Finite Group Databasebeta

← C13×#3516 #13112574

Subgroups — C13×#3516 #13112574

Order 1664.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#557C211yesmaximal, characteristic, complemented
2C13×#556C213yesmaximal, complemented
3C13×#554C213yesmaximal, complemented
4C13×#553C213yesmaximal, complemented
5C13×#552C213yesmaximal, complemented
6D4×Q8×C13C211yesmaximal, characteristic, complemented
7C13×#548C211yesmaximal, characteristic, complemented
8C13×#548C211yesmaximal, characteristic, complemented
9C13×#542C213yesmaximal, complemented
10C13×#541C213yesmaximal, complemented
11C13×#529C213yesmaximal, complemented
12C13×#529C213yesmaximal, complemented
13C13×#520C211yesmaximal, characteristic, complemented
14C13×#519C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C13C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C22×Q8×C13C2211yescharacteristic
19C13×C4⋊Q8C2213yes—
20C13×C4⋊Q8C2213yes—
21C13×#126C2216yes—
22C13×#126C2213yes—
23C13×#126C2213yes—
24C13×#126C2216yes—
25C13×#125C2213yes—
26C13×#125C2213yes—
27C13×#125C2216yes—
28C13×#125C2213yes—
29C13×#124C2213yes—
30C13×#124C2213yes—
31C13×#124C2213yes—
32C13×#123C2211yescharacteristic
33C13×#123C2213yes—
34C13×#123C2216yes—
35C13×C22⋊Q8C2213yes—
36C13×C22⋊Q8C2213yes—
37C13×C22⋊Q8C2213yes—
38C13×C22⋊Q8C2213yes—
39C13×C22⋊Q8C2213yes—
40C13×C22⋊Q8C2216yes—
41C13×#121C2213yes—
42C13×#121C2213yes—
43C13×#121C2213yes—
44C4×Q8×C13C2211yescharacteristic
45C4×Q8×C13C2213yes—
46C4×Q8×C13C2211yescharacteristic
47C4×Q8×C13C2213yes—
48C4×Q8×C13C2213yes—
49C4×Q8×C13C2211yescharacteristic
50C4×Q8×C13C2213yes—
51C4×Q8×C13C2211yescharacteristic
52C4×Q8×C13C2213yes—
53C4×D4×C13C2213yes—
54C4×D4×C13C2213yes—
55C4×D4×C13C2213yes—
56C4×D4×C13C2213yes—
57C4×D4×C13C2213yes—
58C4×D4×C13C2216yes—
59C13×#117C2213yes—
60C13×#117C2213yes—
61C13×#117C2213yes—
62C13×#117C2216yes—
63C2×C13×C4⋊C4C2213yes—
64C2×C13×C4⋊C4C2213yes—
65C2×C42×C13C2213yes—
66C13×#41—24no—
67C2×Q8×C13—24no—
68C2×Q8×C13—24no—
69C2×Q8×C13C2313yes—
70C2×Q8×C13C2313yes—
71C2×Q8×C13C2313yes—
72C2×Q8×C13C2311yescharacteristic
73C2×D4×C13C2313yes—
74C2×D4×C13C2311yescharacteristic
75C2×D4×C13C2313yes—
76C2×D4×C13C2313yes—
77C22×C4×C13C2311yescharacteristic
78C22×C4×C13C2313yes—
79C22×C4×C13C2313yes—
80C22×C4×C13C2313yes—
81C22×C4×C13C2313yes—
82C22×C4×C13C2316yes—
83C13×C4⋊C4C2313yes—
84C13×C4⋊C4C2313yes—
85C13×C4⋊C4C2313yes—
86C13×C4⋊C4C2313yes—
87C13×C4⋊C4C2316yes—
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2313yes—
90C13×C4⋊C4C2313yes—
91C13×C4⋊C4C2313yes—
92C13×C4⋊C4C2313yes—
93C13×C4⋊C4C2316yes—
94C13×C4⋊C4C2313yes—
95C13×C4⋊C4C2313yes—
96C13×C4⋊C4C2316yes—
97C13×C4⋊C4C2313yes—
98C13×C4⋊C4C2311yescharacteristic
99C13×C4⋊C4C2313yes—
100C13×C22⋊C4C2313yes—
101C13×C22⋊C4C2311yescharacteristic
102C13×C22⋊C4C2313yes—
103C13×C22⋊C4C2313yes—
104C13×C22⋊C4C2313yes—
105C13×C22⋊C4C2316yes—
106C13×C22⋊C4C2311yescharacteristic
107C13×C22⋊C4C2313yes—
108C13×C22⋊C4C2311yescharacteristic
109C13×C22⋊C4C2316yes—
110C13×C22⋊C4C2313yes—
111C13×C22⋊C4C2313yes—
112C42×C13C2313yes—
113C42×C13C2313yes—
114C42×C13C2313yes—
115C42×C13C2313yes—
116C42×C13C2316yes—
117C42×C13C2313yes—
118C42×C13C2313yes—
119#3516C1311yesmaximal, characteristic, direct product factor, Sylow
