Finite Group Databasebeta

← C13×#34177 #15720516

Subgroups — C13×#34177 #15720516

Order 3328.

2446 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
1C22×C13×#117C211yesmaximal, characteristic
2C13×#2343C2116yesmaximal, complemented
3C13×#2315C212yesmaximal
4C13×#2313C214yesmaximal, complemented
5C13×#2283C214yesmaximal, complemented
6C2×C13×#381C212yesmaximal
7C13×#2273C212yesmaximal
8C24×C4×C13C2211yescharacteristic
9C2×C13×#117C4116yescomplemented
10C2×C13×#117C2218yes—
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C22⋊C4C2214yes—
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C42×C13C2212yes—
16C13×#387C22132yescomplemented
17C13×#385C22116yes—
18C13×#383C2218yescomplemented
19C13×#382C2218yescomplemented
20C13×#381C2214yes—
21C13×#381C2214yes—
22C13×#381C2218yes—
23C13×#380C2218yes—
24C4×C13×C4⋊C4C2218yescomplemented
25C4×C13×C22⋊C4C2218yes—
26C4×C13×C22⋊C4C22116yes—
27C13×#376C2218yescomplemented
28C2×C13×#95C2218yes—
29C25×C13C2311yescharacteristic
30C23×C4×C13—28no—
31C23×C4×C13C2×C418yes—
32C23×C4×C13C2311yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C23×C4×C13C2314yes—
35C23×C4×C13C2318yes—
36C23×C4×C13C2312yes—
37C23×C4×C13C2312yes—
38C13×#117C2×C4164yescomplemented
39C2×C13×C4⋊C4C2×C4116yescomplemented
40C2×C13×C4⋊C4C23116yes—
41C2×C13×C4⋊C4C2318yes—
42C2×C13×C22⋊C4—216no—
43C2×C13×C22⋊C4C2×C418yes—
44C2×C13×C22⋊C4C2×C418yes—
45C2×C13×C22⋊C4C2318yes—
46C2×C13×C22⋊C4C2318yes—
47C2×C13×C22⋊C4C2314yes—
48C2×C13×C22⋊C4C2314yes—
49C2×C42×C13C2×C4116yescomplemented
50C2×C42×C13C23116yes—
51C2×C42×C13C2314yes—
52C2×C42×C13C2314yes—
53C13×#95C23116yes—
54C13×#95C23116yes—
55C13×#95C23116yes—
56C13×#95C23116yes—
57#34177C1311yesmaximal, characteristic, direct product factor, Sylow
58C24×C13—44no—
59C24×C13C22×C414yes—
60C24×C13#4118yes—
61C24×C13C2412yes—
62C24×C13C2411yescharacteristic
63C22×C4×C13—232no—
64C22×C4×C13—24no—
65C22×C4×C13—24no—
66C22×C4×C13—216no—
67C22×C4×C13—216no—
68C22×C4×C13—44no—
69C22×C4×C13—44no—
70C22×C4×C13—416no—
71C22×C4×C13C22×C414yes—
72C22×C4×C13C22×C414yes—
73C22×C4×C13C22×C4116yes—
74C22×C4×C13C22×C418yes—
75C22×C4×C13C22×C418yes—
76C22×C4×C13C24116yes—
77C22×C4×C13C2412yes—
78C22×C4×C13C2412yes—
79C22×C4×C13C2414yes—
80C22×C4×C13C2414yes—
81C13×C4⋊C4—416no—
82C13×C4⋊C4C22×C4132yes—
83C13×C22⋊C4—216no—
84C13×C22⋊C4—216no—
85C13×C22⋊C4C22×C4116yes—
86C13×C22⋊C4C22×C4116yes—
87C42×C13—416no—
88C42×C13C22×C4116yes—
89C42×C13C22×C4116yes—
90C22×#117C2×C1311yescharacteristic
