Finite Group Databasebeta

← C13×#34346 #15720685

Subgroups — C13×#34346 #15720685

Order 3328.

2442 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#532C211yesmaximal, characteristic
2C13×#2381C212yesmaximal, complemented
3C13×#2380C212yesmaximal, complemented
4C13×#2379C214yesmaximal, complemented
5C13×#2377C218yesmaximal, complemented
6C13×#2297C214yesmaximal, complemented
7C13×#2290C218yesmaximal, complemented
8C13×#2283C212yesmaximal, complemented
9C22×C13×#41C2212yes—
10C13×#532C4116yescomplemented
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×C13×#127C2211yescharacteristic
13C2×C13×#124C2212yes—
14C2×C13×#121C2214yes—
15C2×C4×D4×C13C2214yes—
16C2×C13×#117C2214yes—
17C22×C42×C13C2214yes—
18C22×C42×C13C2211yescharacteristic
19C13×#391C2218yes—
20C13×#390C2218yes—
21C13×#388C22116yes—
22C13×#387C22116yes—
23C13×#386C22116yes—
24C13×#386C2218yes—
25C13×#386C2218yes—
26C13×#385C22116yes—
27C13×#383C2214yes—
28C13×#382C2214yes—
29C13×#381C2214yes—
30C13×#380C2214yes—
31C4×C13×C4⋊C4C2214yes—
32C4×C13×C22⋊C4C2214yes—
33C4×C13×C22⋊C4C2218yes—
34C13×#376C2214yes—
35C2×C13×#41—44no—
36C2×C13×#41—44no—
37C2×C13×#41C2×C4116yescomplemented
38C22×Q8×C13C2312yes—
39C22×D4×C13C2314yes—
40C22×D4×C13C2312yes—
41C22×D4×C13C2314yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2314yes—
44C23×C4×C13C2318yes—
45C23×C4×C13C2312yes—
46C13×C4⋊Q8C2×C418yescomplemented
47C13×#127C2×C418yes—
48C13×#124C2×C4116yescomplemented
49C13×#121C2×C4132yescomplemented
50C4×D4×C13C2×C4132yescomplemented
51C13×#117—48no—
52C2×C13×C4⋊C4C2318yes—
53C2×C13×C4⋊C4C2318yes—
54C2×C13×C4⋊C4C2314yes—
55C2×C13×C22⋊C4C2318yes—
56C2×C13×C22⋊C4C23116yes—
57C2×C13×C22⋊C4C2318yes—
58C2×C13×C22⋊C4C2318yes—
59C2×C42×C13—48no—
60C2×C42×C13C2×C418yescomplemented
61C2×C42×C13C2318yes—
62C2×C42×C13C2318yes—
63C2×C42×C13C2311yescharacteristic
64C2×C42×C13C2311yescharacteristic
65C2×C42×C13C2312yes—
66C13×#95C2318yes—
67C13×#95C23116yes—
68C13×#95C2318yes—
69C13×#95C2318yes—
70C13×#95C2318yes—
71#34346C1311yesmaximal, characteristic, direct product factor, Sylow
72C24×C13C2414yes—
73C24×C13C2411yescharacteristic
74C13×#41—432no—
75C2×Q8×C13—42no—
76C2×Q8×C13—42no—
77C2×Q8×C13C22×C418yes—
78C2×D4×C13—48no—
79C2×D4×C13—44no—
80C2×D4×C13—44no—
81C2×D4×C13—42no—
82C2×D4×C13—42no—
83C2×D4×C13C22×C4116yes—
84C2×D4×C13C22×C4116yes—
85C2×D4×C13C22×C418yes—
86C22×C4×C13—28no—
87C22×C4×C13—28no—
88C22×C4×C13—24no—
89C22×C4×C13—48no—
90C22×C4×C13—44no—
91C22×C4×C13—416no—
92C22×C4×C13C22×C414yes—
93C22×C4×C13C22×C4116yes—
94C22×C4×C13C22×C418yes—
95C22×C4×C13C24116yes—
96C22×C4×C13C2412yes—
97C22×C4×C13C2411yescharacteristic
98C22×C4×C13C2412yes—
99C22×C4×C13C2414yes—
100C22×C4×C13C2411yescharacteristic
101C13×C4⋊C4—48no—
102C13×C4⋊C4—48no—
103C13×C4⋊C4C22×C4116yes—
104C13×C22⋊C4—48no—
105C13×C22⋊C4—416no—
106C13×C22⋊C4—48no—
107C13×C22⋊C4C22×C4132yes—
108C42×C13—216no—
109C42×C13—48no—
