Finite Group Databasebeta

← C3×D3×D1015 #49141588

Subgroups — C3×D3×D1015 #49141588

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
1C32×D1015C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C29C211yesmaximal, characteristic, complemented
3C3×D3045C211yesmaximal, characteristic, complemented
4C2×C3×D1015—31nomaximal
5D3×D1015C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C3×D3×D203—51nomaximal, Hall
8D3045C2×C311yescharacteristic, complemented
9C5×D3×C7×C29C2×C311yescharacteristic, complemented
10C3×D1015—21no—
11C3×D1015—31no—
12C3×D1015D311yescharacteristic, direct product factor
13C3×D1015C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C29—31no—
15C3×D3×D145—71nomaximal, Hall
16C2×D1015—31noHall
17C3×D609—51no—
18C3×D3×C7×C29D511yescharacteristic, complemented
19C32×D203—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×D435—71no—
24C3×C5×D3×C29D711yescharacteristic, complemented
25C32×D145—71no—
26C2×C3×D203—151no—
27D3×D203—51no—
28D1015—31no—
29D1015C3×D311yescharacteristic, direct product factor
30C2×C5×C7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C3×D145—211no—
33D3×D145—71no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35C3×D3×D35—291nomaximal, Hall
36C2×C3×C7×C29—31no—
37D609—51no—
38D3×C7×C29C3×D511yescharacteristic, complemented
39C3×D203—51no—
40C3×D203—51no—
41C3×D203—101no—
42C3×D203—151no—
43C3×D3×D29—351noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—31no—
46D435—71no—
47C5×D3×C29C3×D711yescharacteristic, complemented
48C3×D145—71no—
49C3×D145—71no—
50C3×D145—141no—
51C3×D145—211no—
52C2×D203—151noHall
53C3×D105—291no—
54C3×C5×D3×C7D2911yescharacteristic, complemented
55C32×D35—291no—
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×C3×D511yescharacteristic, complemented
59C2×D145—211noHall
60C3×D87—351no—
61C3×D3×C29D3511yescharacteristic, complemented
62C32×D29—351no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×C3×D711yescharacteristic, complemented
66C2×C3×D35—871no—
67D3×D35—291no—
68C2×C7×C29—31no—
69D203—51no—
70D203—151no—
71C2×C3×D29—1051no—
72D3×D29—351no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74C2×C5×C29—31no—
75D145—71no—
76D145—211no—
77C32×C29C2×D3511yescharacteristic, complemented, Hall
78C3×D3×D7—1451noHall
79C2×C3×C5×C7—31no—
80D105—291no—
81C5×D3×C7C3×D2911yescharacteristic, complemented
82C3×D35—291no—
83C3×D35—291no—
84C3×D35—581no—
85C3×D35—871no—
86C7×C29C3×D3×D511yescharacteristic, complemented, Hall
87C3×D3×D5—2031noHall
88C2×C3×C29—31no—
89D87—351no—
90C3×D29—351no—
91C3×D29—351no—
92C3×D29—701no—
93C3×D29—1051no—
94D3×C29C3×D3511yescharacteristic, complemented
95C5×C29C3×D3×D711yescharacteristic, complemented, Hall
96C2×D35—871noHall
97C3×D21—1451no—
98C3×D3×C7D14511yescharacteristic, complemented
99C32×D7—1451no—
100C2×D29—1051noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×C3×D2911yescharacteristic, complemented
104C3×D15—2031no—
105C3×C5×D3D20311yescharacteristic, complemented
106C32×D5—2031no—
107C3×C29—21no—
108C3×C29D3×D3511yescharacteristic, complemented
109C3×C29C2×C3×D3511yescharacteristic, complemented
110C2×C3×D7—4351no—
111D3×D7—1451no—
112C2×C5×C7—31no—
113D35—291no—
114D35—871no—
115C32×C7C2×D14511yescharacteristic, complemented, Hall
116C2×C3×D5—6091no—
117D3×D5—2031no—
118C2×C29—31no—
119D29—351no—
120D29—1051no—
