Finite Group Databasebeta

← C3×#10604916 #14284338

Subgroups — C3×#10604916 #14284338

Order 1920.

496 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C2×C3×#4082C211yesmaximal, characteristic
2C3×#65757C212yesmaximal, complemented
3C3×#64921C214yesmaximal, complemented
4#10604916C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×D4C411yescharacteristic
6C22×C3×Dic10C411yescharacteristic
7C2×C3×C22⋊Dic5—22no—
8C3×#4082—22no—
9C3×#4082C412yes—
10C3×#4082C2212yes—
11C2×C3×C4×Dic5C2211yescharacteristic
12C3×C22⋊#170—22no—
13C3×#4004—22no—
14C3×#4002C2214yescomplemented
15C3×#1533—51nomaximal, Hall
16C2×#4082C2×C311yescharacteristic
17#65757C2×C312yescomplemented
18#64921C2×C314yescomplemented
19C24×C3×C5—21no—
20C2×C3×C5×D4—21no—
21C2×C3×C5×D4—42no—
22C2×C3×C5×D4C2×C412yes—
23C22×C3×C4×C5C2×C411yescharacteristic
24C22×C3×Dic5—21no—
25C22×C3×Dic5D412yes—
26C2×C3×Dic10—21no—
27C2×C3×Dic10—42no—
28C2×C3×Dic10C2×C412yes—
29C2×C3×#170—24no—
30C3×C22⋊Dic5—24no—
31C3×C22⋊Dic5—24no—
32C3×C4×Dic5C2×C411yescharacteristic
33C3×C4×Dic5D412yes—
34C3×C4×Dic5C2311yescharacteristic
35C2×C3×#124—51no—
36C3×#432—52no—
37C3×#329—54no—
38C22×C5×D4C3×C411yescharacteristic
39C22×Dic10C3×C411yescharacteristic
40C2×C22⋊Dic5—22no—
41#4082—22no—
42#4082C3×C412yes—
43#4082C22×C312yes—
44C2×C4×Dic5C22×C311yescharacteristic
45C22⋊#170—22no—
46#4004—22no—
47#4002C22×C314yescomplemented
48#1533—51noSylow
49C23×C3×C5—22no—
50C23×C3×C5—44no—
51C23×C3×C5—42no—
52C23×C3×C5C22⋊C411yescharacteristic
53C3×C5×D4—42no—
54C3×C5×D4—42no—
55C2×C3×C4×C5—22no—
56C2×C3×C4×C5C22⋊C411yescharacteristic
57C2×C3×C4×C5C22×C411yescharacteristic
58C2×C3×Dic5—22no—
59C2×C3×Dic5—42no—
60C2×C3×Dic5—42no—
61C2×C3×Dic5C22⋊C412yes—
62C2×C3×Dic5C2×D412yes—
63C3×Dic10—42no—
64C3×Dic10—42no—
65C3×#170—44no—
66C22×C3×Q8—51no—
67C22×C3×D4AGL(1,𝔽5)11yescharacteristic
68C3×#124—52no—
69C3×#124—52no—
70C3×#124—102no—
71C2×C3×C22⋊C4—102no—
72C2×C3×C42—51no—
73C3×C4⋊C8—102no—
74C3×C22⋊C8—102no—
75C3×#97—54no—
76C24×C5—21no—
77C2×C5×D4—21no—
78C2×C5×D4—42no—
79C2×C5×D4C2×C3×C412yes—
80C22×C4×C5C2×C3×C411yescharacteristic
81C22×Dic5—21no—
82C22×Dic5C3×D412yes—
83C2×Dic10—21no—
84C2×Dic10—42no—
85C2×Dic10C2×C3×C412yes—
86C2×#170—24no—
87C22⋊Dic5—24no—
88C22⋊Dic5—24no—
89C4×Dic5C2×C3×C411yescharacteristic
90C4×Dic5C3×D412yes—
91C4×Dic5C23×C311yescharacteristic
92C2×#124—51no—
93#432—52no—
94#329—54no—
95C22×C3×C5—22no—
96C22×C3×C5—42no—
97C22×C3×C5—44no—
98C22×C3×C5—84no—
99C22×C3×C5#10012yes—
100C22×C3×C5C2×C22⋊C411yescharacteristic
101C3×C4×C5—21no—
102C3×C4×C5—21no—
103C3×Dic5—22no—
104C3×Dic5—22no—
105C3×Dic5—42no—
106C24×C3—21no—
107C2×C3×Q8—52no—
108C2×C3×Q8—101no—
109C2×C3×Q8—202no—
110C2×C3×D4—21no—
111C2×C3×D4—42no—
112C2×C3×D4C2×AGL(1,𝔽5)12yes—
113C22×C3×C4—52no—
114C22×C3×C4—101no—
115C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
116C2×C3×C8—104no—
117C3×C22⋊C4—104no—
118C3×C22⋊C4—104no—
119C3×C42—52no—
120C3×C42—51no—
121C3×C42—51no—
122C23×C5—22no—
123C23×C5—44no—
124C23×C5—42no—
125C23×C5C3×C22⋊C411yescharacteristic
126C5×D4—42no—
127C5×D4—42no—
128C2×C4×C5—22no—
129C2×C4×C5C3×C22⋊C411yescharacteristic
