Finite Group Databasebeta

← C3×#10604993 #14283982

Subgroups — C3×#10604993 #14283982

Order 1920.

540 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 124 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×#66166C211yesmaximal, characteristic
2C3×C4×#704C212yesmaximal, complemented
3C3×#64927C212yesmaximal, complemented
4C3×#64921C212yesmaximal, complemented
5#10604993C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C5×#41C411yescharacteristic
7C2×C3×#709C411yescharacteristic
8C2×C3×#704—22no—
9C3×#4093C2211yescharacteristic
10C3×#4090C411yescharacteristic
11C3×#4086C411yescharacteristic
12C3×#4085—22no—
13C3×#4082C2211yescharacteristic
14C3×C4×C22⋊D5—22no—
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4002C2214yes—
17C3×C4×#170—22no—
18C3×#1525—51nomaximal, Hall
19#66166C2×C311yescharacteristic
20C4×#704C2×C312yescomplemented
21#64927C2×C312yescomplemented
22#64921C2×C312yescomplemented
23C3×C5×#41—42no—
24C2×C3×C5×Q8C2×C411yescharacteristic
25C2×C3×C5×D4—21no—
26C2×C3×C5×D4C2×C411yescharacteristic
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C2×C3×C22⋊D5—21no—
30C2×C3×C22⋊D5—22no—
31C22×C3×Dic5D412yes—
32C3×#709—42no—
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×Dic10C2×C411yescharacteristic
36C3×#704—28no—
37C2×C3×#170—24no—
38C3×C22⋊Dic5—22no—
39C3×#685—22no—
40C3×#683—22no—
41C3×C4×Dic5C2×C411yescharacteristic
42C3×C4×Dic5D412yes—
43C3×C4×Dic5C2311yescharacteristic
44C3×#532—51no—
45C3×C4×M16—52no—
46C3×#329—52no—
47C3×#329—52no—
48C2×C5×#41C3×C411yescharacteristic
49C2×#709C3×C411yescharacteristic
50C2×#704—22no—
51#4093C22×C311yescharacteristic
52#4090C3×C411yescharacteristic
53#4086C3×C411yescharacteristic
54#4085—22no—
55#4082C22×C311yescharacteristic
56C4×C22⋊D5—22no—
57C2×C4×Dic5C22×C311yescharacteristic
58#4002C22×C314yes—
59C4×#170—22no—
60#1525—51noSylow
61C23×C3×C5—21no—
62C23×C3×C5C22⋊C411yescharacteristic
63C22×C3×D5—21no—
64C3×C5×Q8—41no—
65C3×C5×D4—41no—
66C3×C5×D4—42no—
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C3×C22⋊D5—42no—
73C3×C22⋊D5—44no—
74C2×C3×Dic5—24no—
75C2×C3×Dic5—21no—
76C2×C3×Dic5C22⋊C412yes—
77C2×C3×Dic5C2×D412yes—
78C3×D20—41no—
79C3×C4×D5—42no—
80C3×Dic10—41no—
81C3×#170—28no—
82C2×C3×#41—51no—
83C2×C3×#41AGL(1,𝔽5)11yescharacteristic
84C2×C3×M16—102no—
85C3×C4⋊Q8—51no—
86C3×#127—51no—
87C3×#124—51no—
88C3×#124—51no—
89C3×#121—102no—
90C3×C4×D4—102no—
91C2×C3×C42—51no—
92C3×#97—54no—
93C3×C4×C8—102no—
94C5×#41—42no—
95C2×C5×Q8C2×C3×C411yescharacteristic
96C2×C5×D4—21no—
97C2×C5×D4C2×C3×C411yescharacteristic
98C22×C4×C5—21no—
99C22×C4×C5C2×C3×C411yescharacteristic
100C2×C22⋊D5—21no—
101C2×C22⋊D5—22no—
102C22×Dic5C3×D412yes—
103#709—42no—
104C2×D20C2×C3×C411yescharacteristic
105C2×C4×D5—21no—
106C2×Dic10C2×C3×C411yescharacteristic
107#704—28no—
108C2×#170—24no—
109C22⋊Dic5—22no—
110#685—22no—
111#683—22no—
112C4×Dic5C2×C3×C411yescharacteristic
113C4×Dic5C3×D412yes—
114C4×Dic5C23×C311yescharacteristic
115#532—51no—
116C4×M16—52no—
117#329—52no—
118#329—52no—
119C22×C3×C5—21no—
120C22×C3×C5—22no—
121C22×C3×C5—41no—
122C22×C3×C5—42no—
123C22×C3×C5C2×C22⋊C411yescharacteristic
124C2×C3×D5—41no—
125C2×C3×D5—42no—
126C3×C4×C5—21no—
127C3×C4×C5—41no—
128C3×C4×C5#10012yes—
129C3×Dic5—22no—
130C3×Dic5—41no—
131C3×Dic5#10414yes—
132C3×#41—42no—
133C3×#41—202no—
134C2×C3×Q8—51no—
135C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
136C2×C3×D4—21no—
137C2×C3×D4—51no—
138C2×C3×D4—102no—
139C2×C3×D4—101no—
140C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
141C22×C3×C4—21no—
142C22×C3×C4—52no—
143C22×C3×C4—101no—
144C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
145C3×M16—108no—
146C2×C3×C8—104no—
147C3×C4⋊C4—102no—
148C3×C22⋊C4—102no—
149C3×C22⋊C4—102no—
150C3×C42—52no—
151C3×C42—51no—
152C3×C42—51no—
153C23×C5—21no—
154C23×C5C3×C22⋊C411yescharacteristic
155C22×D5—21no—
156C5×Q8—41no—
157C5×D4—41no—
