Finite Group Databasebeta

← C3×#10601833 #14292631

Subgroups — C3×#10601833 #14292631

Order 1920.

320 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#461C211yesmaximal, characteristic
2C3×#65368C211yesmaximal, characteristic, complemented
3C3×#65301C211yesmaximal, characteristic
4C3×#65297C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7C3×#64699C211yesmaximal, characteristic, complemented
8#10601833C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C2×C3×#681—21no—
13C3×#4015C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×#103—21no—
16C3×#3964—21no—
17C3×C22⋊#168—21no—
18C3×#3940—21no—
19C3×#3940—21no—
20C3×#3940—21no—
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1691—51nomaximal, Hall
25C5×#461C2×C311yescharacteristic
26#65368C2×C311yescharacteristic, complemented
27#65301C2×C311yescharacteristic
28#65297C2×C311yescharacteristic
29#64767C2×C311yescharacteristic, complemented
30#64701C2×C311yescharacteristic, complemented
31#64699C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4D411yescharacteristic
34C22×C3×C4×C5—21no—
35C2×C3×Dic10—21no—
36C3×C5×SD16—42no—
37C2×C3×C5×C8—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×#681—42no—
46C2×C3×#168—21no—
47C2×C3×#168—21no—
48C2×C3×#168D411yescharacteristic
49C2×C3×#168D411yescharacteristic
50C3×#498—51no—
51C3×#476—51no—
52C3×#461D511yescharacteristic
53C3×#436—51no—
54C3×#335—51no—
55C3×#333—51no—
56C3×#332—51no—
57C2×C5×SD16—21no—
58C5×C4⋊Q8C22×C311yescharacteristic
59C4×C5×D4C22×C311yescharacteristic
60C2×#681—21no—
61#4015C22×C311yescharacteristic
62C5×C4⋊C8C22×C311yescharacteristic
63C5×#103—21no—
64#3964—21no—
65C22⋊#168—21no—
66#3940—21no—
67#3940—21no—
68#3940—21no—
69C4⋊#168C22×C311yescharacteristic
70C4⋊#168C22×C311yescharacteristic
71C4×#168C22×C311yescharacteristic
72#1691—51noSylow
73C23×C3×C5—21no—
74C3×C5×Q8—41no—
75C3×C5×Q8—41no—
76C3×C5×D4—21no—
77C3×C5×D4—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C3×Dic5—41no—
86C3×Dic10—81no—
87C3×C5×C8—41no—
88C3×#168—21no—
89C3×#168—41no—
90C3×#168—41no—
91C3×#168SD1612yescomplemented
92C2×C3×SD16—21no—
93C2×C3×M16—101no—
94C3×C4⋊Q8—51no—
95C3×C4⋊Q8C2×D511yescharacteristic
96C3×C4×D4C2×D511yescharacteristic
97C3×#106—101no—
98C3×#106—101no—
99C3×#106—101no—
100C3×C4⋊C8—51no—
101C3×C4⋊C8—51no—
102C3×C4⋊C8C2×D511yescharacteristic
103C3×#103—21no—
104C3×#102—101no—
105C3×C22⋊C8—101no—
106C3×C4×C8—51no—
107C2×C5×Q8—21no—
108C2×C5×D4C3×D411yescharacteristic
109C22×C4×C5—21no—
110C2×Dic10—21no—
111C5×SD16—42no—
112C2×C5×C8—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4C3×D411yescharacteristic
116C5×C22⋊C4—21no—
117C42×C5C23×C311yescharacteristic
118C4⋊Dic5—21no—
119C4⋊Dic5—21no—
120#681—42no—
121C2×#168—21no—
122C2×#168—21no—
123C2×#168C3×D411yescharacteristic
124C2×#168C3×D411yescharacteristic
125#498—51no—
126#476—51no—
127#461C3×D511yescharacteristic
128#436—51no—
129#335—51no—
130#333—51no—
131#332—51no—
132C22×C3×C5—41no—
133C22×C3×C5—41no—
134C22×C3×C5—41no—
135C22×C3×C5#12111yescharacteristic
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138C3×C4×C5—81no—
139C3×C4×C5C2×SD1611yescharacteristic
140C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
141C3×C4×C5#13711yescharacteristic
142C3×C4×C5#13711yescharacteristic
143C3×Dic5—81no—
144C2×C3×Q8—21no—
145C2×C3×Q8—101no—
146C2×C3×D4C22⋊D511yescharacteristic
147C22×C3×C4—21no—
148C3×SD16—42no—
149C3×M16—202no—
150C2×C3×C8—21no—
151C2×C3×C8—51no—
152C2×C3×C8—51no—
153C2×C3×C8—101no—
154C2×C3×C8—101no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—101no—
158C3×C4⋊C4—101no—
159C3×C4⋊C4C22⋊D511yescharacteristic
160C3×C22⋊C4—21no—
161C3×C42C22×D511yescharacteristic
162C23×C5—21no—
163C5×Q8—41no—
164C5×Q8—41no—
165C5×D4—21no—
166C5×D4—21no—
