Finite Group Databasebeta

← C3×C5×D15×D37 #45686409

Subgroups — C3×C5×D15×D37 #45686409

Order 33300.

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

normal subgroups only

This group has 224 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×C52×D37C211yesmaximal, characteristic, complemented
2C3×C5×D15×C37C211yesmaximal, characteristic, complemented
3C3×C5×D555C211yesmaximal, characteristic, complemented
4C5×D15×D37C311yesmaximal, characteristic, direct product factor
5C3×C5×D5×D37—31nomaximal
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7C3×D15×D37C511yesmaximal, characteristic, direct product factor
8C3×C5×D3×D37—51nomaximal
9C5×D555C2×C311yescharacteristic, complemented
10C5×D15×C37C2×C311yescharacteristic, complemented
11C3×C5×D185—31no—
12C3×C5×D5×C37—31no—
13C3×C52×D37—21no—
14C3×C52×D37D311yescharacteristic, complemented
15C3×C52×D37C2×C311yescharacteristic, complemented
16C5×D5×D37—31noHall
17C3×D555C2×C511yescharacteristic, complemented
18C3×D15×C37C2×C511yescharacteristic, complemented
19C3×C5×D111—51no—
20C3×C5×D3×C37—51no—
21C32×C5×D37—22no—
22C32×C5×D37D511yescharacteristic, complemented
23C32×C5×D37C2×C511yescharacteristic, complemented
24C3×C52×C37—21no—
25C3×C52×C37C2×D311yescharacteristic, complemented
26C3×C52×C37C22×C311yescharacteristic, complemented
27C2×C3×C5×D37—151no—
28D15×D37C3×C511yescharacteristic, direct product factor
29C5×D3×D37—51no—
30C3×D5×D37—31no—
31C5×D185—31no—
32C5×D5×C37—31no—
33C52×D37C3×D311yescharacteristic, complemented
34C32×C5×C37—22no—
35C32×C5×C37C2×D511yescharacteristic, complemented
36C32×C5×C37C22×C511yescharacteristic, complemented
37C3×D3×D37—51noHall
38C2×C3×C5×C37—151no—
39D555C2×C3×C511yescharacteristic, complemented
40D15×C37C2×C3×C511yescharacteristic, complemented
41C5×D111—51no—
42C5×D3×C37—51no—
43C3×D185—31no—
44C3×D5×C37—31no—
45C3×C5×D37—24no—
46C3×C5×D37—21no—
47C3×C5×D37—21no—
48C3×C5×D37—22no—
49C3×C5×D37—22no—
50C3×C5×D37—151no—
51C3×C5×D37C5×D311yescharacteristic, complemented
52C3×C5×D37C3×D511yescharacteristic, complemented
53C3×C5×D37D1511yescharacteristic, direct product factor
54C3×C5×D37C2×C3×C511yescharacteristic, complemented
55C52×C37C2×C3×D311yescharacteristic, complemented, Hall
56C2×C3×C5×D15—371nomaximal, Hall
57C2×C5×D37—151no—
58D5×D37—31no—
59C3×D111—51no—
60C3×D3×C37—51no—
61C32×D37C5×D511yescharacteristic, complemented
62C3×C5×C37—24no—
63C3×C5×C37—22no—
64C3×C5×C37—22no—
65C3×C5×C37—21no—
66C3×C5×C37—21no—
67C3×C5×C37C2×C3×D511yescharacteristic, complemented
68C3×C5×C37C2×C5×D311yescharacteristic, complemented
69C3×C5×C37C2×D1511yescharacteristic, complemented
70C3×C5×C37C22×C3×C511yescharacteristic, complemented
71C2×C32×C52—371no—
