Finite Group Databasebeta

← C3×#10601681 #14318038

Subgroups — C3×#10601681 #14318038

Order 1920.

272 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C5×D8C211yesmaximal, characteristic
2C3×#64972C211yesmaximal, characteristic, complemented
3C3×#64782C211yesmaximal, characteristic
4C3×#64782C211yesmaximal, characteristic
5C3×#64710C211yesmaximal, characteristic, complemented
6C3×#64709C211yesmaximal, characteristic, complemented
7C3×C4⋊#672C211yesmaximal, characteristic, complemented
8#10601681C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×D8C2211yescharacteristic
10C3×C4×C5×D4—21no—
11C3×#4016—21no—
12C3×C5×#107C2211yescharacteristic
13C3×C5×#102—21no—
14C3×C4×C5×C8C2211yescharacteristic
15C3×#3950C2211yescharacteristic
16C3×#3950C2211yescharacteristic
17C3×#3949—21no—
18C2×C3×#672C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20C3×#2228—51nomaximal, Hall
21C4×C5×D8C2×C311yescharacteristic
22#64972C2×C311yescharacteristic, complemented
23#64782C2×C311yescharacteristic
24#64782C2×C311yescharacteristic
25#64710C2×C311yescharacteristic, complemented
26#64709C2×C311yescharacteristic, complemented
27C4⋊#672C2×C311yescharacteristic, complemented
28C2×C3×C5×D4—21no—
29C22×C3×C4×C5—41no—
30C3×C5×D8—21no—
31C3×C5×D8Q812yes—
32C2×C3×C5×C8D411yescharacteristic
33C2×C3×C5×C8C2311yescharacteristic
34C3×C5×C4⋊C4—21no—
35C3×C5×C22⋊C4—41no—
36C3×C42×C5D411yescharacteristic
37C3×C4⋊Dic5—21no—
38C3×C4⋊Dic5—21no—
39C3×#683—41no—
40C3×#683—41no—
41C3×#672—21no—
42C3×#672—21no—
43C3×#499—51no—
44C3×C4×D8D511yescharacteristic
45C3×#367—51no—
46C3×#366—51no—
47C3×C4⋊C16—51no—
48C3×#357—51no—
49C3×#357—51no—
50C2×C5×D8C22×C311yescharacteristic
51C4×C5×D4—21no—
52#4016—21no—
53C5×#107C22×C311yescharacteristic
54C5×#102—21no—
55C4×C5×C8C22×C311yescharacteristic
56#3950C22×C311yescharacteristic
57#3950C22×C311yescharacteristic
58#3949—21no—
59C2×#672C22×C311yescharacteristic
60C2×#672C22×C311yescharacteristic
61#2228—51noSylow
62C23×C3×C5—41no—
63C3×C5×D4—22no—
64C3×C5×D4—41no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—82no—
67C2×C3×C4×C5D811yescharacteristic
68C2×C3×C4×C5D811yescharacteristic
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×Dic5—41no—
71C2×C3×Dic5—41no—
72C3×C5×C8—21no—
73C3×C5×C8C2×Q811yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C2×C3×D8C2×D511yescharacteristic
76C3×#125—101no—
77C3×C4×D4—21no—
78C2×C3×C16—51no—
79C2×C3×C16—51no—
80C3×#107—51no—
81C3×#107—51no—
82C3×#107C2×D511yescharacteristic
83C3×#106—101no—
84C3×#102—21no—
85C3×C4×C8C2×D511yescharacteristic
86C2×C5×D4—21no—
87C22×C4×C5—41no—
88C5×D8—21no—
89C5×D8C3×Q812yes—
90C2×C5×C8C3×D411yescharacteristic
91C2×C5×C8C23×C311yescharacteristic
92C5×C4⋊C4—21no—
93C5×C22⋊C4—41no—
94C42×C5C3×D411yescharacteristic
95C4⋊Dic5—21no—
96C4⋊Dic5—21no—
97#683—41no—
98#683—41no—
99#672—21no—
100#672—21no—
101#499—51no—
102C4×D8C3×D511yescharacteristic
103#367—51no—
104#366—51no—
105C4⋊C16—51no—
106#357—51no—
107#357—51no—
108C22×C3×C5—42no—
109C22×C3×C5—81no—
110C22×C3×C5—81no—
111C22×C3×C5C2×D811yescharacteristic
112C3×C4×C5—21no—
113C3×C4×C5—21no—
114C3×C4×C5—81no—
115C3×C4×C5C22⋊Q811yescharacteristic
116C3×C4×C5#13711yescharacteristic
117C3×Dic5—81no—
118C3×Dic5—81no—
119C2×C3×D4—21no—
120C22×C3×C4—41no—
121C3×D8—21no—
122C3×D8Dic1012yes—
123C2×C3×C8C22⋊D511yescharacteristic
124C2×C3×C8C22×D511yescharacteristic
125C3×C4⋊C4—21no—
126C3×C4⋊C4—101no—
127C3×C4⋊C4—101no—
128C3×C4⋊C4—201no—
129C3×C4⋊C4—201no—
130C3×C22⋊C4—41no—
131C3×C42C22⋊D511yescharacteristic
132C3×C16—101no—
