Finite Group Databasebeta

← C3×#10599184 #14289347

Subgroups — C3×#10599184 #14289347

Order 1920.

628 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 114 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×#66051C211yesmaximal, characteristic
2C3×#65365C211yesmaximal, characteristic, complemented
3C3×#65131C212yesmaximal, complemented
4C3×C5×#331C211yesmaximal, characteristic, complemented
5C3×#64703C212yesmaximal, complemented
6#10599184C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×D4×D5—22no—
8C3×C5×#127C2211yescharacteristic
9C3×#4084—22no—
10C3×#4083—22no—
11C2×C3×#687—22no—
12C3×C4×D20C2212yes—
13C3×#4015C2211yescharacteristic, complemented
14C3×C5×C4⋊C8C2212yescomplemented
15C3×#3953—22no—
16C3×#3949—22no—
17C3×C4×#168C2211yescharacteristic, complemented
18C3×#1629—51nomaximal, Hall
19#66051C2×C311yescharacteristic
20#65365C2×C311yescharacteristic, complemented
21#65131C2×C312yescomplemented
22C5×#331C2×C311yescharacteristic, complemented
23#64703C2×C312yescomplemented
24C23×C3×D5—22no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C2×C3×C22⋊D5—24no—
28C3×D4×D5—44no—
29C3×D4×D5—44no—
30C2×C3×D20D412yes—
31C2×C3×C4×D5—22no—
32C2×C3×Dic10—21no—
33C2×C3×C5×C8—22no—
34C3×C42×C5C2311yescharacteristic
35C3×C22⋊Dic5—22no—
36C3×#687—44no—
37C3×#685—22no—
38C3×C4⋊Dic5—22no—
39C3×C4⋊Dic5D412yes—
40C2×C3×#168—21no—
41C3×D42—51no—
42C3×#492—51no—
43C3×#476—52no—
44C3×#331D511yescharacteristic, complemented
45C3×D4⋊C8—52no—
46C2×D4×D5—22no—
47C5×#127C22×C311yescharacteristic
48#4084—22no—
49#4083—22no—
50C2×#687—22no—
51C4×D20C22×C312yes—
52#4015C22×C311yescharacteristic, complemented
53C5×C4⋊C8C22×C312yescomplemented
54#3953—22no—
55#3949—22no—
56C4×#168C22×C311yescharacteristic, complemented
57#1629—51noSylow
58C23×C3×C5—22no—
59C22×C3×D5—22no—
60C22×C3×D5—48no—
61C22×C3×D5—82no—
62C3×C5×D4—42no—
63C3×C5×D4—42no—
64C3×C5×D4—42no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C3×C22⋊D5—48no—
68C2×C3×Dic5—22no—
69C2×C3×Dic5—41no—
70C3×D20—22no—
71C3×D20SD1614yescomplemented
72C3×C4×D5—42no—
73C3×C4×D5—42no—
74C3×Dic10—42no—
75C3×C5×C8—42no—
76C3×#168—22no—
77C22×C3×D4—102no—
78C2×C3×SD16—102no—
79C3×C4⋊Q8—51no—
80C3×#127C2×D511yescharacteristic
81C3×#121—102no—
82C3×#120—102no—
83C3×C4×D4—52no—
84C3×#106—102no—
85C3×C4⋊C8C2×D512yescomplemented
86C3×#102—102no—
87C3×C4×C8—51no—
88C23×D5—22no—
89C2×C5×D4—22no—
90C2×C5×D4C3×D412yes—
91C2×C22⋊D5—24no—
92D4×D5—44no—
93D4×D5—44no—
94C2×D20C3×D412yes—
95C2×C4×D5—22no—
96C2×Dic10—21no—
97C2×C5×C8—22no—
98C42×C5C23×C311yescharacteristic
99C22⋊Dic5—22no—
100#687—44no—
101#685—22no—
102C4⋊Dic5—22no—
103C4⋊Dic5C3×D412yes—
104C2×#168—21no—
105D42—51no—
106#492—51no—
107#476—52no—
108#331C3×D511yescharacteristic, complemented
109D4⋊C8—52no—
110C22×C3×C5—44no—
111C22×C3×C5—42no—
112C22×C3×C5#12011yescharacteristic
113C2×C3×D5—24no—
114C2×C3×D5—42no—
115C2×C3×D5—42no—
116C2×C3×D5—88no—
117C3×C4×C5—21no—
118C3×C4×C5C2×SD1612yes—
119C3×C4×C5AGL(1,ℤ/8)12yes—
120C3×Dic5—42no—
121C3×Dic5—81no—
122C24×C3—102no—
123C2×C3×Q8—101no—
124C2×C3×D4—22no—
125C2×C3×D4—52no—
126C2×C3×D4—104no—
127C2×C3×D4—204no—
128C2×C3×D4—204no—
129C2×C3×D4D2012yes—
130C22×C3×C4—102no—
131C3×SD16—204no—
132C2×C3×C8—22no—
133C2×C3×C8—101no—
134C3×C4⋊C4—52no—
135C3×C4⋊C4—102no—
136C3×C22⋊C4—102no—
137C3×C22⋊C4—102no—
138C3×C42C22×D511yescharacteristic
139C23×C5—22no—
140C22×D5—22no—
141C22×D5—48no—
142C22×D5—82no—
143C5×D4—42no—
144C5×D4—42no—
145C5×D4—42no—
