Finite Group Databasebeta

← C3×C5×D3×D5×C19 #30685872

Subgroups — C3×C5×D3×D5×C19 #30685872

Order 17100.

212 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 80 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×C19×D15C211yesmaximal, characteristic, complemented
2C3×C52×D3×C19C211yesmaximal, characteristic, complemented
3C32×C5×D5×C19C211yesmaximal, characteristic, complemented
4C2×C3×C5×D5×C19—31nomaximal
5C5×D3×D5×C19C311yesmaximal, characteristic, direct product factor
6C32×C52×C19C2211yescharacteristic, complemented, Hall
7C2×C3×C5×D3×C19—51nomaximal
8C3×D3×D5×C19C511yesmaximal, characteristic, direct product factor
9C5×C19×D15C2×C311yescharacteristic, complemented
10C52×D3×C19C2×C311yescharacteristic, complemented
11C3×C5×D5×C19—21no—
12C3×C5×D5×C19—31no—
13C3×C5×D5×C19D311yescharacteristic, direct product factor
14C3×C5×D5×C19C2×C311yescharacteristic, complemented
15C2×C3×C52×C19—31no—
16C2×C5×D5×C19—31noHall
17C2×C32×C5×C19—51no—
18C3×C19×D15C2×C511yescharacteristic, complemented
19C3×C5×D3×C19—22no—
20C3×C5×D3×C19—51no—
21C3×C5×D3×C19D511yescharacteristic, direct product factor
22C3×C5×D3×C19C2×C511yescharacteristic, complemented
23C32×D5×C19C2×C511yescharacteristic, complemented
24C3×C52×C19—21no—
25C3×C52×C19C2×D311yescharacteristic, complemented
26C3×C52×C19C22×C311yescharacteristic, complemented
27C22×C3×C5×C19—151no—
28C2×C5×D3×C19—51no—
29C2×C3×D5×C19—31no—
30D3×D5×C19C3×C511yescharacteristic, direct product factor
31C2×C52×C19—31no—
32C5×D5×C19—31no—
33C5×D5×C19C3×D311yescharacteristic, direct product factor
34C3×C5×D3×D5C1911yesmaximal, characteristic, direct product factor, Hall
35C32×C5×C19—22no—
36C32×C5×C19C2×D511yescharacteristic, complemented
37C32×C5×C19C22×C511yescharacteristic, complemented
38C2×C3×D3×C19—51noHall
39C2×C3×C5×C19—31no—
40C2×C3×C5×C19—31no—
41C2×C3×C5×C19—51no—
42C2×C3×C5×C19—51no—
43C2×C3×C5×C19—62no—
44C2×C3×C5×C19—101no—
45C2×C3×C5×C19—151no—
46C19×D15C2×C3×C511yescharacteristic, complemented
47C5×D3×C19—22no—
48C5×D3×C19—51no—
49C5×D3×C19C3×D511yescharacteristic, direct product factor
50C5×D3×C19C2×C3×C511yescharacteristic, complemented
51C3×D5×C19—21no—
52C3×D5×C19—31no—
53C3×D5×C19C5×D311yescharacteristic, direct product factor
54C3×D5×C19C2×C3×C511yescharacteristic, complemented
55C52×C19C2×C3×D311yescharacteristic, complemented, Hall
56C3×C5×D15C2×C1911yescharacteristic, complemented
57C3×C52×D3C2×C1911yescharacteristic, complemented
58C32×C5×D5C2×C1911yescharacteristic, complemented
59C22×C5×C19—151no—
60C2×D5×C19—31no—
61C2×C32×C19—51no—
62C3×D3×C19—51no—
63C3×D3×C19C5×D511yescharacteristic, direct product factor
64C2×C3×C5×D5—31no—
65C5×D3×D5C3×C1911yescharacteristic, direct product factor
66C3×C5×C19—22no—
67C3×C5×C19—22no—
68C3×C5×C19—21no—
69C3×C5×C19—21no—
70C3×C5×C19—42no—
71C3×C5×C19D3×D511yescharacteristic, direct product factor
72C3×C5×C19C2×C3×D511yescharacteristic, complemented
73C3×C5×C19C2×C5×D311yescharacteristic, complemented
74C3×C5×C19C22×C3×C511yescharacteristic, complemented
75C22×C3×C19—151no—
76C2×D3×C19—51no—
77C32×C52C22×C1911yescharacteristic, complemented, Hall
78C2×C5×C19—31no—
79C2×C5×C19—31no—
80C2×C5×C19—51no—
81C2×C5×C19—62no—
82C2×C5×C19—151no—
83D5×C19—31no—
84D5×C19C3×C5×D311yescharacteristic, direct product factor
85C2×C3×C5×D3—51no—
86C3×D3×D5C5×C1911yescharacteristic, direct product factor
87C32×C19C2×C5×D511yescharacteristic, complemented, Hall
