Finite Group Databasebeta

← C2×#92030 #11757039

Subgroups — C2×#92030 #11757039

Order 960.

1588 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D15C211yesmaximal, characteristic, complemented
2C2×C5×#239C211yesmaximal, characteristic, complemented
3C2×C3×Q8×D5C211yesmaximal, characteristic, complemented
4#92030C2116yesmaximal, direct product factor
5C2×#6772C213yesmaximal, complemented
6C2×#6771C213yesmaximal, complemented
7C2×#6768C213yesmaximal, complemented
8C2×D3×Dic10C213yesmaximal, complemented
9C2×#4150—31nomaximal, Hall
10C2×C3×C5×Q8C2211yescharacteristic
11Q8×D15C2218yescomplemented
12C2×C4×D15C2213yes—
13C2×Dic30C2213yes—
14C5×#239C2218yescomplemented
15C2×C5×D12C2213yes—
16C2×C4×C5×D3C2213yes—
17C3×Q8×D5C2218yescomplemented
18C2×C3×C4×D5C2213yes—
19C2×C3×Dic10C2213yes—
20C2×#1204C2213yes—
21C2×#1203C2213yes—
22C2×#1202C2211yescharacteristic
23C2×#1201C2213yes—
24C2×D3×Dic5C2216yes—
25#6772C22124yescomplemented
26#6771C22124yescomplemented
27#6768C22124yescomplemented
28D3×Dic10C22124yescomplemented
29C2×#1007—51nomaximal, Hall
30C2×C5×#41—31no—
31#4150—316no—
32C2×Q8×D5—31no—
33C2×Q8×D5D311yescharacteristic, complemented
34C2×#711—33no—
35C2×#711—33no—
36C2×#709—33no—
37C22×Dic10—33no—
38C22×D15C2311yescharacteristic
39C22×C5×D3C2313yes—
40C22×C3×D5C2311yescharacteristic
41C3×C5×Q8C2314yes—
42C2×C3×C4×C5C2313yes—
43C2×Dic15C2313yes—
44C4×D15C23112yes—
45Dic30C23112yes—
46C2×C5×Dic3C2311yescharacteristic
47C5×D12C23112yes—
48C4×C5×D3C23112yes—
49C2×C3×Dic5C2313yes—
50C3×C4×D5C23112yes—
51C3×Dic10C23112yes—
52#1204C23112yes—
53#1203C23112yes—
54#1202C2314yes—
55#1201C23112yes—
56D3×Dic5C23124yes—
57C22×C3×Q8—51no—
58#1007—516no—
59C2×#239—53no—
60C2×#239D511yescharacteristic, complemented
61C2×D3×Q8—51no—
62C2×D3×Q8—53no—
63C2×#235—53no—
64C2×#235—53no—
65C5×#41—38no—
66C2×C5×Q8C2×D311yescharacteristic
67C2×C5×D4—33no—
68C22×C4×C5—33no—
69C2×C22⋊D5—33no—
70C2×C22⋊D5—33no—
71C22×Dic5—36no—
72Q8×D5—38no—
73Q8×D5C2×D318yescomplemented
74#711—324no—
75#711—324no—
76#709—324no—
77C2×D20—31no—
78C2×C4×D5—33no—
79C2×C4×D5C2×D313yes—
80C2×Dic10—33no—
81C2×Dic10—33no—
82C2×Dic10—324no—
83C2×Dic10C2×D313yes—
84C2×2−1+4—151noSylow
85C22×C3×C5C2411yescharacteristic
86C2×D15—22no—
87C2×D15C2412yes—
88C2×C5×D3—26no—
89C2×C5×D3C2416yes—
90C2×C3×D5—22no—
91C2×C3×D5C2412yes—
92C3×C4×C5C2416yes—
93Dic15C2416yes—
94C3×Dic5C2416yes—
95C5×Dic3C2412yes—
96C2×C3×Q8—58no—
97C2×C3×Q8—53no—
98C2×C3×Q8C2×D511yescharacteristic
99C22×C3×C4—53no—
100C2×#67—53no—
101C2×#67—51no—
102#239—524no—
103#239C2×D518yescomplemented
104D3×Q8—58no—
105D3×Q8—524no—
106#235—524no—
107#235—524no—
108C2×D12—53no—
109C2×D12C2×D513yes—
110C2×C4×D3—56no—
111C2×C4×D3—53no—
112C2×C4×D3C2×D513yes—
113C2×Dic6—53no—
114C2×Dic6—53no—
115C23×C5—33no—
116C22×D5—31no—
117C22×D5C22×D311yescharacteristic
118C5×Q8C22×D314yes—
119C5×D4—312no—
120C2×C4×C5—31no—
121C2×C4×C5—312no—
122C2×C4×C5C22×D313yes—
123C22⋊D5—312no—
124C22⋊D5—312no—
125C2×Dic5—33no—
126C2×Dic5—324no—
127C2×Dic5C22×D313yes—
128D20—34no—
129C4×D5—312no—
130C4×D5C22×D3112yes—
131Dic10—312no—
132Dic10—312no—
133Dic10C22×D3112yes—
1342−1+4—1516no—
135C2×#41—31no—
136C2×#41—153no—
137C2×#41—153no—
138C2×#41—153no—
