Finite Group Databasebeta

← C3×#10604920 #14313723

Subgroups — C3×#10604920 #14313723

Order 1920.

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

normal subgroups only

This group has 524 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×#66139C211yesmaximal, characteristic
2C3×#65761C212yesmaximal, complemented
3C3×#64923C214yesmaximal, complemented
4#10604920C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×D4C411yescharacteristic
6C2×C3×#709C2211yescharacteristic
7C3×D5⋊M16—22no—
8C3×#4099—22no—
9C3×#4086C412yes—
10C3×#4084—22no—
11C3×#4082C2212yes—
12C3×#4072C411yescharacteristic
13C3×#4013—22no—
14C3×#4005C2214yescomplemented
15C3×#2134—51nomaximal, Hall
16#66139C2×C311yescharacteristic
17#65761C2×C312yescomplemented
18#64923C2×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
24C2×C3×C22⋊D5—24no—
25C2×C3×C22⋊D5D412yes—
26C3×#709—42no—
27C2×C3×D20C2×C411yescharacteristic
28C2×C3×C4×D5D412yes—
29C2×C3×Dic10C2311yescharacteristic
30C3×#704—24no—
31C3×#700—42no—
32C3×D5⋊C8—42no—
33C3×C22⋊Dic5—21no—
34C3×C22⋊Dic5—24no—
35C3×C4⋊Dic5—21no—
36C3×C4×Dic5C2×C412yes—
37C3×#535—51no—
38C3×#413—52no—
39C3×#355—54no—
40C22×C5×D4C3×C411yescharacteristic
41C2×#709C22×C311yescharacteristic
42D5⋊M16—22no—
43#4099—22no—
44#4086C3×C412yes—
45#4084—22no—
46#4082C22×C312yes—
47#4072C3×C411yescharacteristic
48#4013—22no—
49#4005C22×C314yescomplemented
50#2134—51noSylow
51C23×C3×C5—22no—
52C23×C3×C5—42no—
53C23×C3×C5—82no—
54C23×C3×C5C22⋊C411yescharacteristic
55C22×C3×D5C22⋊C412yes—
56C3×C5×D4—42no—
57C3×C5×D4—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22⋊C411yescharacteristic
60C2×C3×C4×C5C22×C411yescharacteristic
61C3×C22⋊D5—42no—
62C3×C22⋊D5—84no—
63C2×C3×Dic5—22no—
64C2×C3×Dic5C2×D412yes—
65C3×D20—41no—
66C3×C4×D5—22no—
67C3×C4×D5—22no—
68C3×Dic10—41no—
69C3×#170—44no—
70C2×C3×#41—51no—
71C22×C3×D4AGL(1,𝔽5)11yescharacteristic
72C2×C3×M16—102no—
73C3×#127—52no—
74C3×#124—52no—
75C3×#121—102no—
76C3×#120—102no—
77C3×#117—51no—
78C3×#101—54no—
79C3×#100—102no—
80C24×C5—21no—
81C2×C5×D4—21no—
82C2×C5×D4—42no—
83C2×C5×D4C2×C3×C412yes—
84C22×C4×C5C2×C3×C411yescharacteristic
85C2×C22⋊D5—24no—
86C2×C22⋊D5C3×D412yes—
87#709—42no—
88C2×D20C2×C3×C411yescharacteristic
89C2×C4×D5C3×D412yes—
90C2×Dic10C23×C311yescharacteristic
91#704—24no—
92#700—42no—
93D5⋊C8—42no—
94C22⋊Dic5—21no—
95C22⋊Dic5—24no—
96C4⋊Dic5—21no—
97C4×Dic5C2×C3×C412yes—
98#535—51no—
99#413—52no—
100#355—54no—
101C22×C3×C5—21no—
102C22×C3×C5—41no—
103C22×C3×C5—44no—
104C22×C3×C5—42no—
105C22×C3×C5—84no—
106C22×C3×C5C2×C22⋊C411yescharacteristic
107C2×C3×D5—22no—
108C2×C3×D5—42no—
109C3×C4×C5—21no—
110C3×C4×C5#9912yes—
111C3×Dic5—22no—
112C3×Dic5—42no—
113C24×C3—21no—
114C3×#41—202no—
115C2×C3×Q8—51no—
116C2×C3×D4—21no—
117C2×C3×D4—42no—
118C2×C3×D4—52no—
119C2×C3×D4—51no—
120C2×C3×D4—104no—
121C2×C3×D4C2×AGL(1,𝔽5)12yes—
122C22×C3×C4—52no—
123C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
124C3×M16—104no—
125C3×M16—202no—
126C2×C3×C8—202no—
127C3×C4⋊C4—101no—
128C3×C22⋊C4—104no—
129C3×C22⋊C4—101no—
130C3×C42—52no—
131C23×C5—22no—
132C23×C5—42no—
133C23×C5—82no—
134C23×C5C3×C22⋊C411yescharacteristic
135C22×D5C3×C22⋊C412yes—
136C5×D4—42no—
137C5×D4—42no—
138C2×C4×C5—22no—
139C2×C4×C5C3×C22⋊C411yescharacteristic
140C2×C4×C5C22×C3×C411yescharacteristic
141C22⋊D5—42no—
