Finite Group Databasebeta

← C13×#34530 #15720869

Subgroups — C13×#34530 #15720869

Order 3328.

1800 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
1C2×C13×#564C211yesmaximal, characteristic
2C13×#2382C213yesmaximal
3C13×#2371C216yesmaximal
4C13×#2370C216yesmaximal
5C13×#2336C216yesmaximal
6C13×#2330C216yesmaximal
7C4×C13×#125C213yesmaximal
8C13×#564C4116yescomplemented
9C2×C13×#125C2213yes—
10C2×C13×#125C2216yes—
11C2×C13×#125C2216yes—
12C13×#389C2213yes—
13C13×#389C2213yes—
14C13×#389C2216yes—
15C13×#389C2216yes—
16C13×#389C2216yes—
17C13×#389C2216yes—
18C13×#387C2216yes—
19C13×#387C2216yes—
20C13×#387C2216yes—
21C13×#387C2216yes—
22C13×#387C2216yes—
23C13×#387C2216yes—
24C13×#387C2216yes—
25C13×#387C2216yes—
26C13×#387C2216yes—
27C13×#387C2216yes—
28C13×#384C2212yes—
29C13×#383C2212yes—
30C13×#382C2213yes—
31C4×C13×C4⋊C4C2216yes—
32C4×C13×C4⋊C4C2213yes—
33C4×C13×C4⋊C4C2216yes—
34C4×C13×C4⋊C4C2213yes—
35C4×C13×C4⋊C4C2216yes—
36C4×C13×C4⋊C4C2216yes—
37C4×C13×C4⋊C4C2216yes—
38C13×#376C2216yes—
39C43×C13C2211yescharacteristic
40C13×#125C2×C4124yes—
41C13×#125C2×C4148yes—
42C13×#125C2×C4148yes—
43C2×C13×C4⋊C4C2316yes—
44C2×C13×C4⋊C4C2313yes—
45C2×C13×C4⋊C4C2313yes—
46C2×C13×C4⋊C4C2316yes—
47C2×C13×C4⋊C4C2316yes—
48C2×C13×C4⋊C4C2316yes—
49C2×C13×C4⋊C4C2316yes—
50C2×C13×C4⋊C4C2313yes—
51C2×C13×C4⋊C4C2316yes—
52C2×C13×C4⋊C4C2313yes—
53C2×C13×C4⋊C4C2316yes—
54C2×C13×C4⋊C4C2316yes—
55C2×C42×C13C2313yes—
56C2×C42×C13C2316yes—
57C2×C42×C13C2316yes—
58C2×C42×C13C2316yes—
59C2×C42×C13C2313yes—
60C2×C42×C13C2316yes—
61C2×C42×C13C2312yes—
62C2×C42×C13C2311yescharacteristic
63C2×C42×C13C2312yes—
64C13×#95C2316yes—
65C13×#95C2316yes—
66C13×#95C2316yes—
67C13×#95C2316yes—
68C13×#95C2316yes—
69C13×#95C2316yes—
70C13×#95C2316yes—
71C13×#95C2316yes—
72C13×#95C2316yes—
73C13×#95C2316yes—
74#34530C1311yesmaximal, characteristic, direct product factor, Sylow
75C22×C4×C13C2416yes—
76C22×C4×C13C2416yes—
77C22×C4×C13C2411yescharacteristic
78C22×C4×C13C2416yes—
79C22×C4×C13C2413yes—
80C22×C4×C13C2416yes—
81C22×C4×C13C2413yes—
82C13×C4⋊C4—212no—
83C13×C4⋊C4—46no—
84C13×C4⋊C4—43no—
85C13×C4⋊C4—46no—
86C13×C4⋊C4—46no—
87C13×C4⋊C4—43no—
88C13×C4⋊C4C22×C4124yes—
89C13×C4⋊C4C22×C4112yes—
90C13×C4⋊C4C22×C4124yes—
91C13×C4⋊C4C22×C4112yes—
92C13×C4⋊C4C22×C4124yes—
93C13×C4⋊C4C22×C4124yes—
94C42×C13—26no—
95C42×C13—212no—
96C42×C13—46no—
97C42×C13—43no—
98C42×C13—46no—
99C42×C13—46no—
100C42×C13C22×C418yes—
101C42×C13C22×C414yes—
102C42×C13C22×C418yes—
103C2×#564C2×C1311yescharacteristic
104#2382C2×C1313yes—
105#2371C2×C1316yes—
106#2370C2×C1316yes—
107#2336C2×C1316yes—
108#2330C2×C1316yes—
109C4×#125C2×C1313yes—
110C23×C13C2511yescharacteristic
111C2×C4×C13—23no—
112C2×C4×C13—26no—
113C2×C4×C13—23no—
114C2×C4×C13—26no—
115C2×C4×C13—23no—
116C2×C4×C13—26no—
117C2×C4×C13—23no—
118C2×C4×C13—26no—
119C2×C4×C13—26no—
120C2×C4×C13—26no—
121C2×C4×C13—26no—
122C2×C4×C13—26no—
123C2×C4×C13—26no—
124C2×C4×C13—23no—
125C2×C4×C13—26no—
126C2×C4×C13C23×C416yes—
127C2×C4×C13C23×C4112yes—
128C2×C4×C13C23×C4112yes—
129C2×C4×C132−1+416yes—
130#564C4×C13116yescomplemented
131C2×#125C22×C1313yes—
132C2×#125C22×C1316yes—
133C2×#125C22×C1316yes—
134#389C22×C1313yes—