139C22×Q8—51no—
140C22×Q8—153no—
141C22×Q8—151no—
142C2×C3×C52−1+412yescomplemented
143C2×C3×C5C2511yescharacteristic
144D15—22no—
145C3×D5—22no—
146C5×D3—26no—
147C23×C3—51no—
148C22×D3—51no—
149C22×D3C22×D513yes—
150C3×Q8—512no—
151C3×Q8C22×D514yes—
152C2×C3×C4—53no—
153C2×C3×C4—512no—
154C2×C3×C4C22×D513yes—
155#67—512no—
156#67—54no—
157C2×Dic3—53no—
158C2×Dic3C22×D511yescharacteristic
159D12—512no—
160D12C22×D5112yes—
161C4×D3—524no—
162C4×D3—512no—
163C4×D3C22×D5112yes—
164Dic6—512no—
165Dic6—512no—
166C22×C5—36no—
167C22×C5—66no—
168C22×C5C23×D311yescharacteristic
169C2×D5—22no—
170C2×D5—32no—
171C2×D5—62no—
172C2×D5C23×D312yes—
173C4×C5—32no—
174C4×C5C23×D316yes—
175Dic5—36no—
176Dic5C23×D316yes—
177#41—38no—
178#41—1524no—
179#41—1524no—
180#41—1524no—
181C2×Q8—58no—
182C2×Q8—53no—
183C2×Q8—153no—
184C2×Q8—1524no—
185C2×Q8—158no—
186C2×Q8—153no—
187C2×Q8D3×D511yescharacteristic
188C2×D4—33no—
189C2×D4—151no—
190C2×D4—153no—
191C2×D4—153no—
192C22×C4—33no—
193C22×C4—53no—
194C22×C4—156no—
195C22×C4—153no—
196C3×C5C2×2−1+411yescharacteristic, complemented, Hall
197C22×C3—52no—
198C22×C3—102no—
199C22×C3C23×D511yescharacteristic
200C2×D3—26no—
201C2×D3—52no—
202C2×D3—102no—
203C2×D3C23×D516yes—
204C3×C4—56no—
205C3×C4C23×D516yes—
206Dic3—56no—
207Dic3C23×D512yes—
208C2×C5—66no—
209C2×C5#100712yescomplemented
210C2×C5C24×D311yescharacteristic
211D5—22no—
212D5—62no—
213C23—33no—
214C23—51no—
215C23—151no—
216Q8—512no—
217Q8—1512no—
218Q8—1512no—
219Q8C2×D3×D514yes—
220D4—312no—
221D4—154no—
222D4—1512no—
223D4—1512no—
224C2×C4—31no—
225C2×C4—312no—
226C2×C4—53no—
227C2×C4—512no—
228C2×C4—1524no—
229C2×C4—153no—
230C2×C4—1512no—
231C2×C4C2×D3×D513yes—
232C2×C3—102no—
233C2×C3#415012yescomplemented
234C2×C3C24×D511yescharacteristic
235D3—26no—
236D3—102no—
237C5C2×#100711yescharacteristic, complemented, Sylow
238C22—36no—
239C22—52no—
240C22—66no—
241C22—102no—
242C22—152no—
243C22—302no—
244C22C22×D3×D511yescharacteristic
245C4—32no—
246C4—56no—
247C4—156no—
248C4C22×D3×D516yes—
249C3C2×#415011yescharacteristic, complemented, Sylow
250C2—66no—
251C2—102no—
252C2—302no—
253C2#9203012yesdirect product factor
254C2C23×D3×D511yescharacteristic
subgroupG/H
centerC22C22×D3×D5
commutator, cosocleC2×C3×C5C25
FrattiniC2C23×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C24
hypercenterC2×Q8D3×D5
hypocenterC3×C5C2×2−1+4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D15C2semidirect
2. C2×C5×#239C2semidirect
3. C2×C3×Q8×D5C2semidirect
4. #92030C2direct (N × H)
5. C2×#6772C2semidirect
6. C2×#6771C2semidirect
7. C2×#6768C2semidirect
8. C2×D3×Dic10C2semidirect
11. Q8×D15C22semidirect
14. C5×#239C22semidirect
17. C3×Q8×D5C22semidirect
25. #6772C22semidirect
26. #6771C22semidirect
27. #6768C22semidirect
28. D3×Dic10C22semidirect
33. C2×Q8×D5D3semidirect
60. C2×#239D5semidirect
73. Q8×D5C2×D3semidirect
103. #239C2×D5semidirect
142. C2×C3×C52−1+4semidirect
196. C3×C5C2×2−1+4semidirect
209. C2×C5#1007semidirect
233. C2×C3#4150semidirect
237. C5C2×#1007semidirect
249. C3C2×#4150semidirect
253. C2#92030direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D152
C2×C5×#2392
C2×C3×Q8×D52
#920302
C2×#67722
C2×#67712
C2×#67682
C2×D3×Dic102
C2×#41503
C2×#10075