Finite Group Databasebeta

← C3×C5×D3×D95 #30685874

Subgroups — C3×C5×D3×D95 #30685874

Order 17100.

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

normal subgroups only

This group has 212 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
1C3×C5×D285C211yesmaximal, characteristic, complemented
2C3×C52×D3×C19C211yesmaximal, characteristic, complemented
3C32×C5×D95C211yesmaximal, characteristic, complemented
4C2×C3×C5×D95—31nomaximal
5C5×D3×D95C311yesmaximal, characteristic, direct product factor
6C32×C52×C19C2211yescharacteristic, complemented, Hall
7C3×D3×D95C511yesmaximal, characteristic, direct product factor
8C3×C5×D3×D19—51nomaximal
9C5×D285C2×C311yescharacteristic, complemented
10C52×D3×C19C2×C311yescharacteristic, complemented
11C3×C5×D95—21no—
12C3×C5×D95—31no—
13C3×C5×D95D311yescharacteristic, direct product factor
14C3×C5×D95C2×C311yescharacteristic, complemented
15C2×C3×C52×C19—31no—
16C2×C5×D95—31noHall
17C3×D285C2×C511yescharacteristic, complemented
18C3×C5×D57—51no—
19C3×C5×D3×C19—22no—
20C3×C5×D3×C19D511yescharacteristic, complemented
21C3×C5×D3×C19C2×C511yescharacteristic, complemented
22C32×D95C2×C511yescharacteristic, complemented
23C32×C5×D19—51no—
24C3×C52×C19—21no—
25C3×C52×C19C2×D311yescharacteristic, complemented
26C3×C52×C19C22×C311yescharacteristic, complemented
27C2×C3×D95—31no—
28C2×C3×C5×D19—151no—
29D3×D95C3×C511yescharacteristic, direct product factor
30C5×D3×D19—51no—
31C2×C52×C19—31no—
32C5×D95—31no—
33C5×D95C3×D311yescharacteristic, direct product factor
34C3×C5×D3×D5—191nomaximal, Hall
35C32×C5×C19—22no—
36C32×C5×C19C2×D511yescharacteristic, complemented
37C32×C5×C19C22×C511yescharacteristic, complemented
38C3×D3×D19—51noHall
39C2×C3×C5×C19—31no—
40C2×C3×C5×C19—31no—
41C2×C3×C5×C19—62no—
42D285C2×C3×C511yescharacteristic, complemented
43C5×D57—51no—
44C5×D3×C19—22no—
45C5×D3×C19C3×D511yescharacteristic, complemented
46C5×D3×C19C2×C3×C511yescharacteristic, complemented
47C3×D95—21no—
48C3×D95—31no—
49C3×D95C5×D311yescharacteristic, direct product factor
50C3×D95C2×C3×C511yescharacteristic, complemented
51C3×C5×D19—51no—
52C3×C5×D19—51no—
53C3×C5×D19—101no—
54C3×C5×D19—151no—
55C52×C19C2×C3×D311yescharacteristic, complemented, Hall
56C3×C5×D15—191no—
57C3×C52×D3D1911yescharacteristic, complemented
58C32×C5×D5—191no—
59C2×D95—31no—
60C2×C5×D19—151no—
61C3×D57—51no—
62C3×D3×C19C5×D511yescharacteristic, complemented
63C32×D19—51no—
64C2×C3×C5×D5—571no—
65C5×D3×D5—191no—
66C3×C5×C19—22no—
67C3×C5×C19—22no—
68C3×C5×C19—21no—
69C3×C5×C19—21no—
70C3×C5×C19—42no—
71C3×C5×C19D3×D511yescharacteristic, complemented
72C3×C5×C19C2×C3×D511yescharacteristic, complemented
