Finite Group Databasebeta

← C3×C4×#3960 #14315353

Subgroups — C3×C4×#3960 #14315353

Order 1920.

324 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C5×Q16C211yesmaximal, characteristic, complemented
2C2×C3×#3960C211yesmaximal, characteristic
3C3×C4×D40C211yesmaximal, characteristic
4C3×#64784C211yesmaximal, characteristic, complemented
5C3×#64711C211yesmaximal, characteristic
6C3×#64710C211yesmaximal, characteristic, complemented
7C3×C4×#672C211yesmaximal, characteristic, complemented
8C4×#3960C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10C3×C4×C5×Q8—21no—
11C2×C3×D40C2211yescharacteristic
12C3×C4×D20—21no—
13C3×C5×#107C2211yescharacteristic
14C3×C5×#103—21no—
15C3×C4×C5×C8C2211yescharacteristic
16C3×#3960C414yesdirect product factor
17C3×#3953—21no—
18C3×#3950C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20C2×C3×#672C2211yescharacteristic
21C3×C4×SD32—51nomaximal, Hall
22C4×C5×Q16C2×C311yescharacteristic, complemented
23C2×#3960C2×C311yescharacteristic
24C4×D40C2×C311yescharacteristic
25#64784C2×C311yescharacteristic, complemented
26#64711C2×C311yescharacteristic
27#64710C2×C311yescharacteristic, complemented
28C4×#672C2×C311yescharacteristic, complemented
29C2×C3×C5×Q8—21no—
30C2×C3×D20—21no—
31C2×C3×C4×D5—41no—
32C3×C5×Q16—21no—
33C3×C5×Q16C2×C412yescomplemented
34C2×C3×C5×C8D411yescharacteristic
35C2×C3×C5×C8C2311yescharacteristic
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—41no—
38C3×C42×C5—41no—
39C3×C42×C5D411yescharacteristic
40C3×#685—41no—
41C3×C4⋊Dic5—21no—
42C3×D40—21no—
43C3×D40C2×C412yes—
44C3×#672—21no—
45C3×#672C2×C412yescomplemented
46C2×C3×SD32—51no—
47C3×C4×Q16D511yescharacteristic, complemented
48C3×C4×D8—51no—
49C3×#367—51no—
50C3×#358—51no—
51C3×#357—51no—
52C3×C4×C16—51no—
53C2×C5×Q16C22×C311yescharacteristic
54C4×C5×Q8—21no—
55C2×D40C22×C311yescharacteristic
56C4×D20—21no—
57C5×#107C22×C311yescharacteristic
58C5×#103—21no—
59C4×C5×C8C22×C311yescharacteristic
60#3960C3×C414yesdirect product factor
61#3953—21no—
62#3950C22×C311yescharacteristic
63C2×#672C22×C311yescharacteristic
64C2×#672C22×C311yescharacteristic
65C4×SD32—51noSylow
66C22×C3×D5—41no—
67C3×C5×Q8—22no—
68C3×C5×Q8—41no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5D811yescharacteristic
72C2×C3×C4×C5D811yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×Dic5—41no—
75C3×D20—22no—
76C3×D20—41no—
77C3×C4×D5—82no—
78C3×C5×C8—21no—
79C3×C5×C8C22×C411yescharacteristic
80C3×C5×C8#4111yescharacteristic
81C2×C3×Q16C2×D511yescharacteristic
82C2×C3×D8—51no—
83C3×C4×Q8—21no—
84C3×C4×D4—101no—
85C3×SD32—54no—
86C2×C3×C16—51no—
87C2×C3×C16—51no—
88C3×#107—51no—
89C3×#107C2×D511yescharacteristic
90C3×#103—21no—
91C3×#102—101no—
