Finite Group Databasebeta

← C3×#10613522 #14458174

Subgroups — C3×#10613522 #14458174

Order 1920.

952 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 234 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×#66091C214yesmaximal, complemented
2C3×C5×#493C211yesmaximal, characteristic, complemented
3C3×#65449C214yesmaximal, complemented
4C3×#65366C214yesmaximal, complemented
5C3×#64989C212yesmaximal, complemented
6#10613522C311yesmaximal, characteristic, direct product factor, Hall
7C3×#4144C2214yescomplemented
8C2×C3×C5×D8C2214yescomplemented
9C3×C5×#127C2212yescomplemented
10C3×#4078C2218yescomplemented
11C3×#4058—24no—
12C3×#4057—28no—
13C3×D5×D8—24no—
14C3×#4050C2212yes—
15C3×#4047C2214yescomplemented
16C3×C4×C5×C8C2211yescharacteristic, complemented
17C3×#3965C2214yescomplemented
18C3×#3951C2212yescomplemented
19C3×#3937C2214yescomplemented
20C3×#3292—51nomaximal, Hall
21#66091C2×C314yescomplemented
22C5×#493C2×C311yescharacteristic, complemented
23#65449C2×C314yescomplemented
24#65366C2×C314yescomplemented
25#64989C2×C312yescomplemented
26C2×C3×C5×D4—42no—
27C2×C3×C5×D4C2314yes—
28C2×C3×C22⋊D5—44no—
29C3×#711—28no—
30C3×D4×D5—28no—
31C3×#709C2314yes—
32C3×C5×D8—24no—
33C3×C5×D8—24no—
34C2×C3×C5×C8C2312yes—
35C3×C42×C5C2311yescharacteristic
36C3×#687—28no—
37C3×#686—28no—
38C3×#681C2314yes—
39C3×Dic20D412yescomplemented
40C3×D40D412yescomplemented
41C3×#677D414yescomplemented
42C3×#676—24no—
43C3×C8×D5—24no—
44C3×#576—54no—
45C3×#493D511yescharacteristic, complemented
46C3×#472—54no—
47C3×#453—54no—
48C3×#443—52no—
49#4144C22×C314yescomplemented
50C2×C5×D8C22×C314yescomplemented
51C5×#127C22×C312yescomplemented
52#4078C22×C318yescomplemented
53#4058—24no—
54#4057—28no—
55D5×D8—24no—
56#4050C22×C312yes—
57#4047C22×C314yescomplemented
58C4×C5×C8C22×C311yescharacteristic, complemented
59#3965C22×C314yescomplemented
60#3951C22×C312yescomplemented
61#3937C22×C314yescomplemented
62#3292—51noSylow
63C23×C3×C5—24no—
64C22×C3×D5—44no—
65C3×C5×D4—28no—
66C3×C5×D4—84no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5C2411yescharacteristic
69C3×C22⋊D5—24no—
70C3×C22⋊D5—48no—
71C2×C3×Dic5—44no—
72C3×D20C2×D414yes—
73C3×C4×D5—24no—
74C3×Dic10C2×D414yes—
75C3×C5×C8C2×D412yes—
76C3×C5×C8C2×D412yes—
77C3×#168—24no—
78C3×H(5,𝔽2)—54no—
79C3×AGL(1,ℤ/8)—58no—
80C3×AGL(1,ℤ/8)—108no—
81C3×#135—52no—
82C3×#135—104no—
83C2×C3×D8—104no—
84C2×C3×D8C2×D514yescomplemented
85C3×#131—54no—
86C3×#127C2×D512yescomplemented
87C3×#108—52no—
88C3×#104—54no—
89C3×#100—54no—
90C3×C4×C8C2×D511yescharacteristic, complemented
91C2×C5×D4—42no—
92C2×C5×D4C23×C314yes—
93C2×C22⋊D5—44no—
94#711—28no—
95D4×D5—28no—
96#709C23×C314yes—
97C5×D8—24no—
98C5×D8—24no—
99C2×C5×C8C23×C312yes—
100C42×C5C23×C311yescharacteristic
101#687—28no—
102#686—28no—
103#681C23×C314yes—
104Dic20C3×D412yescomplemented
105D40C3×D412yescomplemented
106#677C3×D414yescomplemented
107#676—24no—
108C8×D5—24no—
109#576—54no—
110#493C3×D511yescharacteristic, complemented
111#472—54no—
112#453—54no—
113#443—52no—
114C22×C3×C5—44no—
115C22×C3×C5—84no—
116C22×C3×C5H(5,𝔽2)11yescharacteristic
117C2×C3×D5—24no—
118C2×C3×D5—164no—
119C3×C4×C5—22no—
120C3×C4×C5C22×D412yes—
121C3×Dic5—24no—
122C3×#41—54no—
123C3×#41—108no—
124C2×C3×D4—42no—
125C2×C3×D4—108no—
126C2×C3×D4—204no—
127C2×C3×D4C22×D514yes—
128C3×Q16—52no—
129C3×SD16—54no—
130C3×SD16—108no—
131C3×D8—24no—
132C3×D8—24no—
133C3×D8—52no—
134C3×D8—108no—
135C3×M16—54no—
136C3×M16—104no—
137C2×C3×C8—104no—
138C2×C3×C8C22×D512yes—
139C3×C42C22×D511yescharacteristic
140C23×C5—24no—
141C22×D5—44no—
142C5×D4—28no—
143C5×D4—84no—
144C2×C4×C5—21no—
145C2×C4×C5C24×C311yescharacteristic
146C22⋊D5—24no—
147C22⋊D5—48no—
148C2×Dic5—44no—
149D20C2×C3×D414yes—
150C4×D5—24no—
151Dic10C2×C3×D414yes—
152C5×C8C2×C3×D412yes—
153C5×C8C2×C3×D412yes—
154#168—24no—
155H(5,𝔽2)—54no—
156AGL(1,ℤ/8)—58no—
157AGL(1,ℤ/8)—108no—
158#135—52no—
159#135—104no—
160C2×D8—104no—
161C2×D8C2×C3×D514yescomplemented
162#131—54no—
163#127C2×C3×D512yescomplemented
164#108—52no—
165#104—54no—
166#100—54no—
167C4×C8C2×C3×D511yescharacteristic, complemented
168C2×C3×C5—21no—
169C2×C3×C5—84no—
170C2×C3×C5D4211yescharacteristic
171C3×D5—44no—
172C23×C3—24no—
173C23×C3—204no—
174C3×Q8—54no—
175C3×D4—28no—
176C3×D4—54no—
177C3×D4—84no—
178C3×D4—104no—
179C3×D4—208no—
180C2×C3×C4—21no—
181C2×C3×C4—104no—
182C2×C3×C4—204no—
183C2×C3×C4C23×D511yescharacteristic
184C3×C8—104no—
185C3×C8D4×D512yes—
186C3×C8D4×D512yes—
187C22×C5—44no—
188C22×C5—84no—
189C22×C5C3×H(5,𝔽2)11yescharacteristic
190C2×D5—24no—
191C2×D5—164no—
192C4×C5—22no—
193C4×C5C22×C3×D412yes—
194Dic5—24no—
195#41—54no—
196#41—108no—
197C2×D4—42no—
198C2×D4—108no—
199C2×D4—204no—
200C2×D4C22×C3×D514yes—
201Q16—52no—
202SD16—54no—
203SD16—108no—
204D8—24no—
205D8—24no—
206D8—52no—
207D8—108no—
208M16—54no—
209M16—104no—
210C2×C8—104no—
211C2×C8C22×C3×D512yes—
212C42C22×C3×D511yescharacteristic
213C3×C5#329211yescharacteristic, complemented, Hall
214C22×C3—44no—
215C22×C3—84no—
216C22×C3—104no—
217C22×C3—804no—
218C22×C3#414411yescharacteristic
219C3×C4—22no—
220C3×C4—104no—
221C3×C4C2×D4×D512yes—
222C2×C5—21no—
223C2×C5—84no—
224C2×C5C3×D4211yescharacteristic
225D5—44no—
226C23—24no—
227C23—204no—
228Q8—54no—
229D4—28no—
230D4—54no—
231D4—84no—
232D4—104no—
233D4—208no—
234C2×C4—21no—
235C2×C4—104no—
236C2×C4—204no—
237C2×C4C23×C3×D511yescharacteristic
238C8—104no—
239C8C3×D4×D512yes—
240C8C3×D4×D512yes—
241C2×C3—21no—
242C2×C3—84no—
243C2×C3—204no—
244C2×C3#6605111yescharacteristic
245C5C3×#329211yescharacteristic, complemented, Sylow
246C22—44no—
247C22—84no—
248C22—104no—
249C22—804no—
250C22C3×#414411yescharacteristic
251C4—22no—
252C4—104no—
253C4C2×C3×D4×D512yes—
254C3#1061352211yescharacteristic, direct product factor, Sylow
255C2—21no—
256C2—84no—
257C2—204no—
258C2C3×#6605111yescharacteristic
subgroupG/H
centerC2×C3#66051
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#493C2
socleC2×C3×C5D42
hypercenterC3×#493D5
hypocenterC5C3×#3292
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#493

