Finite Group Databasebeta

← C131×#10220 #45696104

Subgroups — C131×#10220 #45696104

Order 33536.

542 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 122 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
1#3208×C131C212yesmaximal
2#3162×C131C211yesmaximal, characteristic, complemented
3#1961×C131C211yesmaximal, characteristic
4#1518×C131C212yesmaximal, complemented
5#1281×C131C211yesmaximal, characteristic, complemented
6#533×C131C2212yes—
7C2×#127×C131C2211yescharacteristic
8#501×C131—22no—
9#501×C131—22no—
10#492×C131—22no—
11#486×C131—22no—
12#460×C131—24no—
13#450×C131—24no—
14#431×C131C2212yes—
15#427×C131—22no—
16C2×#102×C131—22no—
17C2×#97×C131C2211yescharacteristic
18#382×C131C2211yescharacteristic
19#328×C131—24no—
20C22×D4×C131—21no—
21C22×D4×C131—22no—
22C2×SD16×C131—28no—
23C22×C8×C131D412yes—
24C4⋊Q8×C131D412yes—
25C4⋊Q8×C131D412yes—
26#127×C131—22no—
27#127×C131—21no—
28#127×C131D412yes—
29#125×C131—22no—
30C22⋊Q8×C131—22no—
31C22⋊Q8×C131—22no—
32C4×Q8×C131—22no—
33C4×Q8×C131—22no—
34#117×C131—22no—
35C2×C4⋊C4×C131—21no—
36C2×C42×C131C2311yescharacteristic
37#107×C131—24no—
38#106×C131—22no—
39#106×C131—22no—
40C4⋊C8×C131—22no—
41#102×C131—28no—
42#102×C131—44no—
43C22⋊C8×C131D414yes—
44#97×C131—22no—
45C4×C8×C131—22no—
46#95×C131—22no—
47C24×C131—41no—
48C2×Q8×C131—22no—
49C2×Q8×C131—22no—
50C2×D4×C131—24no—
51C2×D4×C131—22no—
52C2×D4×C131—41no—
53C2×D4×C131—42no—
54C2×D4×C131—42no—
55C2×D4×C131—42no—
56C2×D4×C131—84no—
57C22×C4×C131—41no—
58C22×C4×C131C2×D412yes—
59C22×C4×C131C2×D411yescharacteristic
60SD16×C131—88no—
61C2×C8×C131—22no—
62C2×C8×C131—22no—
63C2×C8×C131—24no—
64C2×C8×C131SD1614yescomplemented
65C4⋊C4×C131—22no—
66C4⋊C4×C131—22no—
67C4⋊C4×C131—22no—
68C4⋊C4×C131—22no—
69C4⋊C4×C131—42no—
70C4⋊C4×C131—42no—
71C4⋊C4×C131—42no—
72C22⋊C4×C131—42no—
73C42×C131—42no—
74C42×C131C2×D412yes—
75C42×C131C2×D411yescharacteristic
76C42×C131#4111yescharacteristic
77C23×C131—42no—
78C23×C131—84no—
79C23×C131—81no—
80C23×C131—81no—
81C23×C131#12711yescharacteristic
82Q8×C131—44no—
83Q8×C131—82no—
84D4×C131—48no—
85D4×C131—44no—
86D4×C131—84no—
87D4×C131—82no—
88C2×C4×C131—42no—
89C2×C4×C131—42no—
90C2×C4×C131—42no—
91C2×C4×C131—82no—
92C2×C4×C131—81no—
93C2×C4×C131#12012yes—
94C2×C4×C131#12011yescharacteristic
95C2×C4×C131#12112yes—
96C2×C4×C131#12111yescharacteristic
97C2×C4×C131C2×SD1612yes—
98C2×C4×C131#13712yes—
99C8×C131—24no—
100C8×C131—44no—
101C22×C131—22no—
102C22×C131—84no—
103C22×C131—82no—
104C22×C131—162no—
105C22×C131—162no—
106C22×C131#39211yescharacteristic
107C22×C131#49211yescharacteristic
108C22×C131#49711yescharacteristic
109C4×C131—22no—
110C4×C131—22no—
111C4×C131—82no—
112C4×C131—82no—
113C4×C131—161no—
114C4×C131#44812yes—
115C4×C131#46112yes—
116C2×C131—21no—
117C2×C131—21no—
118C2×C131—162no—
119C2×C131#200812yes—
120C2×C131#201311yescharacteristic
