Finite Group Databasebeta

← C3×C5×D15⋊D37 #45686413

Subgroups — C3×C5×D15⋊D37 #45686413

Order 33300.

212 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 60 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×C5×D185C211yesmaximal, characteristic, complemented
2C3×C52×D111C211yesmaximal, characteristic, complemented
3C3×C5×D15×C37C211yesmaximal, 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×D15×C37C2×C311yescharacteristic, complemented
10C52×D111C2×C311yescharacteristic, complemented
11C3×C5×D185—21no—
12C3×C5×D185D311yescharacteristic, complemented
13C3×C5×D185C2×C311yescharacteristic, complemented
14C3×C5×D5×C37—31no—
15C3×C52×D37—31no—
16C5×D5×D37—31noHall
17C3×D15×C37C2×C511yescharacteristic, complemented
18C3×C5×D111—22no—
19C3×C5×D111D511yescharacteristic, complemented
20C3×C5×D111C2×C511yescharacteristic, complemented
21C3×C5×D3×C37—51no—
22C32×D185C2×C511yescharacteristic, complemented
23C32×C5×D37—51no—
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×D185C3×D311yescharacteristic, complemented
32C5×D5×C37—31no—
33C52×D37—31no—
34C32×C5×C37—22no—
35C32×C5×C37C2×D511yescharacteristic, complemented
36C32×C5×C37C22×C511yescharacteristic, complemented
37C3×D3×D37—51noHall
38C2×C3×C5×C37—151no—
39D15×C37C2×C3×C511yescharacteristic, complemented
40C5×D111—22no—
41C5×D111C3×D511yescharacteristic, complemented
42C5×D111C2×C3×C511yescharacteristic, complemented
43C5×D3×C37—51no—
44C3×D185—21no—
45C3×D185C5×D311yescharacteristic, complemented
46C3×D185C2×C3×C511yescharacteristic, complemented
47C3×D5×C37—31no—
48C3×C5×D37—31no—
49C3×C5×D37—31no—
50C3×C5×D37—51no—
51C3×C5×D37—51no—
52C3×C5×D37—62no—
53C3×C5×D37—101no—
54C52×C37C2×C3×D311yescharacteristic, complemented, Hall
55C3×C5×D3×D5—371nomaximal, Hall
56C2×C5×D37—151no—
57D5×D37—31no—
58C3×D111C5×D511yescharacteristic, complemented
59C3×D3×C37—51no—
60C32×D37—51no—
61C3×C5×C37—22no—
62C3×C5×C37—22no—
63C3×C5×C37—21no—
64C3×C5×C37—21no—
65C3×C5×C37—42no—
66C3×C5×C37D3×D511yescharacteristic, complemented
67C3×C5×C37C2×C3×D511yescharacteristic, complemented
68C3×C5×C37C2×C5×D311yescharacteristic, complemented
69C3×C5×C37C22×C3×C511yescharacteristic, complemented
70C3×C5×D15D3711yescharacteristic, complemented
71C3×C52×D3—371no—
72C32×C5×D5—371no—
73C2×C3×D37—151no—
74D3×D37—51no—
75C2×C5×C37—151no—
76D185C3×C5×D311yescharacteristic, complemented
77C5×D37—31no—
78C5×D37—31no—
79C5×D37—51no—
80C5×D37—62no—
81D5×C37—31no—
82C32×C37C2×C5×D511yescharacteristic, complemented, Hall
83C2×C3×C5×D5—1111no—
84C5×D3×D5—371no—
85C32×C52C2×D3711yescharacteristic, complemented, Hall
86C2×C3×C37—151no—
87D111C3×C5×D511yescharacteristic, complemented
88C3×D37—31no—
89C3×D37—51no—
90C3×D37—51no—
91C3×D37—101no—
92D3×C37—51no—
93C5×C37—22no—
94C5×C37C3×D3×D511yescharacteristic, complemented
95C5×C37C2×C3×C5×D311yescharacteristic, complemented
96C2×C3×C5×D3—1851no—
97C3×D3×D5—371no—
98C2×C3×C52—1111no—
99C5×D15C3×D3711yescharacteristic, complemented
100C52×D3—371no—
101C3×C5×D5—31no—
102C3×C5×D5—371no—
103C3×C5×D5—371no—
104C3×C5×D5—741no—
105C2×D37—151noHall
106C3×C37—21no—
107C3×C37C5×D3×D511yescharacteristic, complemented
108C3×C37C2×C3×C5×D511yescharacteristic, complemented
109C2×C5×D5—1111noHall
110C2×C32×C5—1851no—
111C3×D15C5×D3711yescharacteristic, complemented
112C3×C5×D3—51no—
113C3×C5×D3—371no—
114C3×C5×D3—371no—
115C3×C5×D3—742no—
116C32×D5—371no—
117C3×C52—21no—
118C3×C52D3×D3711yescharacteristic, complemented
119C3×C52C2×C3×D3711yescharacteristic, complemented
120C2×C37—151no—
121D37—31no—
122D37—51no—