91#2343C2×C13116yescomplemented
92#2315C2×C1312yes—
93#2313C2×C1314yescomplemented
94#2283C2×C1314yescomplemented
95C2×#381C2×C1312yes—
96#2273C2×C1312yes—
97C23×C13—24no—
98C23×C13—28no—
99C23×C13—48no—
100C23×C13—416no—
101C23×C13#117116yes—
102C23×C13C23×C414yes—
103C23×C13C23×C412yes—
104C23×C13C2×#4114yes—
105C23×C13C2×#4118yes—
106C23×C13C2511yescharacteristic
107C2×C4×C13—28no—
108C2×C4×C13—28no—
109C2×C4×C13—232no—
110C2×C4×C13—24no—
111C2×C4×C13—24no—
112C2×C4×C13—28no—
113C2×C4×C13—28no—
114C2×C4×C13—216no—
115C2×C4×C13—232no—
116C2×C4×C13—48no—
117C2×C4×C13—48no—
118C2×C4×C13—816no—
119C2×C4×C13C23×C414yes—
120C2×C4×C13C23×C418yes—
121C2×C4×C13C23×C418yes—
122C2×C4×C13C23×C414yes—
123C24×C4C22×C1311yescharacteristic
124C2×#117C4×C13116yescomplemented
125C2×#117C22×C1318yes—
126C22×C4⋊C4C22×C1312yes—
127C22×C22⋊C4C22×C1314yes—
128C22×C22⋊C4C22×C1311yescharacteristic
129C22×C22⋊C4C22×C1311yescharacteristic
130C22×C42C22×C1312yes—
131#387C22×C13132yescomplemented
132#385C22×C13116yes—
133#383C22×C1318yescomplemented
134#382C22×C1318yescomplemented
135#381C22×C1314yes—
136#381C22×C1318yes—
137#381C22×C1314yes—
138#380C22×C1318yes—
139C4×C4⋊C4C22×C1318yescomplemented
140C4×C22⋊C4C22×C1318yes—
141C4×C22⋊C4C22×C13116yes—
142#376C22×C1318yescomplemented
143C2×#95C22×C1318yes—
144C22×C13—24no—
145C22×C13—28no—
146C22×C13—216no—
147C22×C13—28no—
148C22×C13—416no—
149C22×C13C2×#11718yes—
150C22×C13C2×#11714yes—
151C22×C13C24×C411yescharacteristic
152C22×C13C22×#4112yes—
153C22×C13#58514yes—
154C4×C13—24no—
155C4×C13—24no—
156C4×C13—28no—
157C4×C13—28no—
158C4×C13—416no—
159C25C23×C1311yescharacteristic
160C23×C4—28no—
161C23×C4C2×C4×C1318yes—
162C23×C4C23×C1311yescharacteristic
163C23×C4C23×C1314yes—
164C23×C4C23×C1311yescharacteristic
165C23×C4C23×C1318yes—
166C23×C4C23×C1312yes—
167C23×C4C23×C1312yes—
168#117C2×C4×C13164yescomplemented
169C2×C4⋊C4C2×C4×C13116yescomplemented
170C2×C4⋊C4C23×C13116yes—
171C2×C4⋊C4C23×C1318yes—
172C2×C22⋊C4—216no—
173C2×C22⋊C4C2×C4×C1318yes—
174C2×C22⋊C4C2×C4×C1318yes—
175C2×C22⋊C4C23×C1318yes—
176C2×C22⋊C4C23×C1318yes—
177C2×C22⋊C4C23×C1314yes—
178C2×C22⋊C4C23×C1314yes—
179C2×C42C2×C4×C13116yescomplemented
180C2×C42C23×C13116yes—
181C2×C42C23×C1314yes—
182C2×C42C23×C1314yes—
183#95C23×C13116yes—
184#95C23×C13116yes—
185#95C23×C13116yes—
186#95C23×C13116yes—
187C2×C13—24no—
188C2×C13—28no—
189C2×C13C22×#11711yescharacteristic
190C2×C13#342812yes—
191C2×C13#349114yes—
192C24—44no—
193C24C22×C4×C1314yes—
194C24C13×#4118yes—
