Finite Group Databasebeta

← C3×C5×#1629 #14274663

Subgroups — C3×C5×#1629 #14274663

Order 1920.

628 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 152 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×D42C211yesmaximal, characteristic
2C3×C5×#492C211yesmaximal, characteristic, complemented
3C3×C5×#476C212yesmaximal, complemented
4C3×C5×#331C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C212yesmaximal, complemented
6C5×#1629C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4—22no—
8C2×C3×C5×SD16—22no—
9C3×C5×C4⋊Q8C2211yescharacteristic, complemented
10C3×C5×#127C2211yescharacteristic
11C3×C5×#121—22no—
12C3×C5×#120—22no—
13C3×C4×C5×D4C2212yes—
14C3×C5×#106—22no—
15C3×C5×C4⋊C8C2212yescomplemented
16C3×C5×#102—22no—
17C3×C4×C5×C8C2211yescharacteristic, complemented
18C3×#1629C511yesmaximal, characteristic, direct product factor, Hall
19C5×D42C2×C311yescharacteristic
20C5×#492C2×C311yescharacteristic, complemented
21C5×#476C2×C312yescomplemented
22C5×#331C2×C311yescharacteristic, complemented
23C5×D4⋊C8C2×C312yescomplemented
24C24×C3×C5—22no—
25C2×C3×C5×Q8—21no—
26C2×C3×C5×D4—24no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4—44no—
29C2×C3×C5×D4—44no—
30C2×C3×C5×D4D412yes—
31C2×C3×C5×D4D412yes—
32C22×C3×C4×C5—22no—
33C3×C5×SD16—44no—
34C2×C3×C5×C8—21no—
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—22no—
37C3×C5×C4⋊C4D412yes—
38C3×C5×C22⋊C4—22no—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2311yescharacteristic
41C3×D42C2×C511yescharacteristic
42C3×#492C2×C511yescharacteristic, complemented
43C3×#476C2×C512yescomplemented
44C3×#331C2×C511yescharacteristic, complemented
45C3×D4⋊C8C2×C512yescomplemented
46C22×C5×D4—22no—
47C2×C5×SD16—22no—
48C5×C4⋊Q8C22×C311yescharacteristic, complemented
49C5×#127C22×C311yescharacteristic
50C5×#121—22no—
51C5×#120—22no—
52C4×C5×D4C22×C312yes—
53C5×#106—22no—
54C5×C4⋊C8C22×C312yescomplemented
55C5×#102—22no—
56C4×C5×C8C22×C311yescharacteristic, complemented
57#1629C3×C511yescharacteristic, direct product factor, Sylow
58C23×C3×C5—22no—
59C23×C3×C5—22no—
60C23×C3×C5—48no—
61C23×C3×C5—82no—
62C3×C5×Q8—42no—
63C3×C5×D4—22no—
64C3×C5×D4—42no—
65C3×C5×D4—48no—
66C3×C5×D4—42no—
67C3×C5×D4—42no—
68C3×C5×D4SD1614yescomplemented
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—42no—
71C2×C3×C4×C5—42no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C3×C5×C8—22no—
76C3×C5×C8—42no—
77C22×C3×D4—22no—
78C2×C3×SD16—22no—
79C3×C4⋊Q8C22×C511yescharacteristic, complemented
80C3×#127C22×C511yescharacteristic
81C3×#121—22no—
82C3×#120—22no—
83C3×C4×D4C22×C512yes—
84C3×#106—22no—
85C3×C4⋊C8C22×C512yescomplemented
86C3×#102—22no—