123C22×C3×C5—5551no—
124C2×C5×D3—1851no—
125C2×C3×D5—1111no—
126D3×D5—371no—
127C2×C52—1111no—
128C5×D5—31no—
129C5×D5—371no—
130C32×C5—22no—
131C32×C5D5×D3711yescharacteristic, complemented
132C32×C5C2×C5×D3711yescharacteristic, complemented
133C37C3×C5×D3×D511yescharacteristic, complemented, Sylow
134C2×C3×D3—1851noHall
135C2×C3×C5—151no—
136C2×C3×C5—1111no—
137C2×C3×C5—1111no—
138C2×C3×C5—3701no—
139C2×C3×C5—1851no—
140C2×C3×C5—1851no—
141C2×C3×C5—2222no—
142D15C3×C5×D3711yescharacteristic, complemented
143C3×D5—31no—
144C3×D5—371no—
145C3×D5—371no—
146C3×D5—741no—
147C5×D3—51no—
148C5×D3—371no—
149C5×D3—371no—
150C5×D3—742no—
151C52C3×D3×D3711yescharacteristic, complemented, Sylow
152C22×C5—5551no—
153C2×D5—1111no—
154C2×C32—1851no—
155C3×D3—51no—
156C3×D3—371no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C3×D5×D3711yescharacteristic, complemented
163C3×C5C5×D3×D3711yescharacteristic, complemented
164C3×C5D15⋊D3711yescharacteristic, direct product factor
165C3×C5C2×C3×C5×D3711yescharacteristic, complemented
166C22×C3—5551no—
167C2×D3—1851no—
168C2×C5—151no—
169C2×C5—1111no—
170C2×C5—1111no—
171C2×C5—1851no—
172C2×C5—2222no—
173D5—31no—
174D5—371no—
175C32C5×D5×D3711yescharacteristic, complemented, Sylow
176C2×C3—151no—
177C2×C3—1111no—
178C2×C3—3701no—
179C2×C3—1851no—
180C2×C3—1851no—
181D3—51no—
182D3—371no—
183C5—22no—
184C5C3×C5×D3×D3711yescharacteristic, complemented
185C5C3×D15⋊D3711yescharacteristic, direct product factor
186C22—5551noSylow
187C3—21no—
188C3C3×C5×D5×D3711yescharacteristic, complemented
189C3C5×D15⋊D3711yescharacteristic, direct product factor
190C2—151no—
191C2—1111no—
192C2—1851no—
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×C5×D185C2semidirect
2. C3×C52×D111C2semidirect
3. C3×C5×D15×C37C2semidirect
4. C5×D15⋊D37C3direct (N × H)
6. C32×C52×C37C22semidirect
7. C3×D15⋊D37C5direct (N × H)
9. C5×D15×C37C2×C3semidirect
10. C52×D111C2×C3semidirect
12. C3×C5×D185D3semidirect
13. C3×C5×D185C2×C3semidirect
17. C3×D15×C37C2×C5semidirect
19. C3×C5×D111D5semidirect
20. C3×C5×D111C2×C5semidirect
22. C32×D185C2×C5semidirect
25. C3×C52×C37C2×D3semidirect
26. C3×C52×C37C22×C3semidirect
28. D15⋊D37C3×C5direct (N × H)
31. C5×D185C3×D3semidirect
35. C32×C5×C37C2×D5semidirect
36. C32×C5×C37C22×C5semidirect
39. D15×C37C2×C3×C5semidirect
41. C5×D111C3×D5semidirect
42. C5×D111C2×C3×C5semidirect
45. C3×D185C5×D3semidirect
46. C3×D185C2×C3×C5semidirect
54. C52×C37C2×C3×D3semidirect
58. C3×D111C5×D5semidirect
66. C3×C5×C37D3×D5semidirect
67. C3×C5×C37C2×C3×D5semidirect
68. C3×C5×C37C2×C5×D3semidirect
69. C3×C5×C37C22×C3×C5semidirect
70. C3×C5×D15D37semidirect
76. D185C3×C5×D3semidirect
82. C32×C37C2×C5×D5semidirect
85. C32×C52C2×D37semidirect
87. D111C3×C5×D5semidirect
94. C5×C37C3×D3×D5semidirect
95. C5×C37C2×C3×C5×D3semidirect
99. C5×D15C3×D37semidirect
107. C3×C37C5×D3×D5semidirect
108. C3×C37C2×C3×C5×D5semidirect
111. C3×D15C5×D37semidirect
118. C3×C52D3×D37semidirect
119. C3×C52C2×C3×D37semidirect
131. C32×C5D5×D37semidirect
132. C32×C5C2×C5×D37semidirect
133. C37C3×C5×D3×D5semidirect
142. D15C3×C5×D37semidirect
151. C52C3×D3×D37semidirect
162. C3×C5C3×D5×D37semidirect
163. C3×C5C5×D3×D37semidirect
164. C3×C5D15⋊D37direct (N × H)
165. C3×C5C2×C3×C5×D37semidirect
175. C32C5×D5×D37semidirect
184. C5C3×C5×D3×D37semidirect
185. C5C3×D15⋊D37direct (N × H)
188. C3C3×C5×D5×D37semidirect
189. 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×C5×D1852
C3×C52×D1112
C3×C5×D15×C372
C5×D15⋊D373
C3×C5×D5×D373
C3×D15⋊D375
C3×C5×D3×D375
C3×C5×D3×D537