167C2×C4×C5—21no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5C2×C3×D411yescharacteristic
172C2×C4×C5C2×C3×D411yescharacteristic
173C2×C4×C5C3×#4111yescharacteristic
174C2×Dic5—41no—
175Dic10—81no—
176C5×C8—41no—
177#168—21no—
178#168—41no—
179#168—41no—
180#168C3×SD1612yescomplemented
181C2×SD16—21no—
182C2×M16—101no—
183C4⋊Q8—51no—
184C4⋊Q8C2×C3×D511yescharacteristic
185C4×D4C2×C3×D511yescharacteristic
186#106—101no—
187#106—101no—
188#106—101no—
189C4⋊C8—51no—
190C4⋊C8—51no—
191C4⋊C8C2×C3×D511yescharacteristic
192#103—21no—
193#102—101no—
194C22⋊C8—101no—
195C4×C8—51no—
196C2×C3×C5—81no—
197C2×C3×C5#46111yescharacteristic
198C2×C3×C5#46811yescharacteristic
199C2×C3×C5#47111yescharacteristic
200C23×C3—21no—
201C3×Q8—41no—
202C3×Q8—41no—
203C3×Q8—401no—
204C3×D4—21no—
205C3×D4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—201no—
211C2×C3×C4D4×D511yescharacteristic
212C2×C3×C4#71111yescharacteristic
213C2×C3×C4C2×C22⋊D511yescharacteristic
214C3×C8—41no—
215C3×C8—52no—
216C3×C8—101no—
217C3×C8—201no—
218C3×C8—201no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5C3×#12111yescharacteristic
223C4×C5—21no—
224C4×C5—41no—
225C4×C5—81no—
226C4×C5C2×C3×SD1611yescharacteristic
227C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
228C4×C5C3×#13711yescharacteristic
229C4×C5C3×#13711yescharacteristic
230Dic5—81no—
231C2×Q8—21no—
232C2×Q8—101no—
233C2×D4C3×C22⋊D511yescharacteristic
234C22×C4—21no—
235SD16—42no—
236M16—202no—
237C2×C8—21no—
238C2×C8—51no—
239C2×C8—51no—
240C2×C8—101no—
241C2×C8—101no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4C3×C22⋊D511yescharacteristic
247C22⋊C4—21no—
248C42C22×C3×D511yescharacteristic
249C3×C5#169111yescharacteristic, complemented, Hall
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3#408511yescharacteristic
254C3×C4—21no—
255C3×C4—41no—
256C3×C4—81no—
257C3×C4—401no—
258C3×C4D5×SD1611yescharacteristic
259C3×C4#406111yescharacteristic
260C3×C4#407811yescharacteristic
261C3×C4#409711yescharacteristic
262C2×C5—81no—
263C2×C5C3×#46111yescharacteristic
264C2×C5C3×#46811yescharacteristic
265C2×C5C3×#47111yescharacteristic
266C23—21no—
267Q8—41no—
268Q8—41no—
269Q8—401no—
270D4—21no—
271D4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—201no—
277C2×C4C3×D4×D511yescharacteristic
278C2×C4C3×#71111yescharacteristic
279C2×C4C2×C3×C22⋊D511yescharacteristic
280C8—41no—
281C8—52no—
282C8—101no—
283C8—201no—
284C8—201no—
285C2×C3—81no—
286C2×C3#6533111yescharacteristic
287C2×C3#6545111yescharacteristic
288C2×C3#6549211yescharacteristic
289C5C3×#169111yescharacteristic, complemented, Sylow
290C22—41no—
291C22—41no—
292C22—41no—
293C22C3×#408511yescharacteristic
294C4—21no—
295C4—41no—
296C4—81no—
297C4—401no—
298C4C3×D5×SD1611yescharacteristic
299C4C3×#406111yescharacteristic
300C4C3×#407811yescharacteristic
301C4C3×#409711yescharacteristic
302C3#1060183311yescharacteristic, direct product factor, Sylow
303C2—81no—
304C2C3×#6533111yescharacteristic
305C2C3×#6545111yescharacteristic
306C2C3×#6549211yescharacteristic
subgroupG/H
centerC22×C3#4085
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#461C2
socleC22×C3×C5#121
prime radicalC2×C3×C5×D4D4
hypercenterC3×#461D5
hypocenterC5C3×#1691
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
2. C3×#65368C2semidirect
5. C3×#64767C2semidirect
6. C3×#64701C2semidirect
7. C3×#64699C2semidirect
8. #10601833C3direct (N × H)
26. #65368C2×C3semidirect
29. #64767C2×C3semidirect
30. #64701C2×C3semidirect
31. #64699C2×C3semidirect
91. C3×#168SD16semidirect
180. #168C3×SD16semidirect
249. C3×C5#1691semidirect
289. C5C3×#1691semidirect
302. C3#10601833direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4612
C3×#653682
C3×#653012
C3×#652972
C3×#647672
C3×#647012
C3×#646992
#106018333
C3×#16915