Finite Group Databasebeta

← C5×D3×D609 #49141598

Subgroups — C5×D3×D609 #49141598

Order 36540.

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
1C3×C5×D3×C7×C29C211yesmaximal, characteristic, complemented
2C3×C5×D609C211yesmaximal, characteristic, complemented
3C5×C3⋊D609C211yesmaximal, characteristic, complemented
4C2×C5×D609—31nomaximal
5C5×D3×D203—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D3×D609C511yesmaximal, characteristic, direct product factor, Hall
8C5×D609—31no—
9C5×D609—31no—
10C5×D609—61no—
11C5×D609D311yescharacteristic, direct product factor
12C5×D3×C7×C29D311yescharacteristic, complemented
13C3×C5×D203—31no—
14C2×C3×C5×C7×C29—31no—
15C5×D3×D87—71nomaximal, Hall
16C2×C5×D203—91noHall
17C3⋊D609C2×C511yescharacteristic, complemented
18C3×D609C2×C511yescharacteristic, complemented
19C3×D3×C7×C29C2×C511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C5×C3⋊D87—71no—
24C3×C5×D87—71no—
25C3×C5×D3×C29D711yescharacteristic, complemented
26C2×D609—31no—
27D3×D203—31no—
28C5×D203—31no—
29C5×D203—91no—
30C2×C5×C7×C29—31no—
31C32×C7×C29C22×C511yescharacteristic, complemented, Hall
32C2×C5×D87—211no—
33C5×D3×D29—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35C5×D3×D21—291nomaximal, Hall
36C2×C3×C7×C29—31no—
37D609—31no—
38D609—31no—
39D609—61no—
40D609C5×D311yescharacteristic, direct product factor
41D3×C7×C29C5×D311yescharacteristic, complemented
42C3×D203—31no—
43D3×D87—71noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45C2×C3×C5×C29—31no—
46C5×D87—71no—
47C5×D87—211no—
48C5×D87—211no—
49C5×D87—421no—
50C5×D3×C29D2111yescharacteristic, complemented
51C3×C5×D29—211no—
52C2×D203—91noHall
53C5×C3⋊D21—291no—
54C3×C5×D21—291no—
55C3×C5×D3×C7D2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29C2×C5×D311yescharacteristic, complemented
58C3×C7×C29C2×C5×D311yescharacteristic, complemented
59C2×C5×D29—631noHall
60C3⋊D87—71no—
61C3×D87—71no—
62C3×D3×C29C5×D711yescharacteristic, complemented
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×D2111yescharacteristic, complemented
66C2×C5×D21—871no—
67C5×D3×D7—871no—
68C2×C7×C29—31no—
69D203—31no—
70D203—91no—
71C2×D87—211no—
72D3×D29—211no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74C2×C5×C29—31no—
75C5×D29—211no—
76C5×D29—631no—
77C32×C29C2×C5×D711yescharacteristic, complemented, Hall
78D3×D21—291noHall
79C2×C3×C5×C7—31no—
80C5×D21—291no—
81C5×D21—871no—
82C5×D21—871no—
83C5×D21—1741no—
84C5×D3×C7D8711yescharacteristic, complemented
85C3×C5×D7—871no—
86C7×C29C5×D3211yescharacteristic, complemented, Hall
87C5×D32—2031noHall
88C2×C3×C29—31no—
89D87—71no—
90D87—211no—
91D87—211no—
92D87—421no—
93C3×D29—211no—
94D3×C29C5×D2111yescharacteristic, complemented
95C5×C29D3×D2111yescharacteristic, complemented, Hall
96C2×C5×D7—2611noHall
97C3⋊D21—291no—
98C3×D21—291no—
99C3×D3×C7C5×D2911yescharacteristic, complemented
100C2×D29—631noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×D8711yescharacteristic, complemented
104C5×C3⋊D3—2031no—
105C3×C5×D3—2031no—
106C3×C5×D3D20311yescharacteristic, complemented
107C3×C29—21no—
108C3×C29C5×D3×D711yescharacteristic, complemented
109C3×C29C2×C5×D2111yescharacteristic, complemented
110C2×D21—871no—
111D3×D7—871no—
112C2×C5×C7—31no—
113C5×D7—2611no—
114C5×D7—871no—
115C32×C7C2×C5×D2911yescharacteristic, complemented, Hall
116C2×C5×D3—6091no—
117C2×C5×D3—6091no—