120C23×C13C2411yescharacteristic
121C23×C13C2413yes—
122C23×C13C2411yescharacteristic
123Q8×C13—26no—
124Q8×C13—26no—
125Q8×C13—43no—
126Q8×C13#4114yes—
127D4×C13—26no—
128D4×C13—22no—
129D4×C13—26no—
130D4×C13—43no—
131C2×C4×C13—22no—
132C2×C4×C13—26no—
133C2×C4×C13—26no—
134C2×C4×C13—26no—
135C2×C4×C13—46no—
136C2×C4×C13—43no—
137C2×C4×C13C2411yescharacteristic
138C2×C4×C13C2411yescharacteristic
139C2×C4×C13C2413yes—
140C2×C4×C13C2411yescharacteristic
141C2×C4×C13C2413yes—
142C2×C4×C13C2411yescharacteristic
143C2×C4×C13C2413yes—
144C2×C4×C13C2413yes—
145C2×C4×C13C2413yes—
146C2×C4×C13C2413yes—
147C2×C4×C13C2411yescharacteristic
148C2×C4×C13C2413yes—
149#557C2×C1311yescharacteristic, complemented
150#556C2×C1313yescomplemented
151#554C2×C1313yescomplemented
152#553C2×C1313yescomplemented
153#552C2×C1313yescomplemented
154D4×Q8C2×C1311yescharacteristic, complemented
155#548C2×C1311yescharacteristic, complemented
156#548C2×C1311yescharacteristic, complemented
157#542C2×C1313yescomplemented
158#541C2×C1313yescomplemented
159#529C2×C1313yescomplemented
160#529C2×C1313yescomplemented
161#520C2×C1311yescharacteristic, complemented
162#519C2×C1311yescharacteristic, complemented
163C2×C4×Q8C2×C1311yescharacteristic, complemented
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—23no—
168C22×C13—21no—
169C22×C13—23no—
170C22×C13—23no—
171C22×C13—21no—
172C22×C132−1+412yes—
173C22×C13C2511yescharacteristic
174C4×C13—21no—
175C4×C13—23no—
176C4×C13—23no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—23no—
180C4×C13—21no—
181C4×C13—23no—
182C4×C13—23no—
183C4×C13—23no—
184C4×C13—21no—
185C4×C13C2×#4116yes—
186C2×#41C22×C1311yescharacteristic
187C22×Q8C22×C1311yescharacteristic
188C22×Q8C22×C1311yescharacteristic
189C4⋊Q8C22×C1313yes—
190C4⋊Q8C22×C1313yes—
191#126C22×C1316yes—
192#126C22×C1313yes—
193#126C22×C1313yes—
194#126C22×C1316yes—
195#125C22×C1313yes—
196#125C22×C1313yes—
197#125C22×C1316yes—
198#125C22×C1313yes—
199#124C22×C1313yes—
200#124C22×C1313yes—
201#124C22×C1313yes—
202#123C22×C1311yescharacteristic
203#123C22×C1313yes—
204#123C22×C1316yes—
205C22⋊Q8C22×C1313yes—
206C22⋊Q8C22×C1313yes—
207C22⋊Q8C22×C1313yes—
208C22⋊Q8C22×C1313yes—
209C22⋊Q8C22×C1313yes—
210C22⋊Q8C22×C1316yes—
211#121C22×C1313yes—
212#121C22×C1313yes—
213#121C22×C1313yes—
214C4×Q8C22×C1311yescharacteristic
215C4×Q8C22×C1313yes—
216C4×Q8C22×C1311yescharacteristic
217C4×Q8C22×C1313yes—
218C4×Q8C22×C1313yes—
219C4×Q8C22×C1311yescharacteristic
220C4×Q8C22×C1313yes—
221C4×Q8C22×C1311yescharacteristic
222C4×Q8C22×C1313yes—
223C4×D4C22×C1313yes—
224C4×D4C22×C1313yes—
225C4×D4C22×C1313yes—
226C4×D4C22×C1313yes—
227C4×D4C22×C1313yes—
228C4×D4C22×C1316yes—
229#117C22×C1313yes—
230#117C22×C1313yes—
231#117C22×C1313yes—
232#117C22×C1316yes—
233C2×C4⋊C4C22×C1313yes—
234C2×C4⋊C4C22×C1313yes—
235C2×C42C22×C1313yes—
236C2×C13—22no—
237C2×C13—41no—
238C2×C13—43no—
239C2×C13C22×#4111yescharacteristic
240C2×C13C2×2−1+411yescharacteristic
241C2×C13#58511yescharacteristic
242#41—24no—
243C2×Q8—24no—
244C2×Q8—24no—
245C2×Q8C23×C1313yes—
246C2×Q8C23×C1313yes—
247C2×Q8C23×C1313yes—
248C2×Q8C23×C1311yescharacteristic
249C2×D4C23×C1313yes—
250C2×D4C23×C1311yescharacteristic
251C2×D4C23×C1313yes—
252C2×D4C23×C1313yes—