121#10220C13111yesmaximal, characteristic, direct product factor, Sylow
122C131#1022011yescharacteristic, direct product factor, Sylow
123#3208C2×C13112yes—
124#3162C2×C13111yescharacteristic, complemented
125#1961C2×C13111yescharacteristic
126#1518C2×C13112yescomplemented
127#1281C2×C13111yescharacteristic, complemented
128#533C22×C13112yes—
129C2×#127C22×C13111yescharacteristic
130#501—22no—
131#501—22no—
132#492—22no—
133#486—22no—
134#460—24no—
135#450—24no—
136#431C22×C13112yes—
137#427—22no—
138C2×#102—22no—
139C2×#97C22×C13111yescharacteristic
140#382C22×C13111yescharacteristic
141#328—24no—
142C22×D4—21no—
143C22×D4—22no—
144C2×SD16—28no—
145C22×C8D4×C13112yes—
146C4⋊Q8D4×C13112yes—
147C4⋊Q8D4×C13112yes—
148#127—22no—
149#127—21no—
150#127D4×C13112yes—
151#125—22no—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156#117—22no—
157C2×C4⋊C4—21no—
158C2×C42C23×C13111yescharacteristic
159#107—24no—
160#106—22no—
161#106—22no—
162C4⋊C8—22no—
163#102—28no—
164#102—44no—
165C22⋊C8D4×C13114yes—
166#97—22no—
167C4×C8—22no—
168#95—22no—
169C24—41no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×D4—24no—
173C2×D4—22no—
174C2×D4—41no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—84no—
179C22×C4—41no—
180C22×C4C2×D4×C13112yes—
181C22×C4C2×D4×C13111yescharacteristic
182SD16—88no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—24no—
186C2×C8SD16×C13114yescomplemented
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C22⋊C4—42no—
195C42—42no—
196C42C2×D4×C13112yes—
197C42C2×D4×C13111yescharacteristic
198C42#41×C13111yescharacteristic
199C23—42no—
200C23—84no—
201C23—81no—
202C23—81no—
203C23#127×C13111yescharacteristic
204Q8—44no—
205Q8—82no—
206D4—48no—
207D4—44no—
208D4—84no—
209D4—82no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—82no—
214C2×C4—81no—
215C2×C4#120×C13112yes—
216C2×C4#120×C13111yescharacteristic
217C2×C4#121×C13112yes—
218C2×C4#121×C13111yescharacteristic
219C2×C4C2×SD16×C13112yes—
220C2×C4#137×C13112yes—
221C8—24no—
222C8—44no—
223C22—22no—
224C22—84no—
225C22—82no—
226C22—162no—
227C22—162no—
228C22#392×C13111yescharacteristic
229C22#492×C13111yescharacteristic
230C22#497×C13111yescharacteristic
231C4—22no—
232C4—22no—
233C4—82no—
234C4—82no—
235C4—161no—
236C4#448×C13112yes—
237C4#461×C13112yes—
238C2—21no—
239C2—21no—
240C2—162no—
241C2#2008×C13112yes—
242C2#2013×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC2×#127×C131C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3162×C131C2semidirect
4. #1518×C131C2semidirect
5. #1281×C131C2semidirect
64. C2×C8×C131SD16semidirect
121. #10220C131direct (N × H)
122. C131#10220direct (N × H)
124. #3162C2×C131semidirect
126. #1518C2×C131semidirect
127. #1281C2×C131semidirect
186. C2×C8SD16×C131semidirect

Maximal subgroups

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

subgroupindex
#3208×C1312
#3162×C1312
#1961×C1312
#1518×C1312
#1281×C1312
#10220131