92C3×C4×C8C2×D511yescharacteristic
93C2×C5×Q8—21no—
94C2×D20—21no—
95C2×C4×D5—41no—
96C5×Q16—21no—
97C5×Q16C2×C3×C412yescomplemented
98C2×C5×C8C3×D411yescharacteristic
99C2×C5×C8C23×C311yescharacteristic
100C5×C4⋊C4—21no—
101C5×C4⋊C4—41no—
102C42×C5—41no—
103C42×C5C3×D411yescharacteristic
104#685—41no—
105C4⋊Dic5—21no—
106D40—21no—
107D40C2×C3×C412yes—
108#672—21no—
109#672C2×C3×C412yescomplemented
110C2×SD32—51no—
111C4×Q16C3×D511yescharacteristic, complemented
112C4×D8—51no—
113#367—51no—
114#358—51no—
115#357—51no—
116C4×C16—51no—
117C22×C3×C5C2×D811yescharacteristic
118C2×C3×D5—42no—
119C2×C3×D5—81no—
120C2×C3×D5—81no—
121C3×C4×C5—21no—
122C3×C4×C5—42no—
123C3×C4×C5—81no—
124C3×C4×C5SD3212yescomplemented
125C3×C4×C5C4×D411yescharacteristic
126C3×C4×C5#13511yescharacteristic
127C3×Dic5—81no—
128C2×C3×Q8—21no—
129C2×C3×D4—101no—
130C22×C3×C4—201no—
131C3×Q16—21no—
132C3×Q16C4×D512yescomplemented
133C3×D8—52no—
134C3×D8—101no—
135C2×C3×C8C22⋊D511yescharacteristic
136C2×C3×C8C22×D511yescharacteristic
137C3×C4⋊C4—21no—
138C3×C4⋊C4—41no—
139C3×C4⋊C4—101no—
140C3×C22⋊C4—201no—
141C3×C42—41no—
142C3×C42C22⋊D511yescharacteristic
143C3×C16—52no—
144C3×C16—101no—
145C22×D5—41no—
146C5×Q8—22no—
147C5×Q8—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5C3×D811yescharacteristic
151C2×C4×C5C3×D811yescharacteristic
152C2×C4×C5C2×C3×D411yescharacteristic
153C2×Dic5—41no—
154D20—22no—
155D20—41no—
156C4×D5—82no—
157C5×C8—21no—
158C5×C8C22×C3×C411yescharacteristic
159C5×C8C3×#4111yescharacteristic
160C2×Q16C2×C3×D511yescharacteristic
161C2×D8—51no—
162C4×Q8—21no—
163C4×D4—101no—
164SD32—54no—
165C2×C16—51no—
166C2×C16—51no—
167#107—51no—
168#107C2×C3×D511yescharacteristic
169#103—21no—
170#102—101no—
171C4×C8C2×C3×D511yescharacteristic
172C2×C3×C5C4×D811yescharacteristic
173C2×C3×C5C2×SD3211yescharacteristic
174C2×C3×C5#50811yescharacteristic
175C3×D5—82no—
176C23×C3—201no—
177C3×Q8—22no—
178C3×Q8—41no—
179C3×D4—102no—
180C3×D4—201no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—201no—
184C2×C3×C4—402no—
185C2×C3×C4#68611yescharacteristic
186C2×C3×C4#68611yescharacteristic
187C2×C3×C4C2×C22⋊D511yescharacteristic
188C3×C8—21no—
189C3×C8C2×C4×D511yescharacteristic
190C3×C8#70911yescharacteristic
191C22×C5C2×C3×D811yescharacteristic
192C2×D5—42no—
193C2×D5—81no—
194C2×D5—81no—
195C4×C5—21no—
196C4×C5—42no—
197C4×C5—81no—
198C4×C5C3×SD3212yescomplemented
199C4×C5C3×C4×D411yescharacteristic
200C4×C5C3×#13511yescharacteristic
201Dic5—81no—
202C2×Q8—21no—
203C2×D4—101no—
204C22×C4—201no—
205Q16—21no—
206Q16C3×C4×D512yescomplemented
207D8—52no—
208D8—101no—
209C2×C8C3×C22⋊D511yescharacteristic
210C2×C8C22×C3×D511yescharacteristic