88C2×C3×C52—31no—
89C5×D15C2×C3×C1911yescharacteristic, complemented
90C52×D3C2×C3×C1911yescharacteristic, complemented
91C3×C5×D5—21no—
92C3×C5×D5—31no—
93C3×C5×D5D3×C1911yescharacteristic, direct product factor
94C3×C5×D5C2×C3×C1911yescharacteristic, complemented
95C2×C3×C19—31no—
96C2×C3×C19—51no—
97C2×C3×C19—51no—
98C2×C3×C19—101no—
99C2×C3×C19—151no—
100D3×C19—51no—
101D3×C19C3×C5×D511yescharacteristic, direct product factor
102C2×C5×D5—31noHall
103C5×C19—22no—
104C5×C19C3×D3×D511yescharacteristic, direct product factor
105C5×C19C2×C3×C5×D311yescharacteristic, complemented
106C2×C32×C5—51no—
107C3×D15C2×C5×C1911yescharacteristic, complemented
108C3×C5×D3—22no—
109C3×C5×D3—51no—
110C3×C5×D3D5×C1911yescharacteristic, direct product factor
111C3×C5×D3C2×C5×C1911yescharacteristic, complemented
112C32×D5C2×C5×C1911yescharacteristic, complemented
113C22×C19—151noHall
114C3×C52—21no—
115C3×C52C2×D3×C1911yescharacteristic, complemented
116C3×C52C22×C3×C1911yescharacteristic, complemented
117C22×C3×C5—151no—
118C2×C5×D3—51no—
119C2×C3×D5—31no—
120D3×D5C3×C5×C1911yescharacteristic, direct product factor
121C3×C19—21no—
122C3×C19C5×D3×D511yescharacteristic, direct product factor
123C3×C19C2×C3×C5×D511yescharacteristic, complemented
124C2×C52—31no—
125C5×D5—31no—
126C5×D5C3×D3×C1911yescharacteristic, direct product factor
127C32×C5—22no—
128C32×C5C2×D5×C1911yescharacteristic, complemented
129C32×C5C22×C5×C1911yescharacteristic, complemented
130C2×C19—31no—
131C2×C19—51no—
132C2×C19—151no—
133C2×C3×D3—51noHall
134C2×C3×C5—31no—
135C2×C3×C5—31no—
136C2×C3×C5—51no—
137C2×C3×C5—51no—
138C2×C3×C5—62no—
139C2×C3×C5—101no—
140C2×C3×C5—151no—
141D15C2×C3×C5×C1911yescharacteristic, complemented
142C3×D5—21no—
143C3×D5—31no—
144C3×D5C5×D3×C1911yescharacteristic, direct product factor
145C3×D5C2×C3×C5×C1911yescharacteristic, complemented
146C5×D3—22no—
147C5×D3—51no—
148C5×D3C3×D5×C1911yescharacteristic, direct product factor
149C5×D3C2×C3×C5×C1911yescharacteristic, complemented
150C52C2×C3×D3×C1911yescharacteristic, complemented, Sylow
151C22×C5—151no—
152C2×D5—31no—
153C19C3×C5×D3×D511yescharacteristic, direct product factor, Sylow
154C2×C32—51no—
155C3×D3—51no—
156C3×D3C5×D5×C1911yescharacteristic, direct product factor
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D3×D5×C1911yescharacteristic, direct product factor
163C3×C5C2×C3×D5×C1911yescharacteristic, complemented
164C3×C5C2×C5×D3×C1911yescharacteristic, complemented
165C3×C5C22×C3×C5×C1911yescharacteristic, complemented
166C22×C3—151no—
167C2×D3—51no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—51no—
171C2×C5—62no—
172C2×C5—151no—
173D5—31no—
174D5C3×C5×D3×C1911yescharacteristic, direct product factor
175C32C2×C5×D5×C1911yescharacteristic, complemented, Sylow
176C2×C3—31no—
177C2×C3—51no—
178C2×C3—51no—
179C2×C3—101no—
180C2×C3—151no—
181D3—51no—
182D3C3×C5×D5×C1911yescharacteristic, direct product factor
183C5—22no—
184C5C3×D3×D5×C1911yescharacteristic, direct product factor
185C5C2×C3×C5×D3×C1911yescharacteristic, complemented
186C22—151noSylow
187C3—21no—
188C3C5×D3×D5×C1911yescharacteristic, direct product factor
189C3C2×C3×C5×D5×C1911yescharacteristic, complemented
190C2—31no—
191C2—51no—
192C2—151no—
subgroupG/H
center, hypercenterC3×C5×C19D3×D5
commutator, cosocle, hypocenterC3×C5C22×C3×C5×C19
FrattiniC1G
Fitting, socleC32×C52×C19C22
LCSG ▷ C3×C5
UCSC1 ◁ C3×C5×C19