133C3×C16—101no—
134C23×C5—41no—
135C5×D4—22no—
136C5×D4—41no—
137C2×C4×C5—41no—
138C2×C4×C5—82no—
139C2×C4×C5C3×D811yescharacteristic
140C2×C4×C5C3×D811yescharacteristic
141C2×C4×C5C2×C3×D411yescharacteristic
142C2×Dic5—41no—
143C2×Dic5—41no—
144C5×C8—21no—
145C5×C8C2×C3×Q811yescharacteristic
146C5×C8C3×#4111yescharacteristic
147C2×D8C2×C3×D511yescharacteristic
148#125—101no—
149C4×D4—21no—
150C2×C16—51no—
151C2×C16—51no—
152#107—51no—
153#107—51no—
154#107C2×C3×D511yescharacteristic
155#106—101no—
156#102—21no—
157C4×C8C2×C3×D511yescharacteristic
158C2×C3×C5—82no—
159C2×C3×C5#47411yescharacteristic
160C2×C3×C5#50811yescharacteristic
161C2×C3×C5#50911yescharacteristic
162C23×C3—41no—
163C3×D4—22no—
164C3×D4—41no—
165C2×C3×C4—41no—
166C2×C3×C4—82no—
167C2×C3×C4—201no—
168C2×C3×C4—201no—
169C2×C3×C4#68611yescharacteristic
170C2×C3×C4#68611yescharacteristic
171C2×C3×C4C2×C22⋊D511yescharacteristic
172C3×C8—21no—
173C3×C8C2×Dic1011yescharacteristic
174C3×C8#70911yescharacteristic
175C22×C5—42no—
176C22×C5—81no—
177C22×C5—81no—
178C22×C5C2×C3×D811yescharacteristic
179C4×C5—21no—
180C4×C5—21no—
181C4×C5—81no—
182C4×C5C3×C22⋊Q811yescharacteristic
183C4×C5C3×#13711yescharacteristic
184Dic5—81no—
185Dic5—81no—
186C2×D4—21no—
187C22×C4—41no—
188D8—21no—
189D8C3×Dic1012yes—
190C2×C8C3×C22⋊D511yescharacteristic
191C2×C8C22×C3×D511yescharacteristic
192C4⋊C4—21no—
193C4⋊C4—101no—
194C4⋊C4—101no—
195C4⋊C4—201no—
196C4⋊C4—201no—
197C22⋊C4—41no—
198C42C3×C22⋊D511yescharacteristic
199C16—101no—
200C16—101no—
201C3×C5#222811yescharacteristic, complemented, Hall
202C22×C3—42no—
203C22×C3—81no—
204C22×C3—81no—
205C22×C3C2×#68611yescharacteristic
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—81no—
209C3×C4—401no—
210C3×C4—401no—
211C3×C4#407011yescharacteristic
212C3×C4#409711yescharacteristic
213C2×C5—82no—
214C2×C5C3×#47411yescharacteristic
215C2×C5C3×#50811yescharacteristic
216C2×C5C3×#50911yescharacteristic
217C23—41no—
218D4—22no—
219D4—41no—
220C2×C4—41no—
221C2×C4—82no—
222C2×C4—201no—
223C2×C4—201no—
224C2×C4C3×#68611yescharacteristic
225C2×C4C3×#68611yescharacteristic
226C2×C4C2×C3×C22⋊D511yescharacteristic
227C8—21no—
228C8C2×C3×Dic1011yescharacteristic
229C8C3×#70911yescharacteristic
230C2×C3—82no—
231C2×C3#6529611yescharacteristic
232C2×C3#6543611yescharacteristic
233C2×C3#6548311yescharacteristic
234C5C3×#222811yescharacteristic, complemented, Sylow
235C22—42no—
236C22—81no—
237C22—81no—
238C22C2×C3×#68611yescharacteristic
239C4—21no—
240C4—21no—
241C4—81no—
242C4—401no—
243C4—401no—
244C4C3×#407011yescharacteristic
245C4C3×#409711yescharacteristic
246C3#1060168111yescharacteristic, direct product factor, Sylow
247C2—82no—
248C2C3×#6529611yescharacteristic
249C2C3×#6543611yescharacteristic
250C2C3×#6548311yescharacteristic
subgroupG/H
centerC22×C3C2×#686
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C4×C5×D8C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×C5×D8C22
hypercenterC3×C4×D8D5
hypocenterC5C3×#2228
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×C8 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
2. C3×#64972C2semidirect
5. C3×#64710C2semidirect
6. C3×#64709C2semidirect
7. C3×C4⋊#672C2semidirect
8. #10601681C3direct (N × H)
22. #64972C2×C3semidirect
25. #64710C2×C3semidirect
26. #64709C2×C3semidirect
27. C4⋊#672C2×C3semidirect
201. C3×C5#2228semidirect
234. C5C3×#2228semidirect
246. C3#10601681direct (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×D82
C3×#649722
C3×#647822
C3×#647102
C3×#647092
C3×C4⋊#6722
#106016813
C3×#22285