C29—51no—
38C2×C3×C7×C29—101no—
39C7×D87—51no—
40C7×D87C3×D511yescharacteristic, direct product factor
41C3×C7×D29—31no—
42C3×C7×D29—151no—
43C2×C3×D87—51noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45D435C2×C3×C711yescharacteristic, complemented
46C5×D87C2×C3×C711yescharacteristic, complemented
47C3×D145—31no—
48C3×D5×C29—21no—
49C3×D5×C29D3×C711yescharacteristic, complemented
50C3×D5×C29C2×C3×C711yescharacteristic, complemented
51C3×C5×D29—31no—
52C2×C7×D29—151noHall
53C3×C7×D15—291no—
54C3×C5×D3×C7—291no—
55C32×C7×D5D2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×C3×D511yescharacteristic, complemented
59D5×D29—31noHall
60C2×C32×C29—51no—
61C3×D87—51no—
62C3×D87C7×D511yescharacteristic, direct product factor
63C3×C5×C29—21no—
64C3×C5×C29C2×D3×C711yescharacteristic, complemented
65C3×C5×C29C22×C3×C711yescharacteristic, complemented
66C2×C3×C7×D5—871no—
67D3×C7×D5—291no—
68C2×C7×C29—51no—
69C7×D29—31no—
70C7×D29—151no—
71C2×D87—51no—
72C2×C3×D29—151no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74D145—31no—
75C5×D29—31no—
76D5×C29C3×D3×C711yescharacteristic, complemented
77C32×C29C2×C7×D511yescharacteristic, complemented, Hall
78C2×C3×D3×C7—1451noHall
79C2×C3×C5×C7—871no—
80C7×D15—291no—
81C5×D3×C7—291no—
82C3×C7×D5—21no—
83C3×C7×D5—871no—
84C3×C7×D5C3×D2911yescharacteristic, complemented
85C3×C7×D5D8711yescharacteristic, direct product factor
86C7×C29C3×D3×D511yescharacteristic, complemented, Hall
87C3×D3×D5—291noHall
88C2×C3×C29—51no—
89C2×C3×C29—51no—
90C2×C3×C29—101no—
91D87—51no—
92D87C3×C7×D511yescharacteristic, direct product factor
93C3×D29—31no—
94C3×D29—151no—
95C5×C29C2×C3×D3×C711yescharacteristic, complemented, Hall
96C2×C7×D5—871noHall
97C2×C32×C7—51no—
98C3×D3×C7—291no—
99C3×D3×C7—1451no—
100C2×D29—151noHall
101C3×C5×C7—21no—
102C3×C5×C7C2×C3×D2911yescharacteristic, complemented
103C3×C5×C7C2×D8711yescharacteristic, complemented
104C3×D15—291no—
105C3×C5×D3—291no—
106C32×D5C7×D2911yescharacteristic, complemented
107C3×C29—21no—
108C3×C29D3×C7×D511yescharacteristic, complemented
109C3×C29C2×C3×C7×D511yescharacteristic, complemented
110C22×C3×C7—4351no—
111C2×D3×C7—1451no—
112C2×C5×C7—871no—
113C7×D5—871no—
114C7×D5C3×D8711yescharacteristic, direct product factor
115C32×C7D5×D2911yescharacteristic, complemented, Hall
116C2×C3×D5—871no—
117D3×D5—291no—
118C2×C29—51no—
119D29—31no—
120D29—151no—
121C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
122C2×C3×C7—51no—
123C2×C3×C7—51no—
124C2×C3×C7—101no—
125C2×C3×C7—871no—
126C2×C3×C7—4351no—
127D3×C7—291no—
128D3×C7—1451no—
129C2×C3×D3—1451noHall
130C5×C7C2×C3×D8711yescharacteristic, complemented, Hall
131C2×C3×C5—871no—
132D15—291no—
133C3×D5—21no—
134C3×D5—871no—
135C3×D5C3×C7×D2911yescharacteristic, complemented
136C3×D5C7×D8711yescharacteristic, direct product factor
137C5×D3—291no—
138C29C3×D3×C7×D511yescharacteristic, complemented, Sylow
139C22×C7—4351noHall
140C3×C7—21no—
141C3×C7C3×D5×D2911yescharacteristic, complemented
142C3×C7D5×D8711yescharacteristic, direct product factor