Complements

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

NH ≅ G/Ntype
1. C3×C5×C19×D15C2semidirect
2. C3×C52×D3×C19C2semidirect
3. C32×C5×D5×C19C2semidirect
5. C5×D3×D5×C19C3direct (N × H)
6. C32×C52×C19C22semidirect
8. C3×D3×D5×C19C5direct (N × H)
9. C5×C19×D15C2×C3semidirect
10. C52×D3×C19C2×C3semidirect
13. C3×C5×D5×C19D3direct (N × H)
14. C3×C5×D5×C19C2×C3semidirect
18. C3×C19×D15C2×C5semidirect
21. C3×C5×D3×C19D5direct (N × H)
22. C3×C5×D3×C19C2×C5semidirect
23. C32×D5×C19C2×C5semidirect
25. C3×C52×C19C2×D3semidirect
26. C3×C52×C19C22×C3semidirect
30. D3×D5×C19C3×C5direct (N × H)
33. C5×D5×C19C3×D3direct (N × H)
34. C3×C5×D3×D5C19direct (N × H)
36. C32×C5×C19C2×D5semidirect
37. C32×C5×C19C22×C5semidirect
46. C19×D15C2×C3×C5semidirect
49. C5×D3×C19C3×D5direct (N × H)
50. C5×D3×C19C2×C3×C5semidirect
53. C3×D5×C19C5×D3direct (N × H)
54. C3×D5×C19C2×C3×C5semidirect
55. C52×C19C2×C3×D3semidirect
56. C3×C5×D15C2×C19semidirect
57. C3×C52×D3C2×C19semidirect
58. C32×C5×D5C2×C19semidirect
63. C3×D3×C19C5×D5direct (N × H)
65. C5×D3×D5C3×C19direct (N × H)
71. C3×C5×C19D3×D5direct (N × H)
72. C3×C5×C19C2×C3×D5semidirect
73. C3×C5×C19C2×C5×D3semidirect
74. C3×C5×C19C22×C3×C5semidirect
77. C32×C52C22×C19semidirect
84. D5×C19C3×C5×D3direct (N × H)
86. C3×D3×D5C5×C19direct (N × H)
87. C32×C19C2×C5×D5semidirect
89. C5×D15C2×C3×C19semidirect
90. C52×D3C2×C3×C19semidirect
93. C3×C5×D5D3×C19direct (N × H)
94. C3×C5×D5C2×C3×C19semidirect
101. D3×C19C3×C5×D5direct (N × H)
104. C5×C19C3×D3×D5direct (N × H)
105. C5×C19C2×C3×C5×D3semidirect
107. C3×D15C2×C5×C19semidirect
110. C3×C5×D3D5×C19direct (N × H)
111. C3×C5×D3C2×C5×C19semidirect
112. C32×D5C2×C5×C19semidirect
115. C3×C52C2×D3×C19semidirect
116. C3×C52C22×C3×C19semidirect
120. D3×D5C3×C5×C19direct (N × H)
122. C3×C19C5×D3×D5direct (N × H)
123. C3×C19C2×C3×C5×D5semidirect
126. C5×D5C3×D3×C19direct (N × H)
128. C32×C5C2×D5×C19semidirect
129. C32×C5C22×C5×C19semidirect
141. D15C2×C3×C5×C19semidirect
144. C3×D5C5×D3×C19direct (N × H)
145. C3×D5C2×C3×C5×C19semidirect
148. C5×D3C3×D5×C19direct (N × H)
149. C5×D3C2×C3×C5×C19semidirect
150. C52C2×C3×D3×C19semidirect
153. C19C3×C5×D3×D5direct (N × H)
156. C3×D3C5×D5×C19direct (N × H)
162. C3×C5D3×D5×C19direct (N × H)
163. C3×C5C2×C3×D5×C19semidirect
164. C3×C5C2×C5×D3×C19semidirect
165. C3×C5C22×C3×C5×C19semidirect
174. D5C3×C5×D3×C19direct (N × H)
175. C32C2×C5×D5×C19semidirect
182. D3C3×C5×D5×C19direct (N × H)
184. C5C3×D3×D5×C19direct (N × H)
185. C5C2×C3×C5×D3×C19semidirect
188. C3C5×D3×D5×C19direct (N × H)
189. C3C2×C3×C5×D5×C19semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C19×D152
C3×C52×D3×C192
C32×C5×D5×C192
C2×C3×C5×D5×C193
C5×D3×D5×C193
C2×C3×C5×D3×C195
C3×D3×D5×C195
C3×C5×D3×D519