87C3×C4×C8C22×C511yescharacteristic, complemented
88C24×C5—22no—
89C2×C5×Q8—21no—
90C2×C5×D4—24no—
91C2×C5×D4—22no—
92C2×C5×D4—44no—
93C2×C5×D4—44no—
94C2×C5×D4C3×D412yes—
95C2×C5×D4C3×D412yes—
96C22×C4×C5—22no—
97C5×SD16—44no—
98C2×C5×C8—21no—
99C2×C5×C8—22no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4C3×D412yes—
102C5×C22⋊C4—22no—
103C5×C22⋊C4—22no—
104C42×C5C23×C311yescharacteristic
105D42C2×C3×C511yescharacteristic
106#492C2×C3×C511yescharacteristic, complemented
107#476C2×C3×C512yescomplemented
108#331C2×C3×C511yescharacteristic, complemented
109D4⋊C8C2×C3×C512yescomplemented
110C22×C3×C5—24no—
111C22×C3×C5—42no—
112C22×C3×C5—42no—
113C22×C3×C5—44no—
114C22×C3×C5—42no—
115C22×C3×C5—88no—
116C22×C3×C5#12011yescharacteristic
117C3×C4×C5—21no—
118C3×C4×C5—42no—
119C3×C4×C5—81no—
120C3×C4×C5C2×SD1612yes—
121C3×C4×C5AGL(1,ℤ/8)12yes—
122C24×C3—22no—
123C2×C3×Q8—21no—
124C2×C3×D4—24no—
125C2×C3×D4—22no—
126C2×C3×D4—44no—
127C2×C3×D4—44no—
128C2×C3×D4C5×D412yes—
129C2×C3×D4C5×D412yes—
130C22×C3×C4—22no—
131C3×SD16—44no—
132C2×C3×C8—21no—
133C2×C3×C8—22no—
134C3×C4⋊C4—22no—
135C3×C4⋊C4C5×D412yes—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138C3×C42C23×C511yescharacteristic
139C23×C5—22no—
140C23×C5—22no—
141C23×C5—48no—
142C23×C5—82no—
143C5×Q8—42no—
144C5×D4—22no—
145C5×D4—42no—
146C5×D4—48no—
147C5×D4—42no—
148C5×D4—42no—
149C5×D4C3×SD1614yescomplemented
150C2×C4×C5—22no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—41no—
154C2×C4×C5C2×C3×D411yescharacteristic
155C2×C4×C5C2×C3×D412yes—
156C5×C8—22no—
157C5×C8—42no—
158C22×D4—22no—
159C2×SD16—22no—
160C4⋊Q8C22×C3×C511yescharacteristic, complemented
161#127C22×C3×C511yescharacteristic
162#121—22no—
163#120—22no—
164C4×D4C22×C3×C512yes—
165#106—22no—
166C4⋊C8C22×C3×C512yescomplemented
167#102—22no—
168C4×C8C22×C3×C511yescharacteristic, complemented
169C2×C3×C5—44no—
170C2×C3×C5—82no—
171C2×C3×C5#45012yes—
172C2×C3×C5#45311yescharacteristic
173C23×C3—22no—
174C23×C3—22no—
175C23×C3—48no—
176C23×C3—82no—
177C3×Q8—42no—
178C3×D4—22no—
179C3×D4—42no—
180C3×D4—48no—
181C3×D4—42no—
182C3×D4—42no—
183C3×D4C5×SD1614yescomplemented
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4—41no—
188C2×C3×C4C2×C5×D411yescharacteristic
189C2×C3×C4C2×C5×D412yes—
190C3×C8—22no—
191C3×C8—42no—
192C22×C5—24no—
193C22×C5—42no—
194C22×C5—42no—
195C22×C5—44no—
196C22×C5—42no—
197C22×C5—88no—
198C22×C5C3×#12011yescharacteristic
199C4×C5—21no—
200C4×C5—42no—
201C4×C5—81no—
202C4×C5C2×C3×SD1612yes—
203C4×C5C3×AGL(1,ℤ/8)12yes—
204C24—22no—
205C2×Q8—21no—
206C2×D4—24no—
207C2×D4—22no—
208C2×D4—44no—
209C2×D4—44no—
210C2×D4C3×C5×D412yes—
211C2×D4C3×C5×D412yes—