146C2×C4×C5C2×C3×D411yescharacteristic
147C2×C4×C5C2×C3×D412yes—
148C22⋊D5—48no—
149C2×Dic5—22no—
150C2×Dic5—41no—
151D20—22no—
152D20C3×SD1614yescomplemented
153C4×D5—42no—
154C4×D5—42no—
155Dic10—42no—
156C5×C8—42no—
157#168—22no—
158C22×D4—102no—
159C2×SD16—102no—
160C4⋊Q8—51no—
161#127C2×C3×D511yescharacteristic
162#121—102no—
163#120—102no—
164C4×D4—52no—
165#106—102no—
166C4⋊C8C2×C3×D512yescomplemented
167#102—102no—
168C4×C8—51no—
169C2×C3×C5—82no—
170C2×C3×C5#45012yes—
171C2×C3×C5#45311yescharacteristic
172C3×D5—44no—
173C23×C3—22no—
174C23×C3—102no—
175C23×C3—208no—
176C23×C3—402no—
177C3×Q8—202no—
178C3×D4—42no—
179C3×D4—42no—
180C3×D4—42no—
181C3×D4—54no—
182C3×D4—102no—
183C3×D4—208no—
184C2×C3×C4—102no—
185C2×C3×C4—202no—
186C2×C3×C4—202no—
187C2×C3×C4—201no—
188C2×C3×C4C2×D2011yescharacteristic
189C2×C3×C4D4×D512yes—
190C3×C8—42no—
191C3×C8—102no—
192C22×C5—44no—
193C22×C5—42no—
194C22×C5C3×#12011yescharacteristic
195C2×D5—24no—
196C2×D5—42no—
197C2×D5—42no—
198C2×D5—88no—
199C4×C5—21no—
200C4×C5C2×C3×SD1612yes—
201C4×C5C3×AGL(1,ℤ/8)12yes—
202Dic5—42no—
203Dic5—81no—
204C24—102no—
205C2×Q8—101no—
206C2×D4—22no—
207C2×D4—52no—
208C2×D4—104no—
209C2×D4—204no—
210C2×D4—204no—
211C2×D4C3×D2012yes—
212C22×C4—102no—
213SD16—204no—
214C2×C8—22no—
215C2×C8—101no—
216C4⋊C4—52no—
217C4⋊C4—102no—
218C22⋊C4—102no—
219C22⋊C4—102no—
220C42C22×C3×D511yescharacteristic
221C3×C5#162911yescharacteristic, complemented, Hall
222C22×C3—42no—
223C22×C3—44no—
224C22×C3—104no—
225C22×C3—202no—
226C22×C3—202no—
227C22×C3—408no—
228C22×C3#402811yescharacteristic
229C3×C4—21no—
230C3×C4—202no—
231C3×C4—401no—
232C3×C4#405712yes—
233C3×C4D5×SD1612yes—
234C2×C5—82no—
235C2×C5C3×#45012yes—
236C2×C5C3×#45311yescharacteristic
237D5—44no—
238C23—22no—
239C23—102no—
240C23—208no—
241C23—402no—
242Q8—202no—
243D4—42no—
244D4—42no—
245D4—42no—
246D4—54no—
247D4—102no—
248D4—208no—
249C2×C4—102no—
250C2×C4—202no—
251C2×C4—202no—
252C2×C4—201no—
253C2×C4C2×C3×D2011yescharacteristic
254C2×C4C3×D4×D512yes—
255C8—42no—
256C8—102no—
257C2×C3—82no—
258C2×C3—204no—
259C2×C3#6503611yescharacteristic
260C2×C3#6506512yes—
261C5C3×#162911yescharacteristic, complemented, Sylow
262C22—42no—
263C22—44no—
264C22—104no—
265C22—202no—
266C22—202no—
267C22—408no—
268C22C3×#402811yescharacteristic
269C4—21no—
270C4—202no—
271C4—401no—
272C4C3×#405712yes—
273C4C3×D5×SD1612yes—
274C3#1059918411yescharacteristic, direct product factor, Sylow
275C2—82no—
276C2—204no—
277C2C3×#6503611yescharacteristic
278C2C3×#6506512yes—
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#331C2
socleC22×C3×C5#120
prime radicalC3×#66051C2
hypercenterC3×#331D5
hypocenterC5C3×#1629
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
2. C3×#65365C2semidirect
3. C3×#65131C2semidirect
4. C3×C5×#331C2semidirect
5. C3×#64703C2semidirect
6. #10599184C3direct (N × H)
13. C3×#4015C22semidirect
14. C3×C5×C4⋊C8C22semidirect
17. C3×C4×#168C22semidirect
20. #65365C2×C3semidirect
21. #65131C2×C3semidirect
22. C5×#331C2×C3semidirect
23. #64703C2×C3semidirect
44. C3×#331D5semidirect
52. #4015C22×C3semidirect
53. C5×C4⋊C8C22×C3semidirect
56. C4×#168C22×C3semidirect
71. C3×D20SD16semidirect
85. C3×C4⋊C8C2×D5semidirect
108. #331C3×D5semidirect
152. D20C3×SD16semidirect
166. C4⋊C8C2×C3×D5semidirect
221. C3×C5#1629semidirect
261. C5C3×#1629semidirect
274. C3#10599184direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660512
C3×#653652
C3×#651312
C3×C5×#3312
C3×#647032
#105991843
C3×#16295