73C3×C5×C19C2×C5×D311yescharacteristic, complemented
74C3×C5×C19C22×C3×C511yescharacteristic, complemented
75C2×C3×D19—151no—
76D3×D19—51no—
77C32×C52C2×D1911yescharacteristic, complemented, Hall
78C2×C5×C19—31no—
79C2×C5×C19—31no—
80C2×C5×C19—62no—
81D95—31no—
82D95C3×C5×D311yescharacteristic, direct product factor
83C5×D19—51no—
84C5×D19—151no—
85C2×C3×C5×D3—951no—
86C3×D3×D5—191no—
87C32×C19C2×C5×D511yescharacteristic, complemented, Hall
88C2×C3×C52—31no—
89C5×D15—191no—
90C52×D3C3×D1911yescharacteristic, complemented
91C3×C5×D5—191no—
92C3×C5×D5—191no—
93C3×C5×D5—381no—
94C3×C5×D5—571no—
95C2×C3×C19—31no—
96D57—51no—
97C3×D19—51no—
98C3×D19—51no—
99C3×D19—101no—
100C3×D19—151no—
101D3×C19C3×C5×D511yescharacteristic, complemented
102C2×C5×D5—571noHall
103C5×C19—22no—
104C5×C19C3×D3×D511yescharacteristic, complemented
105C5×C19C2×C3×C5×D311yescharacteristic, complemented
106C2×C32×C5—951no—
107C3×D15—191no—
108C3×C5×D3—22no—
109C3×C5×D3—951no—
110C3×C5×D3C5×D1911yescharacteristic, complemented
111C3×C5×D3D9511yescharacteristic, direct product factor
112C32×D5—191no—
113C2×D19—151noHall
114C3×C52—21no—
115C3×C52D3×D1911yescharacteristic, complemented
116C3×C52C2×C3×D1911yescharacteristic, complemented
117C22×C3×C5—2851no—
118C2×C5×D3—951no—
119C2×C3×D5—571no—
120D3×D5—191no—
121C3×C19—21no—
122C3×C19C5×D3×D511yescharacteristic, complemented
123C3×C19C2×C3×C5×D511yescharacteristic, complemented
124C2×C52—31no—
125C5×D5—191no—
126C5×D5—571no—
127C32×C5—22no—
128C32×C5C2×C5×D1911yescharacteristic, complemented
129C32×C5C2×D9511yescharacteristic, complemented
130C2×C19—31no—
131D19—51no—
132D19—151no—
133C2×C3×D3—951noHall
134C2×C3×C5—31no—
135C2×C3×C5—31no—
136C2×C3×C5—62no—
137C2×C3×C5—2851no—
138C2×C3×C5—951no—
139C2×C3×C5—951no—
140C2×C3×C5—1901no—
141D15—191no—
142C3×D5—191no—
143C3×D5—191no—
144C3×D5—381no—
145C3×D5—571no—
146C5×D3—22no—
147C5×D3—951no—
148C5×D3C3×C5×D1911yescharacteristic, complemented
149C5×D3C3×D9511yescharacteristic, direct product factor
150C52C3×D3×D1911yescharacteristic, complemented, Sylow
151C22×C5—2851no—
152C2×D5—571no—
153C19C3×C5×D3×D511yescharacteristic, complemented, Sylow
154C2×C32—951no—
155C3×D3—951no—
156C3×D3C5×D9511yescharacteristic, direct product factor
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C5×D3×D1911yescharacteristic, complemented
163C3×C5D3×D9511yescharacteristic, direct product factor
164C3×C5C2×C3×C5×D1911yescharacteristic, complemented
165C3×C5C2×C3×D9511yescharacteristic, complemented
166C22×C3—2851no—
167C2×D3—951no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—62no—
171C2×C5—2851no—
172C2×C5—951no—
173D5—191no—
174D5—571no—