72C3×C5×D15—371no—
73C3×C5×D15D3711yescharacteristic, direct product factor
74C2×C3×D37—151no—
75D3×D37—51no—
76C2×C5×C37—151no—
77D185—31no—
78C5×D37—22no—
79C5×D37—151no—
80C5×D37C3×C5×D311yescharacteristic, complemented
81C5×D37C3×D1511yescharacteristic, direct product factor
82D5×C37—31no—
83C32×C37C2×C5×D511yescharacteristic, complemented, Hall
84C2×C5×D15—371no—
85C2×C3×C5×D5—1111no—
86C32×C52C2×D3711yescharacteristic, complemented, Hall
87C2×C3×C37—151no—
88D111—51no—
89C3×D37—21no—
90C3×D37—151no—
91C3×D37C3×C5×D511yescharacteristic, complemented
92C3×D37C5×D1511yescharacteristic, direct product factor
93D3×C37—51no—
94C5×C37—22no—
95C5×C37C2×C3×C5×D311yescharacteristic, complemented
96C5×C37C2×C3×D1511yescharacteristic, complemented
97C2×C3×D15—371no—
98C2×C3×C5×D3—1851no—
99C2×C3×C52—371no—
100C2×C3×C52—371no—
101C2×C3×C52—741no—
102C5×D15—371no—
103C5×D15C3×D3711yescharacteristic, direct product factor
104C3×C5×D5—31no—
105C3×C5×D5—1111no—
106C2×D37—151noHall
107C3×C37—21no—
108C3×C37C2×C3×C5×D511yescharacteristic, complemented
109C3×C37C2×C5×D1511yescharacteristic, complemented
110C2×C5×D5—1111noHall
111C2×C32×C5—371no—
112C2×C32×C5—371no—
113C2×C32×C5—742no—
114C3×D15—371no—
115C3×D15C5×D3711yescharacteristic, direct product factor
116C3×C5×D3—51no—
117C3×C5×D3—1851no—
118C3×C52—21no—
119C3×C52D3×D3711yescharacteristic, complemented
120C3×C52C2×C3×D3711yescharacteristic, complemented
121C2×C37—151no—
122D37—151no—
123D37C3×C5×D1511yescharacteristic, direct product factor
124C22×C3×C5—5551no—
125C2×D15—371no—
126C2×C5×D3—1851no—
127C2×C3×D5—1111no—
128C2×C52—371no—
129C5×D5—31no—
130C5×D5—1111no—
131C32×C5—22no—
132C32×C5D5×D3711yescharacteristic, complemented
133C32×C5C2×C5×D3711yescharacteristic, complemented
134C37C2×C3×C5×D1511yescharacteristic, complemented, Sylow
135C2×C3×D3—1851noHall
136C2×C3×C5—151no—
137C2×C3×C5—371no—
138C2×C3×C5—371no—
139C2×C3×C5—371no—
140C2×C3×C5—371no—
141C2×C3×C5—5551no—
142C2×C3×C5—742no—
143C2×C3×C5—742no—
144C2×C3×C5—741no—
145C2×C3×C5—741no—
146C2×C3×C5—744no—
147D15—371no—
148D15C3×C5×D3711yescharacteristic, direct product factor
149C3×D5—31no—
150C3×D5—1111no—
151C5×D3—51no—
152C5×D3—1851no—
153C52C3×D3×D3711yescharacteristic, complemented, Sylow
154C22×C5—5551no—
155C2×D5—1111no—
156C2×C32—371no—
157C3×D3—51no—
158C3×D3—1851no—
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5C3×D5×D3711yescharacteristic, complemented
165C3×C5C5×D3×D3711yescharacteristic, complemented
166C3×C5D15×D3711yescharacteristic, direct product factor
167C3×C5C2×C3×C5×D3711yescharacteristic, complemented
168C22×C3—5551no—
169C2×D3—1851no—
170C2×C5—151no—
171C2×C5—371no—
172C2×C5—371no—
173C2×C5—5551no—
174C2×C5—742no—
