Finite Group Databasebeta

← C3×#91821 #13088034

Subgroups — C3×#91821 #13088034

Order 1440.

326 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×C32×C5×D4C211yesmaximal, characteristic, complemented
2C3×#6817C211yesmaximal, characteristic, complemented
3C3×#6716C212yesmaximal, complemented
4C3×#6715C212yesmaximal, complemented
5C3×#6710C211yesmaximal, characteristic, complemented
6#91821C311yesmaximal, characteristic, direct product factor
7C3×#4078—31nomaximal
8C23×C32×C5—21no—
9C32×C5×D4—21no—
10C32×C5×D4C2212yes—
11C2×C32×C4×C5C2211yescharacteristic
12C3×#1220—21no—
13C3×D60C2211yescharacteristic, complemented
14C3×C4×D15—21no—
15C3×Dic30C2211yescharacteristic, complemented
16C3×C3⋊#168C2212yescomplemented
17C3×#932—51nomaximal, Hall
18C2×C3×C5×D4—21no—
19C2×C3×C5×D4D311yescharacteristic, complemented
20C2×C3×C5×D4C2×C311yescharacteristic, complemented
21#6817C2×C311yescharacteristic, complemented
22C3×#709—31no—
23#6716C2×C312yescomplemented
24#6715C2×C312yescomplemented
25#6710C2×C311yescharacteristic, complemented
26C3×#687—32no—
27C3×#686—32no—
28C3×#681—31no—
29C22×C32×C5—22no—
30C22×C32×C5—42no—
31C22×C32×C5D411yescharacteristic
32C2×C3×D15—21no—
33C32×C4×C5D411yescharacteristic
34C32×C4×C5C2311yescharacteristic
35C3×Dic15—21no—
36#4078—31noHall
37C2×C32×D4D511yescharacteristic, complemented
38C3×#235—51no—
39C3×#214—52no—
40C3×#213—52no—
41C3×#208—51no—
42C23×C3×C5—22no—
43C23×C3×C5—21no—
44C23×C3×C5—21no—
45C3×C5×D4—22no—
46C3×C5×D4—22no—
47C3×C5×D4—21no—
48C3×C5×D4—21no—
49C3×C5×D4C2×D312yes—
50C3×C5×D4C22×C312yes—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5C2×D311yescharacteristic
53C2×C3×C4×C5C22×C311yescharacteristic
54#1220—21no—
55D60C22×C311yescharacteristic, complemented
56C4×D15—21no—
57Dic30C22×C311yescharacteristic, complemented
58C3×C22⋊D5—61no—
59C3×D20—31no—
60C3×C4×D5—61no—
61C3×Dic10—31no—
62C3⋊#168C22×C312yescomplemented
63C3×#168—32no—
64C3×AGL(1,ℤ/8)—151no—
65#932—51no—
66C2×C32×C5—21no—
67C2×C32×C5—42no—
68C2×C32×C5C2×D411yescharacteristic
69C3×D15—41no—
70C2×C5×D4C3×D311yescharacteristic, complemented
71#709—31no—
72#687—32no—
73#686—32no—
74#681—31no—
75C23×C32—21no—
76C32×D4—21no—
77C32×D4C2×D512yes—
78C2×C32×C4C2×D511yescharacteristic
79C3×#67—101no—
80C3×D12—51no—
81C3×C4×D3—101no—
82C3×Dic6—51no—
83C3×C3⋊C8—52no—
84C22×C3×C5—24no—
85C22×C3×C5—22no—
86C22×C3×C5—22no—
87C22×C3×C5—21no—
88C22×C3×C5—44no—
89C22×C3×C5—42no—
90C22×C3×C5—42no—
91C22×C3×C5#6711yescharacteristic
92C22×C3×C5C3×D411yescharacteristic
93C2×D15—21no—
94C2×C3×D5—61no—
95C3×C4×C5—21no—
96C3×C4×C5—21no—
97C3×C4×C5#6711yescharacteristic
98C3×C4×C5C3×D411yescharacteristic
99C3×C4×C5C22×D311yescharacteristic
100C3×C4×C5C23×C311yescharacteristic
101Dic15—21no—
102C3×Dic5—61no—
103C3×#41—151no—
104C2×C3×D4—21no—
105C2×C3×D4C3×D511yescharacteristic, complemented
106C2×C3×D4D1511yescharacteristic, complemented
107#235—51no—
108C3×SD16—152no—
109C3×D8—152no—
110C3×M16—151no—
111#214—52no—
112#213—52no—
113#208—51no—
114C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
115C23×C5—21no—
116C5×D4—21no—
117C5×D4C2×C3×D312yes—
118C2×C4×C5C2×C3×D311yescharacteristic
119C22⋊D5—61no—
120D20—31no—
121C4×D5—61no—
122Dic10—31no—
123#168—32no—
124C22×C32—22no—
125C22×C32—42no—
126C22×C32C22⋊D511yescharacteristic
127C2×C3×D3—101no—
128C32×C4C22⋊D511yescharacteristic
129C32×C4C22×D511yescharacteristic
130C3×Dic3—101no—
131AGL(1,ℤ/8)—151noSylow
132C2×C3×C5—22no—
133C2×C3×C5—21no—
134C2×C3×C5—21no—