121C32×C5C2×D20311yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123D21—1451no—
124C3×D7—2901no—
125C3×D7—1451no—
126C3×D7—1451no—
127C3×D7—4351no—
128D3×C7C3×D14511yescharacteristic, complemented
129C2×C3×D3—10151noHall
130C5×C7C3×D3×D2911yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132D15—2031no—
133C3×D5—6091no—
134C3×D5—4061no—
135C3×D5—2031no—
136C3×D5—2031no—
137C5×D3C3×D20311yescharacteristic, complemented
138C29C3×D3×D3511yescharacteristic, complemented, Sylow
139C2×D7—4351noHall
140C3×C7—21no—
141C3×C7D3×D14511yescharacteristic, complemented
142C3×C7C2×C3×D14511yescharacteristic, complemented
143C2×D5—6091noHall
144C2×C32—10151no—
145C3×D3—10151no—
146C3×D3D101511yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5D3×D20311yescharacteristic, complemented
149C3×C5C2×C3×D20311yescharacteristic, complemented
150C2×C7—31no—
151D7—1451no—
152D7—4351no—
153C22×C3—30451no—
154C2×D3—10151no—
155C2×C5—31no—
156D5—6091no—
157D5—2031no—
158C32C2×D101511yescharacteristic, complemented, Sylow
159C7C3×D3×D14511yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—30451no—
162C2×C3—20301no—
163C2×C3—10151no—
164C2×C3—10151no—
165D3—10151no—
166D3C3×D101511yescharacteristic, direct product factor
167C5C3×D3×D20311yescharacteristic, complemented, Sylow
168C22—30451noSylow
169C3—21no—
170C3D3×D101511yescharacteristic, direct product factor
171C3C2×C3×D101511yescharacteristic, complemented
172C2—31no—
173C2—30451no—
174C2—10151no—
subgroupG/H
center, hypercenterC3D3×D1015
commutator, cosocle, hypocenterC3×C5×C7×C29C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C5×C7×C29
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×D1015C2semidirect
2. C3×C5×D3×C7×C29C2semidirect
3. C3×D3045C2semidirect
5. D3×D1015C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
8. D3045C2×C3semidirect
9. C5×D3×C7×C29C2×C3semidirect
12. C3×D1015D3direct (N × H)
13. C3×D1015C2×C3semidirect
18. C3×D3×C7×C29D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
24. C3×C5×D3×C29D7semidirect
29. D1015C3×D3direct (N × H)
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
38. D3×C7×C29C3×D5semidirect
44. C5×C7×C29C2×C3×D3semidirect
47. C5×D3×C29C3×D7semidirect
54. C3×C5×D3×C7D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×C3×D5semidirect
61. C3×D3×C29D35semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×C3×D7semidirect
73. C32×C5×C7C2×D29semidirect
77. C32×C29C2×D35semidirect
81. C5×D3×C7C3×D29semidirect
86. C7×C29C3×D3×D5semidirect
94. D3×C29C3×D35semidirect
95. C5×C29C3×D3×D7semidirect
98. C3×D3×C7D145semidirect
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×C3×D29semidirect
105. C3×C5×D3D203semidirect
108. C3×C29D3×D35semidirect
109. C3×C29C2×C3×D35semidirect
115. C32×C7C2×D145semidirect
121. C32×C5C2×D203semidirect
128. D3×C7C3×D145semidirect
130. C5×C7C3×D3×D29semidirect
137. C5×D3C3×D203semidirect
138. C29C3×D3×D35semidirect
141. C3×C7D3×D145semidirect
142. C3×C7C2×C3×D145semidirect
146. C3×D3D1015direct (N × H)
148. C3×C5D3×D203semidirect
149. C3×C5C2×C3×D203semidirect
158. C32C2×D1015semidirect
159. C7C3×D3×D145semidirect
166. D3C3×D1015direct (N × H)
167. C5C3×D3×D203semidirect
170. C3D3×D1015direct (N × H)
171. C3C2×C3×D1015semidirect

Maximal subgroups

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

subgroupindex
C32×D10152
C3×C5×D3×C7×C292
C3×D30452
C2×C3×D10153
D3×D10153
C3×D3×D2035
C3×D3×D1457
C3×D3×D3529