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—101no—
214C22⋊C4—201no—
215C42—41no—
216C42C3×C22⋊D511yescharacteristic
217C16—52no—
218C16—101no—
219C3×C5C4×SD3211yescharacteristic, complemented, Hall
220C22×C3—202no—
221C22×C3—401no—
222C22×C3—401no—
223C22×C3C2×#68611yescharacteristic
224C3×C4—21no—
225C3×C4—42no—
226C3×C4—81no—
227C3×C4—401no—
228C3×C4#396012yesdirect product factor
229C3×C4C4×C22⋊D511yescharacteristic
230C3×C4#409611yescharacteristic
231C2×C5C3×C4×D811yescharacteristic
232C2×C5C2×C3×SD3211yescharacteristic
233C2×C5C3×#50811yescharacteristic
234D5—82no—
235C23—201no—
236Q8—22no—
237Q8—41no—
238D4—102no—
239D4—201no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—201no—
243C2×C4—402no—
244C2×C4C3×#68611yescharacteristic
245C2×C4C3×#68611yescharacteristic
246C2×C4C2×C3×C22⋊D511yescharacteristic
247C8—21no—
248C8C2×C3×C4×D511yescharacteristic
249C8C3×#70911yescharacteristic
250C2×C3—402no—
251C2×C3C4×#68611yescharacteristic
252C2×C3C2×#396011yescharacteristic
253C2×C3#6548311yescharacteristic
254C5C3×C4×SD3211yescharacteristic, complemented, Sylow
255C22—202no—
256C22—401no—
257C22—401no—
258C22C2×C3×#68611yescharacteristic
259C4—21no—
260C4—42no—
261C4—81no—
262C4—401no—
263C4C3×#396012yesdirect product factor
264C4C3×C4×C22⋊D511yescharacteristic
265C4C3×#409611yescharacteristic
266C3C4×#396011yescharacteristic, direct product factor, Sylow
267C2—402no—
268C2C3×C4×#68611yescharacteristic
269C2C2×C3×#396011yescharacteristic
270C2C3×#6548311yescharacteristic
subgroupG/H
centerC2×C3×C4#686
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
FittingC3×C4×C5×Q16C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
cosocleC2×C5×C8C23×C3
hypercenterC3×C4×Q16D5
hypocenterC5C3×C4×SD32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×C8 ◁ C3×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C3×C4×C5×Q16C2semidirect
4. C3×#64784C2semidirect
6. C3×#64710C2semidirect
7. C3×C4×#672C2semidirect
8. C4×#3960C3direct (N × H)
16. C3×#3960C4direct (N × H)
22. C4×C5×Q16C2×C3semidirect
25. #64784C2×C3semidirect
27. #64710C2×C3semidirect
28. C4×#672C2×C3semidirect
33. C3×C5×Q16C2×C4semidirect
45. C3×#672C2×C4semidirect
47. C3×C4×Q16D5semidirect
60. #3960C3×C4direct (N × H)
97. C5×Q16C2×C3×C4semidirect
109. #672C2×C3×C4semidirect
111. C4×Q16C3×D5semidirect
124. C3×C4×C5SD32semidirect
132. C3×Q16C4×D5semidirect
198. C4×C5C3×SD32semidirect
206. Q16C3×C4×D5semidirect
219. C3×C5C4×SD32semidirect
228. C3×C4#3960direct (N × H)
254. C5C3×C4×SD32semidirect
263. C4C3×#3960direct (N × H)
266. C3C4×#3960direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C5×Q162
C2×C3×#39602
C3×C4×D402
C3×#647842
C3×#647112
C3×#647102
C3×C4×#6722
C4×#39603
C3×C4×SD325