Finite Group Databasebeta

← C3×#10602700 #14289344

Subgroups — C3×#10602700 #14289344

Order 1920.

628 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 130 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×#65365C211yesmaximal, characteristic, complemented
3C3×#65297C212yesmaximal, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C212yesmaximal, complemented
6#10602700C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4—22no—
8C3×C5×#127C2211yescharacteristic
9C3×C5×#121—22no—
10C3×C5×#120—22no—
11C3×C4×C5×D4C2212yes—
12C2×C3×#687—22no—
13C3×#4015C2211yescharacteristic, complemented
14C3×#3964—22no—
15C3×#3940—22no—
16C3×C4⋊#168C2212yescomplemented
17C3×C4×#168C2211yescharacteristic, complemented
18C3×#1629—51nomaximal, Hall
19C5×D42C2×C311yescharacteristic
20#65365C2×C311yescharacteristic, complemented
21#65297C2×C312yescomplemented
22#64764C2×C311yescharacteristic, complemented
23D4⋊#168C2×C312yescomplemented
24C24×C3×C5—22no—
25C2×C3×C5×D4—24no—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—44no—
28C2×C3×C5×D4—44no—
29C2×C3×C5×D4D412yes—
30C2×C3×C5×D4D412yes—
31C22×C3×C4×C5—22no—
32C2×C3×Dic10—21no—
33C3×C5×C4⋊C4D412yes—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37C3×#687—44no—
38C3×C4⋊Dic5—22no—
39C2×C3×#168—21no—
40C2×C3×#168—22no—
41C3×D42D511yescharacteristic
42C3×#492—51no—
43C3×#476—52no—
44C3×#331—51no—
45C3×D4⋊C8—52no—
46C22×C5×D4—22no—
47C5×#127C22×C311yescharacteristic
48C5×#121—22no—
49C5×#120—22no—
50C4×C5×D4C22×C312yes—
51C2×#687—22no—
52#4015C22×C311yescharacteristic, complemented
53#3964—22no—
54#3940—22no—
55C4⋊#168C22×C312yescomplemented
56C4×#168C22×C311yescharacteristic, complemented
57#1629—51noSylow
58C23×C3×C5—22no—
59C23×C3×C5—22no—
60C23×C3×C5—48no—
61C23×C3×C5—82no—
62C3×C5×D4—22no—
63C3×C5×D4—42no—
64C3×C5×D4—48no—
65C3×C5×D4—42no—
66C3×C5×D4—42no—
67C3×C5×D4SD1614yescomplemented
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5—42no—
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D412yes—
73C2×C3×Dic5—41no—
74C3×Dic10—42no—
75C3×#168—22no—
76C3×#168—42no—
77C22×C3×D4—22no—
78C2×C3×SD16—102no—
79C3×C4⋊Q8—51no—
80C3×#127C2×D511yescharacteristic
81C3×#121—22no—
82C3×#120—22no—
83C3×C4×D4C2×D512yes—
84C3×#106—102no—
85C3×C4⋊C8—52no—
86C3×#102—102no—
87C3×C4×C8—51no—
88C24×C5—22no—
89C2×C5×D4—24no—
90C2×C5×D4—22no—
91C2×C5×D4—44no—
92C2×C5×D4—44no—
93C2×C5×D4C3×D412yes—
94C2×C5×D4C3×D412yes—
95C22×C4×C5—22no—
96C2×Dic10—21no—
97C5×C4⋊C4C3×D412yes—
98C5×C22⋊C4—22no—
99C5×C22⋊C4—22no—
100C42×C5C23×C311yescharacteristic
101#687—44no—
102C4⋊Dic5—22no—
103C2×#168—21no—
104C2×#168—22no—
105D42C3×D511yescharacteristic
106#492—51no—
107#476—52no—
108#331—51no—
109D4⋊C8—52no—
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×C5C2×SD1612yes—
120C3×C4×C5AGL(1,ℤ/8)12yes—
121C3×Dic5—81no—
122C24×C3—22no—
123C2×C3×Q8—101no—
124C2×C3×D4—24no—
125C2×C3×D4—22no—
126C2×C3×D4—44no—
127C2×C3×D4—44no—
128C2×C3×D4C22⋊D512yes—
129C2×C3×D4C22⋊D512yes—
130C22×C3×C4—22no—
131C3×SD16—204no—
132C2×C3×C8—101no—
133C2×C3×C8—102no—
134C3×C4⋊C4—102no—
135C3×C4⋊C4C22⋊D512yes—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138C3×C42C22×D511yescharacteristic
139C23×C5—22no—
140C23×C5—22no—
141C23×C5—48no—
142C23×C5—82no—
143C5×D4—22no—
144C5×D4—42no—
145C5×D4—48no—
146C5×D4—42no—