110C42×C13C22×C418yes—
111C42×C13C22×C414yes—
112C42×C13C22×C414yes—
113C2×#532C2×C1311yescharacteristic
114#2381C2×C1312yescomplemented
115#2380C2×C1312yescomplemented
116#2379C2×C1314yescomplemented
117#2377C2×C1318yescomplemented
118#2297C2×C1314yescomplemented
119#2290C2×C1318yescomplemented
120#2283C2×C1312yescomplemented
121C23×C13—24no—
122C23×C13—24no—
123C23×C13—22no—
124C23×C13—24no—
125C23×C13—216no—
126C23×C13C23×C418yes—
127C23×C13C23×C412yes—
128C23×C13C2511yescharacteristic
129Q8×C13—48no—
130D4×C13—416no—
131D4×C13—48no—
132D4×C13—416no—
133C2×C4×C13—24no—
134C2×C4×C13—24no—
135C2×C4×C13—22no—
136C2×C4×C13—24no—
137C2×C4×C13—24no—
138C2×C4×C13—232no—
139C2×C4×C13—28no—
140C2×C4×C13—216no—
141C2×C4×C13—216no—
142C2×C4×C13—216no—
143C2×C4×C13—48no—
144C2×C4×C13—432no—
145C2×C4×C13C23×C414yes—
146C2×C4×C13C23×C414yes—
147C2×C4×C13C23×C412yes—
148C2×C4×C13C23×C418yes—
149C2×C4×C13C23×C412yes—
150C2×C4×C13H(5,𝔽2)14yes—
151C22×#41C22×C1312yes—
152#532C4×C13116yescomplemented
153C2×C4⋊Q8C22×C1311yescharacteristic
154C2×#127C22×C1311yescharacteristic
155C2×#124C22×C1312yes—
156C2×#121C22×C1314yes—
157C2×C4×D4C22×C1314yes—
158C2×#117C22×C1314yes—
159C22×C42C22×C1314yes—
160C22×C42C22×C1311yescharacteristic
161#391C22×C1318yes—
162#390C22×C1318yes—
163#388C22×C13116yes—
164#387C22×C13116yes—
165#386C22×C1318yes—
166#386C22×C13116yes—
167#386C22×C1318yes—
168#385C22×C13116yes—
169#383C22×C1314yes—
170#382C22×C1314yes—
171#381C22×C1314yes—
172#380C22×C1314yes—
173C4×C4⋊C4C22×C1314yes—
174C4×C22⋊C4C22×C1314yes—
175C4×C22⋊C4C22×C1318yes—
176#376C22×C1314yes—
177C22×C13—22no—
178C22×C13—28no—
179C22×C13—24no—
180C22×C13—216no—
181C22×C13—48no—
182C22×C13—48no—
183C22×C13—44no—
184C22×C13C24×C411yescharacteristic
185C22×C13C2×H(5,𝔽2)12yes—
186C22×C13#58514yes—
187C4×C13—22no—
188C4×C13—28no—
189C4×C13—24no—
190C4×C13—24no—
191C4×C13—416no—
192C4×C13#51814yes—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41C2×C4×C13116yescomplemented
196C22×Q8C23×C1312yes—
197C22×D4C23×C1314yes—
198C22×D4C23×C1314yes—
199C22×D4C23×C1312yes—
200C23×C4C23×C1314yes—
201C23×C4C23×C1311yescharacteristic
202C23×C4C23×C1318yes—
203C23×C4C23×C1312yes—
204C4⋊Q8C2×C4×C1318yescomplemented
205#127C2×C4×C1318yes—
206#124C2×C4×C13116yescomplemented
207#121C2×C4×C13132yescomplemented
208C4×D4C2×C4×C13132yescomplemented
209#117—48no—
210C2×C4⋊C4C23×C1318yes—
211C2×C4⋊C4C23×C1318yes—
212C2×C4⋊C4C23×C1314yes—
213C2×C22⋊C4C23×C1318yes—
214C2×C22⋊C4C23×C1318yes—
215C2×C22⋊C4C23×C13116yes—
216C2×C22⋊C4C23×C1318yes—
217C2×C42—48no—
218C2×C42C2×C4×C1318yescomplemented
219C2×C42C23×C1318yes—
220C2×C42C23×C1318yes—
221C2×C42C23×C1312yes—
222C2×C42C23×C1311yescharacteristic
223C2×C42C23×C1311yescharacteristic
224#95C23×C1318yes—
225#95C23×C1318yes—
226#95C23×C1318yes—
227#95C23×C13116yes—
228#95C23×C1318yes—
229C2×C13—42no—
230C2×C13—48no—
231C2×C13C2×#51811yescharacteristic
232C2×C13#342812yes—