130C2×C4×C5C22×C3×C411yescharacteristic
131C2×Dic5—22no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5C3×C22⋊C412yes—
135C2×Dic5C2×C3×D412yes—
136Dic10—42no—
137Dic10—42no—
138#170—44no—
139C22×Q8—51no—
140C22×D4C3×AGL(1,𝔽5)11yescharacteristic
141#124—52no—
142#124—52no—
143#124—102no—
144C2×C22⋊C4—102no—
145C2×C42—51no—
146C4⋊C8—102no—
147C22⋊C8—102no—
148#97—54no—
149C2×C3×C5—22no—
150C2×C3×C5—82no—
151C2×C3×C5C2×#10011yescharacteristic
152C2×C3×C5#42112yes—
153C23×C3—22no—
154C23×C3—44no—
155C23×C3—42no—
156C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
157C3×Q8—202no—
158C3×Q8—202no—
159C3×D4—42no—
160C3×D4—42no—
161C2×C3×C4—22no—
162C2×C3×C4—52no—
163C2×C3×C4—52no—
164C2×C3×C4—102no—
165C2×C3×C4—202no—
166C2×C3×C4—202no—
167C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
168C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
169C3×C8—204no—
170C22×C5—22no—
171C22×C5—42no—
172C22×C5—44no—
173C22×C5—84no—
174C22×C5C3×#10012yes—
175C22×C5C2×C3×C22⋊C411yescharacteristic
176C4×C5—21no—
177C4×C5—21no—
178Dic5—22no—
179Dic5—22no—
180Dic5—42no—
181C24—21no—
182C2×Q8—52no—
183C2×Q8—101no—
184C2×Q8—202no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4C2×C3×AGL(1,𝔽5)12yes—
188C22×C4—52no—
189C22×C4—101no—
190C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
191C2×C8—104no—
192C22⋊C4—104no—
193C22⋊C4—104no—
194C42—52no—
195C42—51no—
196C42—51no—
197C3×C5#153311yescharacteristic, complemented, Hall
198C22×C3—22no—
199C22×C3—42no—
200C22×C3—44no—
201C22×C3—84no—
202C22×C3#401312yes—
203C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—102no—
207C3×C4—102no—
208C3×C4—202no—
209C2×C5—22no—
210C2×C5—82no—
211C2×C5C2×C3×#10011yescharacteristic
212C2×C5C3×#42112yes—
213C23—22no—
214C23—44no—
215C23—42no—
216C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
217Q8—202no—
218Q8—202no—
219D4—42no—
220D4—42no—
221C2×C4—22no—
222C2×C4—52no—
223C2×C4—52no—
224C2×C4—102no—
225C2×C4—202no—
226C2×C4—202no—
227C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
228C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
229C8—204no—
230C2×C3—22no—
231C2×C3—82no—
232C2×C3#6576912yes—
233C2×C3C2×#401311yescharacteristic
234C5C3×#153311yescharacteristic, complemented, Sylow
235C22—22no—
236C22—44no—
237C22—42no—
238C22—84no—
239C22C3×#401312yes—
240C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
241C4—21no—
242C4—21no—
243C4—102no—
244C4—102no—
245C4—202no—
246C3#1060491611yescharacteristic, direct product factor, Sylow
247C2—22no—
248C2—82no—
249C2C3×#6576912yes—
250C2C2×C3×#401311yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
Fitting, prime radicalC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#1533
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65757C2semidirect
3. C3×#64921C2semidirect
4. #10604916C3direct (N × H)
14. C3×#4002C22semidirect
17. #65757C2×C3semidirect
18. #64921C2×C3semidirect
47. #4002C22×C3semidirect
197. C3×C5#1533semidirect
234. C5C3×#1533semidirect
246. C3#10604916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40822
C3×#657572
C3×#649212
#106049163
C3×#15335