142C22⋊D5—84no—
143C2×Dic5—22no—
144C2×Dic5C2×C3×D412yes—
145D20—41no—
146C4×D5—22no—
147C4×D5—22no—
148Dic10—41no—
149#170—44no—
150C2×#41—51no—
151C22×D4C3×AGL(1,𝔽5)11yescharacteristic
152C2×M16—102no—
153#127—52no—
154#124—52no—
155#121—102no—
156#120—102no—
157#117—51no—
158#101—54no—
159#100—102no—
160C2×C3×C5—21no—
161C2×C3×C5—41no—
162C2×C3×C5—82no—
163C2×C3×C5C2×#9911yescharacteristic
164C3×D5—42no—
165C23×C3—22no—
166C23×C3—42no—
167C23×C3—52no—
168C23×C3—82no—
169C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
170C3×Q8—201no—
171C3×D4—42no—
172C3×D4—42no—
173C3×D4—201no—
174C3×D4—202no—
175C3×D4—404no—
176C2×C3×C4—22no—
177C2×C3×C4—52no—
178C2×C3×C4—102no—
179C2×C3×C4—102no—
180C2×C3×C4—102no—
181C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
182C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
183C3×C8—204no—
184C22×C5—21no—
185C22×C5—41no—
186C22×C5—44no—
187C22×C5—42no—
188C22×C5—84no—
189C22×C5C2×C3×C22⋊C411yescharacteristic
190C2×D5—22no—
191C2×D5—42no—
192C4×C5—21no—
193C4×C5C3×#9912yes—
194Dic5—22no—
195Dic5—42no—
196C24—21no—
197#41—202no—
198C2×Q8—51no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—52no—
202C2×D4—51no—
203C2×D4—104no—
204C2×D4C2×C3×AGL(1,𝔽5)12yes—
205C22×C4—52no—
206C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
207M16—104no—
208M16—202no—
209C2×C8—202no—
210C4⋊C4—101no—
211C22⋊C4—104no—
212C22⋊C4—101no—
213C42—52no—
214C3×C5#213411yescharacteristic, complemented, Hall
215C22×C3—21no—
216C22×C3—41no—
217C22×C3—44no—
218C22×C3—42no—
219C22×C3—84no—
220C22×C3—102no—
221C22×C3—202no—
222C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
223C3×C4—21no—
224C3×C4—102no—
225C3×C4—202no—
226C3×C4#401112yes—
227C2×C5—21no—
228C2×C5—41no—
229C2×C5—82no—
230C2×C5C2×C3×#9911yescharacteristic
231D5—42no—
232C23—22no—
233C23—42no—
234C23—52no—
235C23—82no—
236C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
237Q8—201no—
238D4—42no—
239D4—42no—
240D4—201no—
241D4—202no—
242D4—404no—
243C2×C4—22no—
244C2×C4—52no—
245C2×C4—102no—
246C2×C4—102no—
247C2×C4—102no—
248C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
249C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
250C8—204no—
251C2×C3—21no—
252C2×C3—41no—
253C2×C3—82no—
254C2×C3—202no—
255C2×C3C2×#401111yescharacteristic
256C5C3×#213411yescharacteristic, complemented, Sylow
257C22—21no—
258C22—41no—
259C22—44no—
260C22—42no—
261C22—84no—
262C22—102no—
263C22—202no—
264C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
265C4—21no—
266C4—102no—
267C4—202no—
268C4C3×#401112yes—
269C3#1060492011yescharacteristic, direct product factor, Sylow
270C2—21no—
271C2—41no—
272C2—82no—
273C2—202no—
274C2C2×C3×#401111yescharacteristic
subgroupG/H
centerC2×C3C2×#4011
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC2×C3×C5C2×#99
prime radicalC3×#66139C2
cosocleC2×Dic10C23×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#2134
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65761C2semidirect
3. C3×#64923C2semidirect
4. #10604920C3direct (N × H)
14. C3×#4005C22semidirect
17. #65761C2×C3semidirect
18. #64923C2×C3semidirect
49. #4005C22×C3semidirect
214. C3×C5#2134semidirect
256. C5C3×#2134semidirect
269. C3#10604920direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661392
C3×#657612
C3×#649232
#106049203
C3×#21345