Finite Group Databasebeta

← C13×#3321 #13112379

Subgroups — C13×#3321 #13112379

Order 1664.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#555C211yesmaximal, characteristic, complemented
2C13×#548C211yesmaximal, characteristic, complemented
3C13×#489C211yesmaximal, characteristic, complemented
4C13×#485C211yesmaximal, characteristic, complemented
5C13×#482C211yesmaximal, characteristic, complemented
6C13×#475C211yesmaximal, characteristic, complemented
7C13×#469C211yesmaximal, characteristic, complemented
8C13×#465C211yesmaximal, characteristic, complemented
9C13×#463C211yesmaximal, characteristic, complemented
10C13×#449C211yesmaximal, characteristic, complemented
11C13×#448C211yesmaximal, characteristic, complemented
12C13×#440C211yesmaximal, characteristic, complemented
13C13×#435C211yesmaximal, characteristic, complemented
14C13×#419C211yesmaximal, characteristic, complemented
15C13×#416C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C2×C13×M16C2211yescharacteristic
22C22×C8×C13C2211yescharacteristic
23C13×C4⋊Q8C2211yescharacteristic
24C13×#124—21no—
25C13×#124—21no—
26C13×#124—21no—
27C13×#124C2211yescharacteristic
28C13×C22⋊Q8—21no—
29C13×C22⋊Q8C2211yescharacteristic
30C13×#121—21no—
31C13×#121—21no—
32C13×#121C2211yescharacteristic
33C13×#121C2211yescharacteristic
34C13×#121C2211yescharacteristic
35C4×Q8×C13C2211yescharacteristic
36C4×D4×C13—21no—
37C4×D4×C13C2211yescharacteristic
38C4×D4×C13C2211yescharacteristic
39C13×#117—21no—
40C13×#117C2211yescharacteristic
41C13×#117C2211yescharacteristic
42C13×#107C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#106C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic
46C13×#103C2211yescharacteristic
47C13×#103C2211yescharacteristic
48C13×#103C2211yescharacteristic
49C13×#103C2211yescharacteristic
50C13×#103C2211yescharacteristic
51C13×#103C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×#102C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×C22⋊C8C2211yescharacteristic
58C13×#97C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13—21no—
62C2×Q8×C13—21no—
63C2×Q8×C13—22no—
64C2×Q8×C13—41no—
65C2×Q8×C13C2311yescharacteristic
66C2×Q8×C13C2311yescharacteristic
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13D411yescharacteristic
72C2×D4×C13C2311yescharacteristic
73C2×D4×C13C2311yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13C2311yescharacteristic
78C22×C4×C13C2311yescharacteristic
79C13×SD16—22no—
80C13×SD16—41no—
81C13×D8—41no—
82C13×M16—41no—
83C2×C8×C13—41no—
84C2×C8×C13C2311yescharacteristic
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4D411yescharacteristic
92C13×C4⋊C4C2311yescharacteristic
93C13×C4⋊C4C2311yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C4⋊C4C2311yescharacteristic
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4—21no—
100C13×C22⋊C4—21no—
101C13×C22⋊C4—21no—
102C13×C22⋊C4—21no—
103C13×C22⋊C4—21no—
104C13×C22⋊C4—21no—
105C13×C22⋊C4D411yescharacteristic
106C13×C22⋊C4D411yescharacteristic
107C42×C13—21no—
108C42×C13—21no—
109C42×C13—21no—
110C42×C13C2311yescharacteristic
111#3321C1311yesmaximal, characteristic, direct product factor, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C23×C13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—42no—
120Q8×C13—81no—
121Q8×C13#4112yes—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—41no—
127D4×C13—42no—
128D4×C13—42no—
129D4×C13—81no—
130D4×C13—81no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13C2×D411yescharacteristic
145C2×C4×C13C2×D411yescharacteristic
146C2×C4×C13C2×D411yescharacteristic
147C2×C4×C13C2×D411yescharacteristic
148C2×C4×C13C2411yescharacteristic
149C8×C13—21no—
150C8×C13—21no—
151C8×C13—21no—
152C8×C13—21no—
153#555C2×C1311yescharacteristic, complemented
154#548C2×C1311yescharacteristic, complemented
155#489C2×C1311yescharacteristic, complemented
156#485C2×C1311yescharacteristic, complemented
157#482C2×C1311yescharacteristic, complemented
158#475C2×C1311yescharacteristic, complemented
159#469C2×C1311yescharacteristic, complemented
160#465C2×C1311yescharacteristic, complemented
161#463C2×C1311yescharacteristic, complemented
162#449C2×C1311yescharacteristic, complemented
163#448C2×C1311yescharacteristic, complemented
164#440C2×C1311yescharacteristic, complemented
165#435C2×C1311yescharacteristic, complemented
166#419C2×C1311yescharacteristic, complemented
167#416C2×C1311yescharacteristic, complemented