135#389C22×C1313yes—
136#389C22×C1316yes—
137#389C22×C1316yes—
138#389C22×C1316yes—
139#389C22×C1316yes—
140#387C22×C1316yes—
141#387C22×C1316yes—
142#387C22×C1316yes—
143#387C22×C1316yes—
144#387C22×C1316yes—
145#387C22×C1316yes—
146#387C22×C1316yes—
147#387C22×C1316yes—
148#387C22×C1316yes—
149#387C22×C1316yes—
150#384C22×C1312yes—
151#383C22×C1312yes—
152#382C22×C1313yes—
153C4×C4⋊C4C22×C1316yes—
154C4×C4⋊C4C22×C1313yes—
155C4×C4⋊C4C22×C1316yes—
156C4×C4⋊C4C22×C1313yes—
157C4×C4⋊C4C22×C1316yes—
158C4×C4⋊C4C22×C1316yes—
159C4×C4⋊C4C22×C1316yes—
160#376C22×C1316yes—
161C43C22×C1311yescharacteristic
162C22×C13C24×C411yescharacteristic
163C22×C13C2×2−1+413yes—
164C22×C13#58513yes—
165C4×C13—26no—
166C4×C13—212no—
167C4×C13—212no—
168C4×C13—26no—
169C4×C13—46no—
170C4×C13—46no—
171C4×C13—41no—
172#125C2×C4×C13124yes—
173#125C2×C4×C13148yes—
174#125C2×C4×C13148yes—
175C2×C4⋊C4C23×C1316yes—
176C2×C4⋊C4C23×C1313yes—
177C2×C4⋊C4C23×C1313yes—
178C2×C4⋊C4C23×C1316yes—
179C2×C4⋊C4C23×C1316yes—
180C2×C4⋊C4C23×C1316yes—
181C2×C4⋊C4C23×C1313yes—
182C2×C4⋊C4C23×C1316yes—
183C2×C4⋊C4C23×C1316yes—
184C2×C4⋊C4C23×C1313yes—
185C2×C4⋊C4C23×C1316yes—
186C2×C4⋊C4C23×C1316yes—
187C2×C42C23×C1313yes—
188C2×C42C23×C1316yes—
189C2×C42C23×C1313yes—
190C2×C42C23×C1316yes—
191C2×C42C23×C1316yes—
192C2×C42C23×C1316yes—
193C2×C42C23×C1311yescharacteristic
194C2×C42C23×C1312yes—
195C2×C42C23×C1312yes—
196#95C23×C1316yes—
197#95C23×C1316yes—
198#95C23×C1316yes—
199#95C23×C1316yes—
200#95C23×C1316yes—
201#95C23×C1316yes—
202#95C23×C1316yes—
203#95C23×C1316yes—
204#95C23×C1316yes—
205#95C23×C1316yes—
206C2×C13C4×2−1+413yes—
207C2×C13#356313yes—
208C2×C13#356711yescharacteristic
209C22×C4C24×C1316yes—
210C22×C4C24×C1316yes—
211C22×C4C24×C1311yescharacteristic
212C22×C4C24×C1316yes—
213C22×C4C24×C1313yes—
214C22×C4C24×C1316yes—
215C22×C4C24×C1313yes—
216C4⋊C4—212no—
217C4⋊C4—46no—
218C4⋊C4—43no—
219C4⋊C4—46no—
220C4⋊C4—46no—
221C4⋊C4—43no—
222C4⋊C4C22×C4×C13112yes—
223C4⋊C4C22×C4×C13124yes—
224C4⋊C4C22×C4×C13124yes—
225C4⋊C4C22×C4×C13112yes—
226C4⋊C4C22×C4×C13124yes—
227C4⋊C4C22×C4×C13124yes—
228C42—26no—
229C42—212no—
230C42—46no—
231C42—43no—
232C42—46no—
233C42—46no—
234C42C22×C4×C1314yes—
235C42C22×C4×C1318yes—
236C42C22×C4×C1318yes—
237C13#3453011yescharacteristic, direct product factor, Sylow
238C23C25×C1311yescharacteristic
239C2×C4—23no—
240C2×C4—23no—
241C2×C4—26no—
242C2×C4—26no—
243C2×C4—23no—
244C2×C4—26no—
245C2×C4—23no—
246C2×C4—26no—
247C2×C4—26no—
248C2×C4—26no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—26no—
252C2×C4—23no—
253C2×C4—26no—
254C2×C4C23×C4×C1316yes—
255C2×C4C23×C4×C13112yes—
256C2×C4C23×C4×C13112yes—
257C2×C4C13×2−1+416yes—
258C22C24×C4×C1311yescharacteristic
259C22C2×C13×2−1+413yes—
260C22C13×#58513yes—
261C4—26no—
262C4—26no—
263C4—212no—
264C4—212no—
265C4—46no—
266C4—46no—
267C4—41no—
268C2C4×C13×2−1+413yes—
269C2C13×#356313yes—
270C2C13×#356711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
8. C13×#564C4semidirect
74. #34530C13direct (N × H)
130. #564C4×C13semidirect
237. C13#34530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5642
C13×#23822
C13×#23712
C13×#23702
C13×#23362
C13×#23302
C4×C13×#1252
#3453013