Finite Group Databasebeta

← C3×#10604963 #14313536

Subgroups — C3×#10604963 #14313536

Order 1920.

476 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 108 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×#66150C211yesmaximal, characteristic
2C3×#65745C212yesmaximal
3C3×#64928C214yesmaximal, complemented
4#10604963C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×Q8C411yescharacteristic, complemented
6C2×C3×#709C2211yescharacteristic
7C3×#4130—22no—
8C3×#4093C2212yes—
9C3×#4092—22no—
10C3×#4090C412yescomplemented
11C3×#4075—22no—
12C3×#4072C411yescharacteristic, complemented
13C3×#4011—22no—
14C3×#3999C2214yes—
15C3×#2129—51nomaximal, Hall
16#66150C2×C311yescharacteristic
17#65745C2×C312yes—
18#64928C2×C314yescomplemented
19C2×C3×C5×Q8—21no—
20C2×C3×C5×Q8—42no—
21C2×C3×C5×Q8C2×C412yes—
22C22×C3×C4×C5—21no—
23C22×C3×C4×C5C2×C411yescharacteristic
24C2×C3×C22⋊D5D412yes—
25C3×#709—42no—
26C2×C3×D20C2311yescharacteristic
27C2×C3×C4×D5D412yes—
28C2×C3×Dic10C2×C411yescharacteristic
29C3×C22⋊AGL(1,𝔽5)—24no—
30C3×C4⋊AGL(1,𝔽5)—42no—
31C3×C4×AGL(1,𝔽5)—42no—
32C3×C22⋊Dic5—21no—
33C3×#685—24no—
34C3×C4⋊Dic5—21no—
35C3×#683—24no—
36C3×C4×Dic5C2×C412yes—
37C3×#536—51no—
38C3×#410—52no—
39C3×#354—54no—
40C22×C5×Q8C3×C411yescharacteristic, complemented
41C2×#709C22×C311yescharacteristic
42#4130—22no—
43#4093C22×C312yes—
44#4092—22no—
45#4090C3×C412yescomplemented
46#4075—22no—
47#4072C3×C411yescharacteristic, complemented
48#4011—22no—
49#3999C22×C314yes—
50#2129—51noSylow
51C23×C3×C5C22⋊C411yescharacteristic
52C22×C3×D5C2×D412yes—
53C2×C3×AGL(1,𝔽5)—44no—
54C3×C5×Q8—42no—
55C3×C5×Q8—42no—
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5—42no—
59C2×C3×C4×C5C22⋊C411yescharacteristic
60C2×C3×C4×C5C22×C411yescharacteristic
61C3×C22⋊D5—42no—
62C2×C3×Dic5—22no—
63C2×C3×Dic5C22⋊C412yes—
64C3×D20—41no—
65C3×C4×D5—22no—
66C3×C4×D5—22no—
67C3×Dic10—41no—
68C2×C3×#41—51no—
69C22×C3×Q8AGL(1,𝔽5)11yescharacteristic, complemented
70C3×C4⋊Q8—52no—
71C3×#124—52no—
72C3×#123—102no—
73C3×C22⋊Q8—102no—
74C3×#117—51no—
75C3×#117—102no—
76C3×#99—54no—
77C3×#99—102no—
78C2×C5×Q8—21no—
79C2×C5×Q8—42no—
80C2×C5×Q8C2×C3×C412yes—
81C22×C4×C5—21no—
82C22×C4×C5C2×C3×C411yescharacteristic
83C2×C22⋊D5C3×D412yes—
84#709—42no—
85C2×D20C23×C311yescharacteristic
86C2×C4×D5C3×D412yes—
87C2×Dic10C2×C3×C411yescharacteristic
88C22⋊AGL(1,𝔽5)—24no—
89C4⋊AGL(1,𝔽5)—42no—
90C4×AGL(1,𝔽5)—42no—
91C22⋊Dic5—21no—
92#685—24no—
93C4⋊Dic5—21no—
94#683—24no—
95C4×Dic5C2×C3×C412yes—
96#536—51no—
97#410—52no—
98#354—54no—
99C22×C3×C5—21no—
100C22×C3×C5—41no—
101C22×C3×C5C2×C22⋊C411yescharacteristic
102C2×C3×D5—22no—
103C2×C3×D5—42no—
104C3×AGL(1,𝔽5)—84no—
105C3×C4×C5—21no—
106C3×C4×C5—42no—
107C3×C4×C5#9912yes—
108C3×Dic5—22no—
109C3×Dic5—42no—
110C3×#41—202no—
111C2×C3×Q8—21no—
112C2×C3×Q8—42no—
113C2×C3×Q8—51no—
114C2×C3×Q8C2×AGL(1,𝔽5)12yes—
115C2×C3×D4—52no—
116C2×C3×D4—51no—
117C22×C3×C4—21no—
118C22×C3×C4—52no—
119C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
120C3×C4⋊C4—104no—
121C3×C4⋊C4—101no—
122C3×C4⋊C4—202no—
123C3×C22⋊C4—104no—
124C3×C22⋊C4—101no—
125C3×C22⋊C4—104no—
126C3×C42—52no—
127C3×C42—202no—
128C23×C5C3×C22⋊C411yescharacteristic
129C22×D5C2×C3×D412yes—
130C2×AGL(1,𝔽5)—44no—
131C5×Q8—42no—
132C5×Q8—42no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—42no—
136C2×C4×C5C3×C22⋊C411yescharacteristic
137C2×C4×C5C22×C3×C411yescharacteristic