158C5×D4—42no—
159C2×C4×C5—22no—
160C2×C4×C5—21no—
161C2×C4×C5—42no—
162C2×C4×C5C3×C22⋊C411yescharacteristic
163C2×C4×C5C22×C3×C411yescharacteristic
164C22⋊D5—42no—
165C22⋊D5—44no—
166C2×Dic5—24no—
167C2×Dic5—21no—
168C2×Dic5C3×C22⋊C412yes—
169C2×Dic5C2×C3×D412yes—
170D20—41no—
171C4×D5—42no—
172Dic10—41no—
173#170—28no—
174C2×#41—51no—
175C2×#41C3×AGL(1,𝔽5)11yescharacteristic
176C2×M16—102no—
177C4⋊Q8—51no—
178#127—51no—
179#124—51no—
180#124—51no—
181#121—102no—
182C4×D4—102no—
183C2×C42—51no—
184#97—54no—
185C4×C8—102no—
186C2×C3×C5—41no—
187C2×C3×C5—81no—
188C2×C3×C5C2×#10011yescharacteristic
189C2×C3×C5C2×#10412yes—
190C3×D5—81no—
191C23×C3—21no—
192C23×C3—101no—
193C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
194C3×Q8—41no—
195C3×Q8—201no—
196C3×D4—41no—
197C3×D4—42no—
198C3×D4—201no—
199C3×D4—204no—
200C3×D4—202no—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—42no—
204C2×C3×C4—52no—
205C2×C3×C4—52no—
206C2×C3×C4—104no—
207C2×C3×C4—101no—
208C2×C3×C4—202no—
209C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
210C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
211C3×C8—108no—
212C22×C5—21no—
213C22×C5—22no—
214C22×C5—41no—
215C22×C5—42no—
216C22×C5C2×C3×C22⋊C411yescharacteristic
217C2×D5—41no—
218C2×D5—42no—
219C4×C5—21no—
220C4×C5—41no—
221C4×C5C3×#10012yes—
222Dic5—22no—
223Dic5—41no—
224Dic5C3×#10414yes—
225#41—42no—
226#41—202no—
227C2×Q8—51no—
228C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
229C2×D4—21no—
230C2×D4—51no—
231C2×D4—102no—
232C2×D4—101no—
233C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
234C22×C4—21no—
235C22×C4—52no—
236C22×C4—101no—
237C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
238M16—108no—
239C2×C8—104no—
240C4⋊C4—102no—
241C22⋊C4—102no—
242C22⋊C4—102no—
243C42—52no—
244C42—51no—
245C42—51no—
246C3×C5#152511yescharacteristic, complemented, Hall
247C22×C3—22no—
248C22×C3—21no—
249C22×C3—42no—
250C22×C3—41no—
251C22×C3—202no—
252C22×C3—201no—
253C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
254C3×C4—21no—
255C3×C4—41no—
256C3×C4—54no—
257C3×C4—102no—
258C3×C4—201no—
259C3×C4#401312yes—
260C2×C5—41no—
261C2×C5—81no—
262C2×C5C2×C3×#10011yescharacteristic
263C2×C5C2×C3×#10412yes—
264D5—81no—
265C23—21no—
266C23—101no—
267C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
268Q8—41no—
269Q8—201no—
270D4—41no—
271D4—42no—
272D4—201no—
273D4—204no—
274D4—202no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—52no—
279C2×C4—52no—
280C2×C4—104no—
281C2×C4—101no—
282C2×C4—202no—
283C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
284C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
285C8—108no—
286C2×C3—41no—
287C2×C3—81no—
288C2×C3—401no—
289C2×C3D5⋊#10412yes—
290C2×C3C2×#401311yescharacteristic
291C5C3×#152511yescharacteristic, complemented, Sylow
292C22—22no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—202no—
297C22—201no—
298C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
299C4—21no—
300C4—41no—
301C4—54no—
302C4—102no—
303C4—201no—
304C4C3×#401312yes—
305C3#1060499311yescharacteristic, direct product factor, Sylow
306C2—41no—
307C2—81no—
308C2—401no—
309C2C3×D5⋊#10412yes—
310C2C2×C3×#401311yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×#41C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66166C2
cosocleC4×Dic5C23×C3
hypercenterC2×C3×#41AGL(1,𝔽5)
hypocenterC5C3×#1525
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#41

Complements

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

NH ≅ G/Ntype
2. C3×C4×#704C2semidirect
3. C3×#64927C2semidirect
4. C3×#64921C2semidirect
5. #10604993C3direct (N × H)
20. C4×#704C2×C3semidirect
21. #64927C2×C3semidirect
22. #64921C2×C3semidirect
246. C3×C5#1525semidirect
291. C5C3×#1525semidirect
305. C3#10604993direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661662
C3×C4×#7042
C3×#649272
C3×#649212
#106049933
C3×#15255