175D5—31no—
176D5—1111no—
177C32C5×D5×D3711yescharacteristic, complemented, Sylow
178C2×C3—151no—
179C2×C3—371no—
180C2×C3—371no—
181C2×C3—5551no—
182C2×C3—741no—
183D3—51no—
184D3—1851no—
185C5—22no—
186C5C3×C5×D3×D3711yescharacteristic, complemented
187C5C3×D15×D3711yescharacteristic, direct product factor
188C22—5551noSylow
189C3—21no—
190C3C3×C5×D5×D3711yescharacteristic, complemented
191C3C5×D15×D3711yescharacteristic, direct product factor
192C2—151no—
193C2—371no—
194C2—5551no—
subgroupG/H
center, hypercenterC3×C5D15×D37
commutator, cosocle, hypocenterC3×C5×C37C22×C3×C5
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C3×C5×C37
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C52×D37C2semidirect
2. C3×C5×D15×C37C2semidirect
3. C3×C5×D555C2semidirect
4. C5×D15×D37C3direct (N × H)
6. C32×C52×C37C22semidirect
7. C3×D15×D37C5direct (N × H)
9. C5×D555C2×C3semidirect
10. C5×D15×C37C2×C3semidirect
14. C3×C52×D37D3semidirect
15. C3×C52×D37C2×C3semidirect
17. C3×D555C2×C5semidirect
18. C3×D15×C37C2×C5semidirect
22. C32×C5×D37D5semidirect
23. C32×C5×D37C2×C5semidirect
25. C3×C52×C37C2×D3semidirect
26. C3×C52×C37C22×C3semidirect
28. D15×D37C3×C5direct (N × H)
33. C52×D37C3×D3semidirect
35. C32×C5×C37C2×D5semidirect
36. C32×C5×C37C22×C5semidirect
39. D555C2×C3×C5semidirect
40. D15×C37C2×C3×C5semidirect
51. C3×C5×D37C5×D3semidirect
52. C3×C5×D37C3×D5semidirect
53. C3×C5×D37D15direct (N × H)
54. C3×C5×D37C2×C3×C5semidirect
55. C52×C37C2×C3×D3semidirect
61. C32×D37C5×D5semidirect
67. C3×C5×C37C2×C3×D5semidirect
68. C3×C5×C37C2×C5×D3semidirect
69. C3×C5×C37C2×D15semidirect
70. C3×C5×C37C22×C3×C5semidirect
73. C3×C5×D15D37direct (N × H)
80. C5×D37C3×C5×D3semidirect
81. C5×D37C3×D15direct (N × H)
83. C32×C37C2×C5×D5semidirect
86. C32×C52C2×D37semidirect
91. C3×D37C3×C5×D5semidirect
92. C3×D37C5×D15direct (N × H)
95. C5×C37C2×C3×C5×D3semidirect
96. C5×C37C2×C3×D15semidirect
103. C5×D15C3×D37direct (N × H)
108. C3×C37C2×C3×C5×D5semidirect
109. C3×C37C2×C5×D15semidirect
115. C3×D15C5×D37direct (N × H)
119. C3×C52D3×D37semidirect
120. C3×C52C2×C3×D37semidirect
123. D37C3×C5×D15direct (N × H)
132. C32×C5D5×D37semidirect
133. C32×C5C2×C5×D37semidirect
134. C37C2×C3×C5×D15semidirect
148. D15C3×C5×D37direct (N × H)
153. C52C3×D3×D37semidirect
164. C3×C5C3×D5×D37semidirect
165. C3×C5C5×D3×D37semidirect
166. C3×C5D15×D37direct (N × H)
167. C3×C5C2×C3×C5×D37semidirect
177. C32C5×D5×D37semidirect
186. C5C3×C5×D3×D37semidirect
187. C5C3×D15×D37direct (N × H)
190. C3C3×C5×D5×D37semidirect
191. C3C5×D15×D37direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×D372
C3×C5×D15×C372
C3×C5×D5552
C5×D15×D373
C3×C5×D5×D373
C3×D15×D375
C3×C5×D3×D375
C2×C3×C5×D1537