195C24C24×C1312yes—
196C24C24×C1311yescharacteristic
197C22×C4—232no—
198C22×C4—24no—
199C22×C4—24no—
200C22×C4—216no—
201C22×C4—216no—
202C22×C4—44no—
203C22×C4—44no—
204C22×C4—416no—
205C22×C4C22×C4×C1314yes—
206C22×C4C22×C4×C1314yes—
207C22×C4C22×C4×C13116yes—
208C22×C4C22×C4×C1318yes—
209C22×C4C22×C4×C1318yes—
210C22×C4C24×C13116yes—
211C22×C4C24×C1312yes—
212C22×C4C24×C1312yes—
213C22×C4C24×C1314yes—
214C22×C4C24×C1314yes—
215C4⋊C4—416no—
216C4⋊C4C22×C4×C13132yes—
217C22⋊C4—216no—
218C22⋊C4—216no—
219C22⋊C4C22×C4×C13116yes—
220C22⋊C4C22×C4×C13116yes—
221C42—416no—
222C42C22×C4×C13116yes—
223C42C22×C4×C13116yes—
224C13#3417711yescharacteristic, direct product factor, Sylow
225C23—24no—
226C23—28no—
227C23—48no—
228C23—416no—
229C23C13×#117116yes—
230C23C23×C4×C1314yes—
231C23C23×C4×C1312yes—
232C23C2×C13×#4114yes—
233C23C2×C13×#4118yes—
234C23C25×C1311yescharacteristic
235C2×C4—28no—
236C2×C4—28no—
237C2×C4—232no—
238C2×C4—24no—
239C2×C4—24no—
240C2×C4—28no—
241C2×C4—28no—
242C2×C4—216no—
243C2×C4—232no—
244C2×C4—48no—
245C2×C4—48no—
246C2×C4—816no—
247C2×C4C23×C4×C1314yes—
248C2×C4C23×C4×C1318yes—
249C2×C4C23×C4×C1318yes—
250C2×C4C23×C4×C1314yes—
251C22—24no—
252C22—28no—
253C22—216no—
254C22—28no—
255C22—416no—
256C22C2×C13×#11718yes—
257C22C2×C13×#11714yes—
258C22C24×C4×C1311yescharacteristic
259C22C22×C13×#4112yes—
260C22C13×#58514yes—
261C4—24no—
262C4—24no—
263C4—28no—
264C4—28no—
265C4—416no—
266C2—24no—
267C2—28no—
268C2C22×C13×#11711yescharacteristic
269C2C13×#342812yes—
270C2C13×#349114yes—
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC25×C13C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2343C2semidirect
4. C13×#2313C2semidirect
5. C13×#2283C2semidirect
9. C2×C13×#117C4semidirect
16. C13×#387C22semidirect
18. C13×#383C22semidirect
19. C13×#382C22semidirect
24. C4×C13×C4⋊C4C22semidirect
27. C13×#376C22semidirect
38. C13×#117C2×C4semidirect
39. C2×C13×C4⋊C4C2×C4semidirect
49. C2×C42×C13C2×C4semidirect
57. #34177C13direct (N × H)
91. #2343C2×C13semidirect
93. #2313C2×C13semidirect
94. #2283C2×C13semidirect
124. C2×#117C4×C13semidirect
131. #387C22×C13semidirect
133. #383C22×C13semidirect
134. #382C22×C13semidirect
139. C4×C4⋊C4C22×C13semidirect
142. #376C22×C13semidirect
168. #117C2×C4×C13semidirect
169. C2×C4⋊C4C2×C4×C13semidirect
179. C2×C42C2×C4×C13semidirect
224. C13#34177direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1172
C13×#23432
C13×#23152
C13×#23132
C13×#22832
C2×C13×#3812
C13×#22732
#3417713