138C22⋊D5—42no—
139C2×Dic5—22no—
140C2×Dic5C3×C22⋊C412yes—
141D20—41no—
142C4×D5—22no—
143C4×D5—22no—
144Dic10—41no—
145C2×#41—51no—
146C22×Q8C3×AGL(1,𝔽5)11yescharacteristic, complemented
147C4⋊Q8—52no—
148#124—52no—
149#123—102no—
150C22⋊Q8—102no—
151#117—51no—
152#117—102no—
153#99—54no—
154#99—102no—
155C2×C3×C5—21no—
156C2×C3×C5—41no—
157C2×C3×C5C2×#9911yescharacteristic
158C3×D5—42no—
159C23×C3—52no—
160C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
161C3×Q8—42no—
162C3×Q8—42no—
163C3×Q8—201no—
164C3×D4—201no—
165C3×D4—202no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—42no—
169C2×C3×C4—52no—
170C2×C3×C4—102no—
171C2×C3×C4—102no—
172C2×C3×C4—102no—
173C2×C3×C4—204no—
174C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
175C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
176C22×C5—21no—
177C22×C5—41no—
178C22×C5C2×C3×C22⋊C411yescharacteristic
179C2×D5—22no—
180C2×D5—42no—
181AGL(1,𝔽5)—84no—
182C4×C5—21no—
183C4×C5—42no—
184C4×C5C3×#9912yes—
185Dic5—22no—
186Dic5—42no—
187#41—202no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—51no—
191C2×Q8C2×C3×AGL(1,𝔽5)12yes—
192C2×D4—52no—
193C2×D4—51no—
194C22×C4—21no—
195C22×C4—52no—
196C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
197C4⋊C4—104no—
198C4⋊C4—101no—
199C4⋊C4—202no—
200C22⋊C4—104no—
201C22⋊C4—101no—
202C22⋊C4—104no—
203C42—52no—
204C42—202no—
205C3×C5#212911yescharacteristic, complemented, Hall
206C22×C3—21no—
207C22×C3—41no—
208C22×C3—102no—
209C22×C3—202no—
210C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
211C3×C4—21no—
212C3×C4—42no—
213C3×C4—102no—
214C3×C4—202no—
215C3×C4—404no—
216C3×C4#401112yes—
217C2×C5—21no—
218C2×C5—41no—
219C2×C5C2×C3×#9911yescharacteristic
220D5—42no—
221C23—52no—
222C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
223Q8—42no—
224Q8—42no—
225Q8—201no—
226D4—201no—
227D4—202no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—42no—
231C2×C4—52no—
232C2×C4—102no—
233C2×C4—102no—
234C2×C4—102no—
235C2×C4—204no—
236C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
237C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
238C2×C3—21no—
239C2×C3—41no—
240C2×C3—202no—
241C2×C3C2×#401111yescharacteristic
242C5C3×#212911yescharacteristic, complemented, Sylow
243C22—21no—
244C22—41no—
245C22—102no—
246C22—202no—
247C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
248C4—21no—
249C4—42no—
250C4—102no—
251C4—202no—
252C4—404no—
253C4C3×#401112yes—
254C3#1060496311yescharacteristic, direct product factor, Sylow
255C2—21no—
256C2—41no—
257C2—202no—
258C2C2×C3×#401111yescharacteristic
subgroupG/H
centerC2×C3C2×#4011
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×Q8C4
socleC2×C3×C5C2×#99
prime radicalC2×C3×#709C22
cosocleC2×D20C23×C3
hypercenterC22×C3×Q8AGL(1,𝔽5)
hypocenterC5C3×#2129
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C22×C3×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#64928C2semidirect
4. #10604963C3direct (N × H)
5. C22×C3×C5×Q8C4semidirect
10. C3×#4090C4semidirect
12. C3×#4072C4semidirect
18. #64928C2×C3semidirect
40. C22×C5×Q8C3×C4semidirect
45. #4090C3×C4semidirect
47. #4072C3×C4semidirect
69. C22×C3×Q8AGL(1,𝔽5)semidirect
146. C22×Q8C3×AGL(1,𝔽5)semidirect
205. C3×C5#2129semidirect
242. C5C3×#2129semidirect
254. C3#10604963direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661502
C3×#657452
C3×#649282
#106049633
C3×#21295