Finite Group Databasebeta

← C13×#34369 #15720708

Subgroups — C13×#34369 #15720708

Order 3328.

2410 conjugacy classes of subgroups.

The subgroup lattice has 334 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×#2372C214yesmaximal, complemented
5C13×#2352C218yesmaximal, complemented
6C13×#2333C218yesmaximal, complemented
7C13×#2311C214yesmaximal, 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×C13×C4⋊C4C2214yes—
18C22×C42×C13C2211yescharacteristic
19C13×#391C2218yes—
20C13×#390C2218yes—
21C13×#388C22116yes—
22C13×#387C22116yes—
23C13×#386C2218yes—
24C13×#386C2218yes—
25C13×#386C22116yes—
26C13×#383C2214yes—
27C13×#382C2214yes—
28C13×#381C2214yes—
29C13×#380C2214yes—
30C13×#380C2218yes—
31C4×C13×C4⋊C4C2214yes—
32C4×C13×C22⋊C4C2214yes—
33C4×C13×C22⋊C4C22116yes—
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⋊C4—48no—
53C2×C13×C4⋊C4C2318yes—
54C2×C13×C4⋊C4C2318yes—
55C2×C13×C4⋊C4C2314yes—
56C2×C13×C22⋊C4C2318yes—
57C2×C13×C22⋊C4C23116yes—
58C2×C13×C22⋊C4C2318yes—
59C2×C13×C22⋊C4C2318yes—
60C2×C42×C13C2×C418yescomplemented
61C2×C42×C13C2318yes—
62C2×C42×C13C2318yes—
63C2×C42×C13C2312yes—
64C2×C42×C13C2311yescharacteristic
65C2×C42×C13C2311yescharacteristic
66C13×#95C2318yes—
67C13×#95C23116yes—
68C13×#95C2318yes—
69C13×#95C2318yes—
70C13×#95C2318yes—
71#34369C1311yesmaximal, 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—44no—
79C2×D4×C13—44no—
80C2×D4×C13—44no—
81C2×D4×C13—44no—
82C2×D4×C13—42no—
83C2×D4×C13—42no—
84C2×D4×C13C22×C4116yes—
85C2×D4×C13C22×C4116yes—
86C2×D4×C13C22×C418yes—
87C22×C4×C13—28no—
88C22×C4×C13—28no—
89C22×C4×C13—24no—
90C22×C4×C13—44no—
91C22×C4×C13—48no—
92C22×C4×C13—416no—
93C22×C4×C13C22×C414yes—
94C22×C4×C13C22×C4116yes—
95C22×C4×C13C22×C418yes—
96C22×C4×C13C24116yes—
97C22×C4×C13C2412yes—
98C22×C4×C13C2411yescharacteristic
99C22×C4×C13C2412yes—
100C22×C4×C13C2414yes—
101C22×C4×C13C2411yescharacteristic
102C13×C4⋊C4—216no—
103C13×C4⋊C4—48no—
104C13×C4⋊C4C22×C4116yes—
105C13×C22⋊C4—416no—
106C13×C22⋊C4—48no—
107C13×C22⋊C4—48no—
108C13×C22⋊C4C22×C4132yes—
109C42×C13—48no—
110C42×C13—48no—
111C42×C13C22×C418yes—
112C42×C13C22×C414yes—
113C42×C13C22×C414yes—
114C2×#532C2×C1311yescharacteristic
115#2381C2×C1312yescomplemented
116#2380C2×C1312yescomplemented
117#2372C2×C1314yescomplemented
118#2352C2×C1318yescomplemented
119#2333C2×C1318yescomplemented
120#2311C2×C1314yescomplemented
121#2283C2×C1312yescomplemented
122C23×C13—24no—
123C23×C13—24no—
124C23×C13—22no—
125C23×C13—24no—
126C23×C13—28no—
127C23×C13—28no—
128C23×C13C23×C418yes—
129C23×C13C23×C412yes—