212C22×C4—22no—
213SD16—44no—
214C2×C8—21no—
215C2×C8—22no—
216C4⋊C4—22no—
217C4⋊C4C3×C5×D412yes—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C42C23×C3×C511yescharacteristic
221C3×C5#162911yescharacteristic, direct product factor, Hall
222C22×C3—24no—
223C22×C3—42no—
224C22×C3—42no—
225C22×C3—44no—
226C22×C3—42no—
227C22×C3—88no—
228C22×C3C5×#12011yescharacteristic
229C3×C4—21no—
230C3×C4—42no—
231C3×C4—81no—
232C3×C4C2×C5×SD1612yes—
233C3×C4C5×AGL(1,ℤ/8)12yes—
234C2×C5—44no—
235C2×C5—82no—
236C2×C5C3×#45012yes—
237C2×C5C3×#45311yescharacteristic
238C23—22no—
239C23—22no—
240C23—48no—
241C23—82no—
242Q8—42no—
243D4—22no—
244D4—42no—
245D4—48no—
246D4—42no—
247D4—42no—
248D4C3×C5×SD1614yescomplemented
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4C2×C3×C5×D411yescharacteristic
254C2×C4C2×C3×C5×D412yes—
255C8—22no—
256C8—42no—
257C2×C3—44no—
258C2×C3—82no—
259C2×C3C5×#45012yes—
260C2×C3C5×#45311yescharacteristic
261C5C3×#162911yescharacteristic, direct product factor, Sylow
262C22—24no—
263C22—42no—
264C22—42no—
265C22—44no—
266C22—42no—
267C22—88no—
268C22C3×C5×#12011yescharacteristic
269C4—21no—
270C4—42no—
271C4—81no—
272C4C2×C3×C5×SD1612yes—
273C4C3×C5×AGL(1,ℤ/8)12yes—
274C3C5×#162911yescharacteristic, direct product factor, Sylow
275C2—44no—
276C2—82no—
277C2C3×C5×#45012yes—
278C2C3×C5×#45311yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×D42C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#492C2semidirect
3. C3×C5×#476C2semidirect
4. C3×C5×#331C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#1629C3direct (N × H)
9. C3×C5×C4⋊Q8C22semidirect
15. C3×C5×C4⋊C8C22semidirect
17. C3×C4×C5×C8C22semidirect
18. C3×#1629C5direct (N × H)
20. C5×#492C2×C3semidirect
21. C5×#476C2×C3semidirect
22. C5×#331C2×C3semidirect
23. C5×D4⋊C8C2×C3semidirect
42. C3×#492C2×C5semidirect
43. C3×#476C2×C5semidirect
44. C3×#331C2×C5semidirect
45. C3×D4⋊C8C2×C5semidirect
48. C5×C4⋊Q8C22×C3semidirect
54. C5×C4⋊C8C22×C3semidirect
56. C4×C5×C8C22×C3semidirect
57. #1629C3×C5direct (N × H)
68. C3×C5×D4SD16semidirect
79. C3×C4⋊Q8C22×C5semidirect
85. C3×C4⋊C8C22×C5semidirect
87. C3×C4×C8C22×C5semidirect
106. #492C2×C3×C5semidirect
107. #476C2×C3×C5semidirect
108. #331C2×C3×C5semidirect
109. D4⋊C8C2×C3×C5semidirect
149. C5×D4C3×SD16semidirect
160. C4⋊Q8C22×C3×C5semidirect
166. C4⋊C8C22×C3×C5semidirect
168. C4×C8C22×C3×C5semidirect
183. C3×D4C5×SD16semidirect
221. C3×C5#1629direct (N × H)
248. D4C3×C5×SD16semidirect
261. C5C3×#1629direct (N × H)
274. C3C5×#1629direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D422
C3×C5×#4922
C3×C5×#4762
C3×C5×#3312
C3×C5×D4⋊C82
C5×#16293
C3×#16295