233C2×C13#352914yes—
234C24C24×C1314yes—
235C24C24×C1311yescharacteristic
236#41—432no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8C22×C4×C1318yes—
240C2×D4—44no—
241C2×D4—44no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—48no—
245C2×D4C22×C4×C13116yes—
246C2×D4C22×C4×C13116yes—
247C2×D4C22×C4×C1318yes—
248C22×C4—28no—
249C22×C4—28no—
250C22×C4—24no—
251C22×C4—48no—
252C22×C4—44no—
253C22×C4—416no—
254C22×C4C22×C4×C1314yes—
255C22×C4C22×C4×C13116yes—
256C22×C4C22×C4×C1318yes—
257C22×C4C24×C13116yes—
258C22×C4C24×C1312yes—
259C22×C4C24×C1311yescharacteristic
260C22×C4C24×C1312yes—
261C22×C4C24×C1314yes—
262C22×C4C24×C1311yescharacteristic
263C4⋊C4—48no—
264C4⋊C4—48no—
265C4⋊C4C22×C4×C13116yes—
266C22⋊C4—48no—
267C22⋊C4—48no—
268C22⋊C4—416no—
269C22⋊C4C22×C4×C13132yes—
270C42—216no—
271C42—48no—
272C42C22×C4×C1318yes—
273C42C22×C4×C1314yes—
274C42C22×C4×C1314yes—
275C13#3434611yescharacteristic, direct product factor, Sylow
276C23—24no—
277C23—24no—
278C23—22no—
279C23—24no—
280C23—216no—
281C23C23×C4×C1318yes—
282C23C23×C4×C1312yes—
283C23C25×C1311yescharacteristic
284Q8—48no—
285D4—416no—
286D4—48no—
287D4—416no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—232no—
294C2×C4—28no—
295C2×C4—216no—
296C2×C4—216no—
297C2×C4—216no—
298C2×C4—48no—
299C2×C4—432no—
300C2×C4C23×C4×C1314yes—
301C2×C4C23×C4×C1314yes—
302C2×C4C23×C4×C1312yes—
303C2×C4C23×C4×C1318yes—
304C2×C4C23×C4×C1312yes—
305C2×C4C13×H(5,𝔽2)14yes—
306C22—22no—
307C22—28no—
308C22—24no—
309C22—216no—
310C22—48no—
311C22—48no—
312C22—44no—
313C22C24×C4×C1311yescharacteristic
314C22C2×C13×H(5,𝔽2)12yes—
315C22C13×#58514yes—
316C4—22no—
317C4—28no—
318C4—24no—
319C4—24no—
320C4—416no—
321C4C13×#51814yes—
322C2—42no—
323C2—48no—
324C2C2×C13×#51811yescharacteristic
325C2C13×#342812yes—
326C2C13×#352914yes—
subgroupG/H
centerC22×C4×C13C24
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC2×C13×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2381C2semidirect
3. C13×#2380C2semidirect
4. C13×#2379C2semidirect
5. C13×#2377C2semidirect
6. C13×#2297C2semidirect
7. C13×#2290C2semidirect
8. C13×#2283C2semidirect
10. C13×#532C4semidirect
37. C2×C13×#41C2×C4semidirect
46. C13×C4⋊Q8C2×C4semidirect
48. C13×#124C2×C4semidirect
49. C13×#121C2×C4semidirect
50. C4×D4×C13C2×C4semidirect
60. C2×C42×C13C2×C4semidirect
71. #34346C13direct (N × H)
114. #2381C2×C13semidirect
115. #2380C2×C13semidirect
116. #2379C2×C13semidirect
117. #2377C2×C13semidirect
118. #2297C2×C13semidirect
119. #2290C2×C13semidirect
120. #2283C2×C13semidirect
152. #532C4×C13semidirect
195. C2×#41C2×C4×C13semidirect
204. C4⋊Q8C2×C4×C13semidirect
206. #124C2×C4×C13semidirect
207. #121C2×C4×C13semidirect
208. C4×D4C2×C4×C13semidirect
218. C2×C42C2×C4×C13semidirect
275. C13#34346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5322
C13×#23812
C13×#23802
C13×#23792
C13×#23772
C13×#22972
C13×#22902
C13×#22832
#3434613