147C5×D4—42no—
148C5×D4C3×SD1614yescomplemented
149C2×C4×C5—22no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5C2×C3×D411yescharacteristic
153C2×C4×C5C2×C3×D412yes—
154C2×Dic5—41no—
155Dic10—42no—
156#168—22no—
157#168—42no—
158C22×D4—22no—
159C2×SD16—102no—
160C4⋊Q8—51no—
161#127C2×C3×D511yescharacteristic
162#121—22no—
163#120—22no—
164C4×D4C2×C3×D512yes—
165#106—102no—
166C4⋊C8—52no—
167#102—102no—
168C4×C8—51no—
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—202no—
178C3×D4—22no—
179C3×D4—42no—
180C3×D4—48no—
181C3×D4—42no—
182C3×D4—42no—
183C3×D4#68714yescomplemented
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4—201no—
188C2×C3×C4C2×C22⋊D511yescharacteristic
189C2×C3×C4C2×C22⋊D512yes—
190C3×C8—102no—
191C3×C8—202no—
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×C5C2×C3×SD1612yes—
202C4×C5C3×AGL(1,ℤ/8)12yes—
203Dic5—81no—
204C24—22no—
205C2×Q8—101no—
206C2×D4—24no—
207C2×D4—22no—
208C2×D4—44no—
209C2×D4—44no—
210C2×D4C3×C22⋊D512yes—
211C2×D4C3×C22⋊D512yes—
212C22×C4—22no—
213SD16—204no—
214C2×C8—101no—
215C2×C8—102no—
216C4⋊C4—102no—
217C4⋊C4C3×C22⋊D512yes—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C42C22×C3×D511yescharacteristic
221C3×C5#162911yescharacteristic, complemented, Hall
222C22×C3—24no—
223C22×C3—42no—
224C22×C3—42no—
225C22×C3—44no—
226C22×C3—42no—
227C22×C3—88no—
228C22×C3#409911yescharacteristic
229C3×C4—21no—
230C3×C4—42no—
231C3×C4—401no—
232C3×C4#407812yes—
233C3×C4C2×#68712yes—
234C2×C5—44no—
235C2×C5—82no—
236C2×C5C3×#45012yes—
237C2×C5C3×#45311yescharacteristic
238C23—22no—
239C23—22no—
240C23—48no—
241C23—82no—
242Q8—202no—
243D4—22no—
244D4—42no—
245D4—48no—
246D4—42no—
247D4—42no—
248D4C3×#68714yescomplemented
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—201no—
253C2×C4C2×C3×C22⋊D511yescharacteristic
254C2×C4C2×C3×C22⋊D512yes—
255C8—102no—
256C8—202no—
257C2×C3—44no—
258C2×C3—82no—
259C2×C3#6550712yes—
260C2×C3#6553011yescharacteristic
261C5C3×#162911yescharacteristic, complemented, Sylow
262C22—24no—
263C22—42no—
264C22—42no—
265C22—44no—
266C22—42no—
267C22—88no—
268C22C3×#409911yescharacteristic
269C4—21no—
270C4—42no—
271C4—401no—
272C4C3×#407812yes—
273C4C2×C3×#68712yes—
274C3#1060270011yescharacteristic, direct product factor, Sylow
275C2—44no—
276C2—82no—
277C2C3×#6550712yes—
278C2C3×#6553011yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
Fitting, prime radicalC3×C5×D42C2
socleC22×C3×C5#120
hypercenterC3×D42D5
hypocenterC5C3×#1629
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D42

Complements

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

NH ≅ G/Ntype
2. C3×#65365C2semidirect
3. C3×#65297C2semidirect
4. C3×#64764C2semidirect
5. C3×D4⋊#168C2semidirect
6. #10602700C3direct (N × H)
13. C3×#4015C22semidirect
16. C3×C4⋊#168C22semidirect
17. C3×C4×#168C22semidirect
20. #65365C2×C3semidirect
21. #65297C2×C3semidirect
22. #64764C2×C3semidirect
23. D4⋊#168C2×C3semidirect
52. #4015C22×C3semidirect
55. C4⋊#168C22×C3semidirect
56. C4×#168C22×C3semidirect
67. C3×C5×D4SD16semidirect
148. C5×D4C3×SD16semidirect
183. C3×D4#687semidirect
221. C3×C5#1629semidirect
248. D4C3×#687semidirect
261. C5C3×#1629semidirect
274. C3#10602700direct (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×#653652
C3×#652972
C3×#647642
C3×D4⋊#1682
#106027003
C3×#16295