130C23×C13C2511yescharacteristic
131Q8×C13—48no—
132D4×C13—416no—
133D4×C13—48no—
134D4×C13—416no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—22no—
138C2×C4×C13—24no—
139C2×C4×C13—24no—
140C2×C4×C13—232no—
141C2×C4×C13—28no—
142C2×C4×C13—216no—
143C2×C4×C13—216no—
144C2×C4×C13—216no—
145C2×C4×C13—48no—
146C2×C4×C13—816no—
147C2×C4×C13C23×C414yes—
148C2×C4×C13C23×C414yes—
149C2×C4×C13C23×C412yes—
150C2×C4×C13C23×C418yes—
151C2×C4×C13C23×C412yes—
152C2×C4×C13H(5,𝔽2)14yes—
153C22×#41C22×C1312yes—
154#532C4×C13116yescomplemented
155C2×C4⋊Q8C22×C1311yescharacteristic
156C2×#127C22×C1311yescharacteristic
157C2×#124C22×C1312yes—
158C2×#121C22×C1314yes—
159C2×C4×D4C22×C1314yes—
160C2×#117C22×C1314yes—
161C22×C4⋊C4C22×C1314yes—
162C22×C42C22×C1311yescharacteristic
163#391C22×C1318yes—
164#390C22×C1318yes—
165#388C22×C13116yes—
166#387C22×C13116yes—
167#386C22×C1318yes—
168#386C22×C1318yes—
169#386C22×C13116yes—
170#383C22×C1314yes—
171#382C22×C1314yes—
172#381C22×C1314yes—
173#380C22×C1314yes—
174#380C22×C1318yes—
175C4×C4⋊C4C22×C1314yes—
176C4×C22⋊C4C22×C1314yes—
177C4×C22⋊C4C22×C13116yes—
178#376C22×C1314yes—
179C22×C13—22no—
180C22×C13—28no—
181C22×C13—24no—
182C22×C13—216no—
183C22×C13—44no—
184C22×C13—48no—
185C22×C13—44no—
186C22×C13—44no—
187C22×C13C24×C411yescharacteristic
188C22×C13C2×H(5,𝔽2)12yes—
189C22×C13#58514yes—
190C4×C13—22no—
191C4×C13—28no—
192C4×C13—24no—
193C4×C13—24no—
194C4×C13—416no—
195C4×C13#51814yes—
196C2×#41—44no—
197C2×#41—44no—
198C2×#41C2×C4×C13116yescomplemented
199C22×Q8C23×C1312yes—
200C22×D4C23×C1314yes—
201C22×D4C23×C1314yes—
202C22×D4C23×C1312yes—
203C23×C4C23×C1314yes—
204C23×C4C23×C1311yescharacteristic
205C23×C4C23×C1318yes—
206C23×C4C23×C1312yes—
207C4⋊Q8C2×C4×C1318yescomplemented
208#127C2×C4×C1318yes—
209#124C2×C4×C13116yescomplemented
210#121C2×C4×C13132yescomplemented
211C4×D4C2×C4×C13132yescomplemented
212#117—48no—
213C2×C4⋊C4—48no—
214C2×C4⋊C4C23×C1318yes—
215C2×C4⋊C4C23×C1318yes—
216C2×C4⋊C4C23×C1314yes—
217C2×C22⋊C4C23×C1318yes—
218C2×C22⋊C4C23×C1318yes—
219C2×C22⋊C4C23×C13116yes—
220C2×C22⋊C4C23×C1318yes—
221C2×C42C2×C4×C1318yescomplemented
222C2×C42C23×C1318yes—
223C2×C42C23×C1318yes—
224C2×C42C23×C1312yes—
225C2×C42C23×C1311yescharacteristic
226C2×C42C23×C1311yescharacteristic
227#95C23×C1318yes—
228#95C23×C1318yes—
229#95C23×C13116yes—
230#95C23×C1318yes—
231#95C23×C1318yes—
232C2×C13—42no—
233C2×C13—48no—
234C2×C13C2×#51811yescharacteristic
235C2×C13#342812yes—
236C2×C13#355114yes—
237C24C24×C1314yes—
238C24C24×C1311yescharacteristic