118C2×C29—31no—
119D29—211no—
120D29—631no—
121C32×C5C2×D20311yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123D21—291no—
124D21—871no—
125D21—871no—
126D21—1741no—
127C3×D7—871no—
128D3×C7C5×D8711yescharacteristic, complemented
129D32—2031noHall
130C5×C7D3×D8711yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132C2×C3×C5—6091no—
133C5×D3—6091no—
134C5×D3—6091no—
135C5×D3—12181no—
136C5×D3—2031no—
137C5×D3D60911yescharacteristic, direct product factor
138C29C5×D3×D2111yescharacteristic, complemented, Sylow
139C2×D7—2611noHall
140C3×C7—21no—
141C3×C7C5×D3×D2911yescharacteristic, complemented
142C3×C7C2×C5×D8711yescharacteristic, complemented
143C22×C5—18271noHall
144C3⋊D3—2031no—
145C3×D3—2031no—
146C3×D3C5×D20311yescharacteristic, complemented
147C3×C5—21no—
148C3×C5D3×D20311yescharacteristic, complemented
149C3×C5C2×D60911yescharacteristic, complemented
150C2×C7—31no—
151D7—2611no—
152D7—871no—
153C2×D3—6091no—
154C2×D3—6091no—
155C2×C5—31no—
156C2×C5—18271no—
157C2×C5—6091no—
158C32C2×C5×D20311yescharacteristic, complemented, Sylow
159C7C5×D3×D8711yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—6091no—
162D3—6091no—
163D3—6091no—
164D3—12181no—
165D3—2031no—
166D3C5×D60911yescharacteristic, direct product factor
167C5D3×D60911yescharacteristic, direct product factor, Sylow
168C22—18271noSylow
169C3—21no—
170C3C5×D3×D20311yescharacteristic, complemented
171C3C2×C5×D60911yescharacteristic, complemented
172C2—31no—
173C2—18271no—
174C2—6091no—
subgroupG/H
center, hypercenterC5D3×D609
commutator, cosocle, hypocenterC32×C7×C29C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C7×C29
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C7×C29C2semidirect
2. C3×C5×D609C2semidirect
3. C5×C3⋊D609C2semidirect
6. C32×C5×C7×C29C22semidirect
7. D3×D609C5direct (N × H)
11. C5×D609D3direct (N × H)
12. C5×D3×C7×C29D3semidirect
17. C3⋊D609C2×C5semidirect
18. C3×D609C2×C5semidirect
19. C3×D3×C7×C29C2×C5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
25. C3×C5×D3×C29D7semidirect
31. C32×C7×C29C22×C5semidirect
34. C32×C5×C29C2×D7semidirect
40. D609C5×D3direct (N × H)
41. D3×C7×C29C5×D3semidirect
44. C5×C7×C29D32semidirect
50. C5×D3×C29D21semidirect
55. C3×C5×D3×C7D29semidirect
57. C3×C7×C29C2×C5×D3semidirect
58. C3×C7×C29C2×C5×D3semidirect
62. C3×D3×C29C5×D7semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×D21semidirect
73. C32×C5×C7C2×D29semidirect
77. C32×C29C2×C5×D7semidirect
84. C5×D3×C7D87semidirect
86. C7×C29C5×D32semidirect
94. D3×C29C5×D21semidirect
95. C5×C29D3×D21semidirect
99. C3×D3×C7C5×D29semidirect
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×D87semidirect
106. C3×C5×D3D203semidirect
108. C3×C29C5×D3×D7semidirect
109. C3×C29C2×C5×D21semidirect
115. C32×C7C2×C5×D29semidirect
121. C32×C5C2×D203semidirect
128. D3×C7C5×D87semidirect
130. C5×C7D3×D87semidirect
137. C5×D3D609direct (N × H)
138. C29C5×D3×D21semidirect
141. C3×C7C5×D3×D29semidirect
142. C3×C7C2×C5×D87semidirect
146. C3×D3C5×D203semidirect
148. C3×C5D3×D203semidirect
149. C3×C5C2×D609semidirect
158. C32C2×C5×D203semidirect
159. C7C5×D3×D87semidirect
166. D3C5×D609direct (N × H)
167. C5D3×D609direct (N × H)
170. C3C5×D3×D203semidirect
171. C3C2×C5×D609semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C7×C292
C3×C5×D6092
C5×C3⋊D6092
C2×C5×D6093
C5×D3×D2033
D3×D6095
C5×D3×D877
C5×D3×D2129