175C32C2×C5×D9511yescharacteristic, complemented, Sylow
176C2×C3—31no—
177C2×C3—2851no—
178C2×C3—951no—
179C2×C3—951no—
180C2×C3—1901no—
181D3—951no—
182D3C3×C5×D9511yescharacteristic, direct product factor
183C5—22no—
184C5C3×C5×D3×D1911yescharacteristic, complemented
185C5C3×D3×D9511yescharacteristic, direct product factor
186C22—2851noSylow
187C3—21no—
188C3C5×D3×D9511yescharacteristic, direct product factor
189C3C2×C3×C5×D9511yescharacteristic, complemented
190C2—31no—
191C2—2851no—
192C2—951no—
subgroupG/H
center, hypercenterC3×C5D3×D95
commutator, cosocle, hypocenterC3×C5×C19C22×C3×C5
FrattiniC1G
Fitting, socleC32×C52×C19C22
LCSG ▷ C3×C5×C19
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D285C2semidirect
2. C3×C52×D3×C19C2semidirect
3. C32×C5×D95C2semidirect
5. C5×D3×D95C3direct (N × H)
6. C32×C52×C19C22semidirect
7. C3×D3×D95C5direct (N × H)
9. C5×D285C2×C3semidirect
10. C52×D3×C19C2×C3semidirect
13. C3×C5×D95D3direct (N × H)
14. C3×C5×D95C2×C3semidirect
17. C3×D285C2×C5semidirect
20. C3×C5×D3×C19D5semidirect
21. C3×C5×D3×C19C2×C5semidirect
22. C32×D95C2×C5semidirect
25. C3×C52×C19C2×D3semidirect
26. C3×C52×C19C22×C3semidirect
29. D3×D95C3×C5direct (N × H)
33. C5×D95C3×D3direct (N × H)
36. C32×C5×C19C2×D5semidirect
37. C32×C5×C19C22×C5semidirect
42. D285C2×C3×C5semidirect
45. C5×D3×C19C3×D5semidirect
46. C5×D3×C19C2×C3×C5semidirect
49. C3×D95C5×D3direct (N × H)
50. C3×D95C2×C3×C5semidirect
55. C52×C19C2×C3×D3semidirect
57. C3×C52×D3D19semidirect
62. C3×D3×C19C5×D5semidirect
71. C3×C5×C19D3×D5semidirect
72. C3×C5×C19C2×C3×D5semidirect
73. C3×C5×C19C2×C5×D3semidirect
74. C3×C5×C19C22×C3×C5semidirect
77. C32×C52C2×D19semidirect
82. D95C3×C5×D3direct (N × H)
87. C32×C19C2×C5×D5semidirect
90. C52×D3C3×D19semidirect
101. D3×C19C3×C5×D5semidirect
104. C5×C19C3×D3×D5semidirect
105. C5×C19C2×C3×C5×D3semidirect
110. C3×C5×D3C5×D19semidirect
111. C3×C5×D3D95direct (N × H)
115. C3×C52D3×D19semidirect
116. C3×C52C2×C3×D19semidirect
122. C3×C19C5×D3×D5semidirect
123. C3×C19C2×C3×C5×D5semidirect
128. C32×C5C2×C5×D19semidirect
129. C32×C5C2×D95semidirect
148. C5×D3C3×C5×D19semidirect
149. C5×D3C3×D95direct (N × H)
150. C52C3×D3×D19semidirect
153. C19C3×C5×D3×D5semidirect
156. C3×D3C5×D95direct (N × H)
162. C3×C5C5×D3×D19semidirect
163. C3×C5D3×D95direct (N × H)
164. C3×C5C2×C3×C5×D19semidirect
165. C3×C5C2×C3×D95semidirect
175. C32C2×C5×D95semidirect
182. D3C3×C5×D95direct (N × H)
184. C5C3×C5×D3×D19semidirect
185. C5C3×D3×D95direct (N × H)
188. C3C5×D3×D95direct (N × H)
189. C3C2×C3×C5×D95semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D2852
C3×C52×D3×C192
C32×C5×D952
C2×C3×C5×D953
C5×D3×D953
C3×D3×D955
C3×C5×D3×D195
C3×C5×D3×D519