239#41—432no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8C22×C4×C1318yes—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—44no—
248C2×D4—44no—
249C2×D4C22×C4×C13116yes—
250C2×D4C22×C4×C13116yes—
251C2×D4C22×C4×C1318yes—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—44no—
256C22×C4—48no—
257C22×C4—416no—
258C22×C4C22×C4×C1314yes—
259C22×C4C22×C4×C13116yes—
260C22×C4C22×C4×C1318yes—
261C22×C4C24×C13116yes—
262C22×C4C24×C1312yes—
263C22×C4C24×C1311yescharacteristic
264C22×C4C24×C1312yes—
265C22×C4C24×C1314yes—
266C22×C4C24×C1311yescharacteristic
267C4⋊C4—216no—
268C4⋊C4—48no—
269C4⋊C4C22×C4×C13116yes—
270C22⋊C4—48no—
271C22⋊C4—416no—
272C22⋊C4—48no—
273C22⋊C4C22×C4×C13132yes—
274C42—48no—
275C42—48no—
276C42C22×C4×C1318yes—
277C42C22×C4×C1314yes—
278C42C22×C4×C1314yes—
279C13#3436911yescharacteristic, direct product factor, Sylow
280C23—24no—
281C23—24no—
282C23—22no—
283C23—24no—
284C23—28no—
285C23—28no—
286C23C23×C4×C1318yes—
287C23C23×C4×C1312yes—
288C23C25×C1311yescharacteristic
289Q8—48no—
290D4—416no—
291D4—48no—
292D4—416no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—232no—
299C2×C4—28no—
300C2×C4—216no—
301C2×C4—216no—
302C2×C4—216no—
303C2×C4—48no—
304C2×C4—816no—
305C2×C4C23×C4×C1314yes—
306C2×C4C23×C4×C1314yes—
307C2×C4C23×C4×C1312yes—
308C2×C4C23×C4×C1318yes—
309C2×C4C23×C4×C1312yes—
310C2×C4C13×H(5,𝔽2)14yes—
311C22—22no—
312C22—28no—
313C22—24no—
314C22—216no—
315C22—44no—
316C22—48no—
317C22—44no—
318C22—44no—
319C22C24×C4×C1311yescharacteristic
320C22C2×C13×H(5,𝔽2)12yes—
321C22C13×#58514yes—
322C4—22no—
323C4—28no—
324C4—24no—
325C4—24no—
326C4—416no—
327C4C13×#51814yes—
328C2—42no—
329C2—48no—
330C2C2×C13×#51811yescharacteristic
331C2C13×#342812yes—
332C2C13×#355114yes—
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2381C2semidirect
3. C13×#2380C2semidirect
4. C13×#2372C2semidirect
5. C13×#2352C2semidirect
6. C13×#2333C2semidirect
7. C13×#2311C2semidirect
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. #34369C13direct (N × H)
115. #2381C2×C13semidirect
116. #2380C2×C13semidirect
117. #2372C2×C13semidirect
118. #2352C2×C13semidirect
119. #2333C2×C13semidirect
120. #2311C2×C13semidirect
121. #2283C2×C13semidirect
154. #532C4×C13semidirect
198. C2×#41C2×C4×C13semidirect
207. C4⋊Q8C2×C4×C13semidirect
209. #124C2×C4×C13semidirect
210. #121C2×C4×C13semidirect
211. C4×D4C2×C4×C13semidirect
221. C2×C42C2×C4×C13semidirect
279. C13#34369direct (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×#23722
C13×#23522
C13×#23332
C13×#23112
C13×#22832
#3436913