Complements

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

NH ≅ G/Ntype
1. C3×#66091C2semidirect
2. C3×C5×#493C2semidirect
3. C3×#65449C2semidirect
4. C3×#65366C2semidirect
5. C3×#64989C2semidirect
6. #10613522C3direct (N × H)
7. C3×#4144C22semidirect
8. C2×C3×C5×D8C22semidirect
9. C3×C5×#127C22semidirect
10. C3×#4078C22semidirect
15. C3×#4047C22semidirect
16. C3×C4×C5×C8C22semidirect
17. C3×#3965C22semidirect
18. C3×#3951C22semidirect
19. C3×#3937C22semidirect
21. #66091C2×C3semidirect
22. C5×#493C2×C3semidirect
23. #65449C2×C3semidirect
24. #65366C2×C3semidirect
25. #64989C2×C3semidirect
39. C3×Dic20D4semidirect
40. C3×D40D4semidirect
41. C3×#677D4semidirect
45. C3×#493D5semidirect
49. #4144C22×C3semidirect
50. C2×C5×D8C22×C3semidirect
51. C5×#127C22×C3semidirect
52. #4078C22×C3semidirect
57. #4047C22×C3semidirect
58. C4×C5×C8C22×C3semidirect
59. #3965C22×C3semidirect
60. #3951C22×C3semidirect
61. #3937C22×C3semidirect
84. C2×C3×D8C2×D5semidirect
86. C3×#127C2×D5semidirect
90. C3×C4×C8C2×D5semidirect
104. Dic20C3×D4semidirect
105. D40C3×D4semidirect
106. #677C3×D4semidirect
110. #493C3×D5semidirect
161. C2×D8C2×C3×D5semidirect
163. #127C2×C3×D5semidirect
167. C4×C8C2×C3×D5semidirect
213. C3×C5#3292semidirect
245. C5C3×#3292semidirect
254. C3#10613522direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660912
C3×C5×#4932
C3×#654492
C3×#653662
C3×#649892
#106135223
C3×#32925