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13C22×D411yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13C2×#4111yescharacteristic
192C4×C13H(5,𝔽2)11yescharacteristic
193C2×#41C22×C1311yescharacteristic
194C22×Q8C22×C1311yescharacteristic
195C2×SD16C22×C1311yescharacteristic
196C2×SD16C22×C1311yescharacteristic
197C2×D8C22×C1311yescharacteristic
198C2×M16C22×C1311yescharacteristic
199C22×C8C22×C1311yescharacteristic
200C4⋊Q8C22×C1311yescharacteristic
201#124—21no—
202#124—21no—
203#124—21no—
204#124C22×C1311yescharacteristic
205C22⋊Q8—21no—
206C22⋊Q8C22×C1311yescharacteristic
207#121—21no—
208#121—21no—
209#121C22×C1311yescharacteristic
210#121C22×C1311yescharacteristic
211#121C22×C1311yescharacteristic
212C4×Q8C22×C1311yescharacteristic
213C4×D4—21no—
214C4×D4C22×C1311yescharacteristic
215C4×D4C22×C1311yescharacteristic
216#117—21no—
217#117C22×C1311yescharacteristic
218#117C22×C1311yescharacteristic
219#107C22×C1311yescharacteristic
220#106C22×C1311yescharacteristic
221#106C22×C1311yescharacteristic
222C4⋊C8C22×C1311yescharacteristic
223#103C22×C1311yescharacteristic
224#103C22×C1311yescharacteristic
225#103C22×C1311yescharacteristic
226#103C22×C1311yescharacteristic
227#103C22×C1311yescharacteristic
228#103C22×C1311yescharacteristic
229#102C22×C1311yescharacteristic
230#102C22×C1311yescharacteristic
231#102C22×C1311yescharacteristic
232#102C22×C1311yescharacteristic
233C22⋊C8C22×C1311yescharacteristic
234C22⋊C8C22×C1311yescharacteristic
235#97C22×C1311yescharacteristic
236C2×C13—41no—
237C2×C13—41no—
238C2×C13—81no—
239C2×C13—81no—
240C2×C13#54611yescharacteristic
241C2×C13#57511yescharacteristic
242C2×C13#57711yescharacteristic
243#41—22no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C23×C1311yescharacteristic
250C2×Q8C23×C1311yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4D4×C1311yescharacteristic
256C2×D4C23×C1311yescharacteristic
257C2×D4C23×C1311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C23×C1311yescharacteristic
262C22×C4C23×C1311yescharacteristic
263SD16—22no—
264SD16—41no—
265D8—41no—
266M16—41no—
267C2×C8—41no—
268C2×C8C23×C1311yescharacteristic
269C2×C8C23×C1311yescharacteristic
270C2×C8C23×C1311yescharacteristic
271C2×C8C23×C1311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4D4×C1311yescharacteristic
276C4⋊C4C23×C1311yescharacteristic
277C4⋊C4C23×C1311yescharacteristic
278C4⋊C4C23×C1311yescharacteristic
279C4⋊C4C23×C1311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4D4×C1311yescharacteristic
290C22⋊C4D4×C1311yescharacteristic
291C42—21no—
292C42—21no—
293C42—21no—
294C42C23×C1311yescharacteristic
295C13#332111yescharacteristic, direct product factor, Sylow
296C23—21no—
297C23—21no—
298C23C2×D4×C1311yescharacteristic
299C23C2×D4×C1311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8—81no—
305Q8C13×#4112yes—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—42no—
312D4—42no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4C2×D4×C1311yescharacteristic
329C2×C4C2×D4×C1311yescharacteristic
330C2×C4C2×D4×C1311yescharacteristic
331C2×C4C2×D4×C1311yescharacteristic
332C2×C4C24×C1311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22C22×D4×C1311yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4C2×C13×#4111yescharacteristic
361C4C13×H(5,𝔽2)11yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2C13×#54611yescharacteristic
367C2C13×#57511yescharacteristic
368C2C13×#57711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#555C2semidirect
2. C13×#548C2semidirect
3. C13×#489C2semidirect
4. C13×#485C2semidirect
5. C13×#482C2semidirect
6. C13×#475C2semidirect
7. C13×#469C2semidirect
8. C13×#465C2semidirect
9. C13×#463C2semidirect
10. C13×#449C2semidirect
11. C13×#448C2semidirect
12. C13×#440C2semidirect
13. C13×#435C2semidirect
14. C13×#419C2semidirect
15. C13×#416C2semidirect
111. #3321C13direct (N × H)
153. #555C2×C13semidirect
154. #548C2×C13semidirect
155. #489C2×C13semidirect
156. #485C2×C13semidirect
157. #482C2×C13semidirect
158. #475C2×C13semidirect
159. #469C2×C13semidirect
160. #465C2×C13semidirect
161. #463C2×C13semidirect
162. #449C2×C13semidirect
163. #448C2×C13semidirect
164. #440C2×C13semidirect
165. #435C2×C13semidirect
166. #419C2×C13semidirect
167. #416C2×C13semidirect
295. C13#3321direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5552
C13×#5482
C13×#4892
C13×#4852
C13×#4822
C13×#4752
C13×#4692
C13×#4652
C13×#4632
C13×#4492
C13×#4482
C13×#4402
C13×#4352
C13×#4192
C13×#4162
#332113