135C2×C3×C5—21no—
136C2×C3×C5—44no—
137C2×C3×C5—42no—
138C2×C3×C5—42no—
139C2×C3×C5C2×#6711yescharacteristic
140C2×C3×C5C2×C3×D411yescharacteristic
141D15—41no—
142C3×D5—121no—
143C23×C3—22no—
144C23×C3—21no—
145C23×C3—21no—
146C3×Q8—151no—
147C3×D4—22no—
148C3×D4—21no—
149C3×D4—21no—
150C3×D4—22no—
151C3×D4—151no—
152C3×D4—301no—
153C3×D4C2×C3×D512yes—
154C3×D4C2×D1512yes—
155C2×C3×C4—21no—
156C2×C3×C4—301no—
157C2×C3×C4C2×C3×D511yescharacteristic
158C2×C3×C4C2×D1511yescharacteristic
159#67—101no—
160D12—51no—
161C4×D3—101no—
162Dic6—51no—
163C3×C8—152no—
164C3⋊C8—52no—
165C22×C5—22no—
166C22×C5—42no—
167C22×C5C3×#6711yescharacteristic
168C2×D5—61no—
169C4×C5C3×#6711yescharacteristic
170C4×C5C22×C3×D311yescharacteristic
171Dic5—61no—
172C2×C32—21no—
173C2×C32—42no—
174C2×C32C2×C22⋊D511yescharacteristic
175C3×D3—201no—
176#41—151no—
177C2×D4C3×D1511yescharacteristic, complemented
178SD16—152no—
179D8—152no—
180M16—151no—
181C3×C5—21no—
182C3×C5#93211yescharacteristic, complemented
183C3×C5C3×AGL(1,ℤ/8)11yescharacteristic, complemented
184C22×C3—24no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—21no—
188C22×C3—44no—
189C22×C3—42no—
190C22×C3—42no—
191C22×C3—301no—
192C22×C3C3×C22⋊D511yescharacteristic
193C22×C3#122011yescharacteristic
194C2×D3—101no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—301no—
198C3×C4C3×C22⋊D511yescharacteristic
199C3×C4#122011yescharacteristic
200C3×C4C22×C3×D511yescharacteristic
201C3×C4C22×D1511yescharacteristic
202Dic3—101no—
203C2×C5—21no—
204C2×C5—42no—
205C2×C5C2×C3×#6711yescharacteristic
206D5—121no—
207C32#407811yescharacteristic, complemented, Sylow
208C23—21no—
209Q8—151no—
210D4—21no—
211D4—151no—
212D4—301no—
213D4C2×C3×D1512yes—
214C2×C4—301no—
215C2×C4C2×C3×D1511yescharacteristic
216C8—152no—
217C2×C3—22no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—44no—
222C2×C3—42no—
223C2×C3—42no—
224C2×C3—601no—
225C2×C3C2×C3×C22⋊D511yescharacteristic
226C2×C3C2×#122011yescharacteristic
227D3—201no—
228C5C3×#93211yescharacteristic, complemented, Sylow
229C22—22no—
230C22—42no—
231C22—301no—
232C22C3×#122011yescharacteristic
233C4—301no—
234C4C3×#122011yescharacteristic
235C4C22×C3×D1511yescharacteristic
236C3—21no—
237C3C3×#407811yescharacteristic, complemented
238C3#9182111yescharacteristic, direct product factor
239C2—21no—
240C2—42no—
241C2—601no—
242C2C2×C3×#122011yescharacteristic
subgroupG/H
centerC2×C3C2×#1220
commutator, cosocleC3×C4×C5C23×C3
FrattiniC4C22×C3×D15
FittingC2×C32×C5×D4C2
socleC2×C32×C5C2×D4
hypercenterC2×C3×D4D15
hypocenterC3×C5C3×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C3×#6817C2semidirect
3. C3×#6716C2semidirect
4. C3×#6715C2semidirect
5. C3×#6710C2semidirect
6. #91821C3direct (N × H)
13. C3×D60C22semidirect
15. C3×Dic30C22semidirect
16. C3×C3⋊#168C22semidirect
19. C2×C3×C5×D4D3semidirect
20. C2×C3×C5×D4C2×C3semidirect
21. #6817C2×C3semidirect
23. #6716C2×C3semidirect
24. #6715C2×C3semidirect
25. #6710C2×C3semidirect
37. C2×C32×D4D5semidirect
55. D60C22×C3semidirect
57. Dic30C22×C3semidirect
62. C3⋊#168C22×C3semidirect
70. C2×C5×D4C3×D3semidirect
105. C2×C3×D4C3×D5semidirect
106. C2×C3×D4D15semidirect
114. C32×C5AGL(1,ℤ/8)semidirect
177. C2×D4C3×D15semidirect
182. C3×C5#932semidirect
183. C3×C5C3×AGL(1,ℤ/8)semidirect
207. C32#4078semidirect
228. C5C3×#932semidirect
237. C3C3×#4078semidirect
238. C3#91821direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C3×#68172
C3×#67162
C3×#67152
C3×#67102
#918213
C3×#40783
C3×#9325