253C22×C4C23×C1311yescharacteristic
254C22×C4C23×C1313yes—
255C22×C4C23×C1313yes—
256C22×C4C23×C1313yes—
257C22×C4C23×C1313yes—
258C22×C4C23×C1316yes—
259C4⋊C4C23×C1313yes—
260C4⋊C4C23×C1313yes—
261C4⋊C4C23×C1313yes—
262C4⋊C4C23×C1313yes—
263C4⋊C4C23×C1316yes—
264C4⋊C4C23×C1311yescharacteristic
265C4⋊C4C23×C1313yes—
266C4⋊C4C23×C1313yes—
267C4⋊C4C23×C1313yes—
268C4⋊C4C23×C1313yes—
269C4⋊C4C23×C1316yes—
270C4⋊C4C23×C1313yes—
271C4⋊C4C23×C1313yes—
272C4⋊C4C23×C1316yes—
273C4⋊C4C23×C1313yes—
274C4⋊C4C23×C1311yescharacteristic
275C4⋊C4C23×C1313yes—
276C22⋊C4C23×C1313yes—
277C22⋊C4C23×C1311yescharacteristic
278C22⋊C4C23×C1313yes—
279C22⋊C4C23×C1313yes—
280C22⋊C4C23×C1313yes—
281C22⋊C4C23×C1316yes—
282C22⋊C4C23×C1311yescharacteristic
283C22⋊C4C23×C1313yes—
284C22⋊C4C23×C1311yescharacteristic
285C22⋊C4C23×C1316yes—
286C22⋊C4C23×C1313yes—
287C22⋊C4C23×C1313yes—
288C42C23×C1313yes—
289C42C23×C1313yes—
290C42C23×C1313yes—
291C42C23×C1313yes—
292C42C23×C1316yes—
293C42C23×C1313yes—
294C42C23×C1313yes—
295C13#351611yescharacteristic, direct product factor, Sylow
296C23C24×C1311yescharacteristic
297C23C24×C1313yes—
298C23C24×C1311yescharacteristic
299Q8—26no—
300Q8—26no—
301Q8—43no—
302Q8C13×#4114yes—
303D4—26no—
304D4—22no—
305D4—26no—
306D4—43no—
307C2×C4—22no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—46no—
312C2×C4—43no—
313C2×C4C24×C1311yescharacteristic
314C2×C4C24×C1311yescharacteristic
315C2×C4C24×C1313yes—
316C2×C4C24×C1311yescharacteristic
317C2×C4C24×C1313yes—
318C2×C4C24×C1311yescharacteristic
319C2×C4C24×C1313yes—
320C2×C4C24×C1313yes—
321C2×C4C24×C1313yes—
322C2×C4C24×C1313yes—
323C2×C4C24×C1311yescharacteristic
324C2×C4C24×C1313yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—23no—
329C22—21no—
330C22—23no—
331C22—23no—
332C22—21no—
333C22C13×2−1+412yes—
334C22C25×C1311yescharacteristic
335C4—21no—
336C4—23no—
337C4—23no—
338C4—21no—
339C4—21no—
340C4—23no—
341C4—21no—
342C4—23no—
343C4—23no—
344C4—23no—
345C4—21no—
346C4C2×C13×#4116yes—
347C2—22no—
348C2—41no—
349C2—43no—
350C2C22×C13×#4111yescharacteristic
351C2C2×C13×2−1+411yescharacteristic
352C2C13×#58511yescharacteristic
subgroupG/H
center, socleC22×C13C25
commutator, Frattini, cosocleC22C25×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#557C2semidirect
2. C13×#556C2semidirect
3. C13×#554C2semidirect
4. C13×#553C2semidirect
5. C13×#552C2semidirect
6. D4×Q8×C13C2semidirect
7. C13×#548C2semidirect
8. C13×#548C2semidirect
9. C13×#542C2semidirect
10. C13×#541C2semidirect
11. C13×#529C2semidirect
12. C13×#529C2semidirect
13. C13×#520C2semidirect
14. C13×#519C2semidirect
15. C2×C4×Q8×C13C2semidirect
119. #3516C13direct (N × H)
149. #557C2×C13semidirect
150. #556C2×C13semidirect
151. #554C2×C13semidirect
152. #553C2×C13semidirect
153. #552C2×C13semidirect
154. D4×Q8C2×C13semidirect
155. #548C2×C13semidirect
156. #548C2×C13semidirect
157. #542C2×C13semidirect
158. #541C2×C13semidirect
159. #529C2×C13semidirect
160. #529C2×C13semidirect
161. #520C2×C13semidirect
162. #519C2×C13semidirect
163. C2×C4×Q8C2×C13semidirect
295. C13#3516direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5572
C13×#5562
C13×#5542
C13×#5532
C13×#5522
D4×Q8×C132
C13×#5482
C13×#5422
C13×#5412
C13×#5292
C13×#5202
C13×#5192
C2×C4×Q8×C132
#351613