143C2×D5—871noHall
144C2×C32—51no—
145C3×D3—291no—
146C3×D3—1451no—
147C3×C5—21no—
148C3×C5C2×C3×C7×D2911yescharacteristic, complemented
149C3×C5C2×C7×D8711yescharacteristic, complemented
150C2×C7—51no—
151C2×C7—871no—
152C2×C7—4351no—
153C22×C3—4351no—
154C2×D3—1451no—
155C2×C5—871no—
156D5—871no—
157D5C3×C7×D8711yescharacteristic, direct product factor
158C32C7×D5×D2911yescharacteristic, complemented, Sylow
159C7C3×D5×D8711yescharacteristic, direct product factor, Sylow
160C2×C3—51no—
161C2×C3—51no—
162C2×C3—101no—
163C2×C3—871no—
164C2×C3—4351no—
165D3—291no—
166D3—1451no—
167C5C2×C3×C7×D8711yescharacteristic, complemented, Sylow
168C22—4351noSylow
169C3—21no—
170C3C3×C7×D5×D2911yescharacteristic, complemented
171C3C7×D5×D8711yescharacteristic, direct product factor
172C2—51no—
173C2—871no—
174C2—4351no—
subgroupG/H
center, hypercenterC3×C7D5×D87
commutator, cosocle, hypocenterC3×C5×C29C22×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C5×C29
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C29C2semidirect
2. C3×C5×C7×D87C2semidirect
3. C3×C7×D435C2semidirect
4. C7×D5×D87C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
8. C7×D435C2×C3semidirect
9. C5×C7×D87C2×C3semidirect
12. C3×C7×D5×C29D3semidirect
13. C3×C7×D5×C29C2×C3semidirect
15. C3×D5×D87C7direct (N × H)
18. C3×C7×D87D5direct (N × H)
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
23. C3×D435C2×C7semidirect
24. C3×C5×D87C2×C7semidirect
25. C32×D5×C29C2×C7semidirect
29. C7×D5×C29C3×D3semidirect
31. C32×C7×C29C2×D5semidirect
32. D5×D87C3×C7direct (N × H)
34. C32×C5×C29C22×C7semidirect
40. C7×D87C3×D5direct (N × H)
44. C5×C7×C29C2×C3×D3semidirect
45. D435C2×C3×C7semidirect
46. C5×D87C2×C3×C7semidirect
49. C3×D5×C29D3×C7semidirect
50. C3×D5×C29C2×C3×C7semidirect
55. C32×C7×D5D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×C3×D5semidirect
62. C3×D87C7×D5direct (N × H)
64. C3×C5×C29C2×D3×C7semidirect
65. C3×C5×C29C22×C3×C7semidirect
73. C32×C5×C7C2×D29semidirect
76. D5×C29C3×D3×C7semidirect
77. C32×C29C2×C7×D5semidirect
84. C3×C7×D5C3×D29semidirect
85. C3×C7×D5D87direct (N × H)
86. C7×C29C3×D3×D5semidirect
92. D87C3×C7×D5direct (N × H)
95. C5×C29C2×C3×D3×C7semidirect
102. C3×C5×C7C2×C3×D29semidirect
103. C3×C5×C7C2×D87semidirect
106. C32×D5C7×D29semidirect
108. C3×C29D3×C7×D5semidirect
109. C3×C29C2×C3×C7×D5semidirect
114. C7×D5C3×D87direct (N × H)
115. C32×C7D5×D29semidirect
121. C32×C5C2×C7×D29semidirect
130. C5×C7C2×C3×D87semidirect
135. C3×D5C3×C7×D29semidirect
136. C3×D5C7×D87direct (N × H)
138. C29C3×D3×C7×D5semidirect
141. C3×C7C3×D5×D29semidirect
142. C3×C7D5×D87direct (N × H)
148. C3×C5C2×C3×C7×D29semidirect
149. C3×C5C2×C7×D87semidirect
157. D5C3×C7×D87direct (N × H)
158. C32C7×D5×D29semidirect
159. C7C3×D5×D87direct (N × H)
167. C5C2×C3×C7×D87semidirect
170. C3C3×C7×D5×D29semidirect
171. C3C7×D5×D87direct (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×C292
C3×C5×C7×D872
C3×C7×D4352
C7×D5×D873
C3×C7×D5×D293
C2×C3×C7×D875
C3×D5×D877
C3×D3×C7×D529