Finite Group Databasebeta

← C13×#3297 #13112355

Subgroups — C13×#3297 #13112355

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#553C211yesmaximal, characteristic, complemented
2C13×#546C211yesmaximal, characteristic, complemented
3C13×#488C211yesmaximal, characteristic, complemented
4C13×#484C211yesmaximal, characteristic, complemented
5C13×#482C211yesmaximal, characteristic, complemented
6C13×#478C211yesmaximal, characteristic, complemented
7C13×#466C211yesmaximal, characteristic, complemented
8C13×#465C211yesmaximal, characteristic, complemented
9C13×#463C211yesmaximal, characteristic, complemented
10C13×#449C211yesmaximal, characteristic, complemented
11C13×#447C211yesmaximal, characteristic, complemented
12C4×C13×D8C211yesmaximal, characteristic, complemented
13C8×D4×C13C211yesmaximal, characteristic, complemented
14C13×#416C211yesmaximal, characteristic, complemented
15C2×C13×#102C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic, complemented
19C2×C13×D8C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C22×C8×C13C2211yescharacteristic
22C22×C8×C13C2211yescharacteristic, complemented
23C13×#126—21no—
24C13×#125C2211yescharacteristic, complemented
25C13×#124C2211yescharacteristic
26C13×#123—21no—
27C13×#123—21no—
28C13×C22⋊Q8C2211yescharacteristic
29C13×#121—21no—
30C13×#121—21no—
31C13×#121C2211yescharacteristic
32C13×#121C2211yescharacteristic
33C13×#121C2211yescharacteristic, complemented
34C13×#120—21no—
35C4×D4×C13—21no—
36C4×D4×C13C2211yescharacteristic
37C4×D4×C13C2211yescharacteristic
38C4×D4×C13C2211yescharacteristic, complemented
39C13×#117C2211yescharacteristic, complemented
40C2×C13×C4⋊C4C2211yescharacteristic
41C2×C13×C22⋊C4—21no—
42C13×#107C2211yescharacteristic, complemented
43C13×#107C2211yescharacteristic, complemented
44C13×#106C2211yescharacteristic, complemented
45C13×C4⋊C8C2211yescharacteristic, complemented
46C13×#103C2211yescharacteristic, complemented
47C13×#103C2211yescharacteristic, complemented
48C13×#103C2211yescharacteristic, complemented
49C13×#102C2211yescharacteristic
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×#102C2211yescharacteristic, complemented
56C13×C22⋊C8C2211yescharacteristic
57C13×C22⋊C8C2211yescharacteristic, complemented
58C4×C8×C13C2211yescharacteristic, complemented
59C24×C13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—22no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—41no—
70C2×D4×C13D411yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C2×D4×C13C2311yescharacteristic
73C2×D4×C13C2311yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C2311yescharacteristic
79C22×C4×C13C2311yescharacteristic
80C13×SD16—41no—
81C13×D8—22no—
82C13×D8—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C2×C8×C13C2311yescharacteristic
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4D411yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C4⋊C4C2311yescharacteristic
96C13×C4⋊C4C2311yescharacteristic
97C13×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4D411yescharacteristic
108C13×C22⋊C4D411yescharacteristic
109C42×C13—21no—
110C42×C13C2311yescharacteristic
111#3297C1311yesmaximal, characteristic, direct product factor, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—81no—
118C23×C13C2×D411yescharacteristic
119C23×C13C2×D411yescharacteristic
120Q8×C13—21no—
121Q8×C13—21no—
122D4×C13—22no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—42no—
129D4×C13—42no—
130D4×C13—42no—
131D4×C13—81no—
132D4×C13—81no—
133D4×C13#4112yes—
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—21no—
142C2×C4×C13—21no—
143C2×C4×C13—42no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13C2×D411yescharacteristic
148C2×C4×C13C2×D411yescharacteristic
149C2×C4×C13C2×D411yescharacteristic
150C2×C4×C13C2×D411yescharacteristic
151C2×C4×C13C2411yescharacteristic
152C8×C13—21no—
153C8×C13—21no—
154C8×C13—21no—
155C8×C13—21no—
156#553C2×C1311yescharacteristic, complemented
157#546C2×C1311yescharacteristic, complemented
158#488C2×C1311yescharacteristic, complemented
159#484C2×C1311yescharacteristic, complemented
160#482C2×C1311yescharacteristic, complemented
161#478C2×C1311yescharacteristic, complemented
162#466C2×C1311yescharacteristic, complemented
163#465C2×C1311yescharacteristic, complemented
164#463C2×C1311yescharacteristic, complemented
165#449C2×C1311yescharacteristic, complemented
166#447C2×C1311yescharacteristic, complemented
167C4×D8C2×C1311yescharacteristic, complemented
168C8×D4C2×C1311yescharacteristic, complemented
169#416C2×C1311yescharacteristic, complemented
170C2×#102C2×C1311yescharacteristic, complemented
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—22no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—84no—
186C22×C13#13512yes—
187C22×C13C22×D411yescharacteristic
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13C2×#4111yescharacteristic
198C4×C13H(5,𝔽2)11yescharacteristic
199C2×#41C22×C1311yescharacteristic
200C22×D4C22×C1311yescharacteristic
201C2×SD16C22×C1311yescharacteristic, complemented
202C2×D8C22×C1311yescharacteristic
203C2×D8C22×C1311yescharacteristic
204C22×C8C22×C1311yescharacteristic
205C22×C8C22×C1311yescharacteristic, complemented
206#126—21no—
207#125C22×C1311yescharacteristic, complemented
208#124C22×C1311yescharacteristic
209#123—21no—
210#123—21no—
211C22⋊Q8C22×C1311yescharacteristic
212#121—21no—
213#121—21no—
214#121C22×C1311yescharacteristic
215#121C22×C1311yescharacteristic
216#121C22×C1311yescharacteristic, complemented
217#120—21no—
218C4×D4—21no—
219C4×D4C22×C1311yescharacteristic
220C4×D4C22×C1311yescharacteristic
221C4×D4C22×C1311yescharacteristic, complemented
222#117C22×C1311yescharacteristic, complemented
223C2×C4⋊C4C22×C1311yescharacteristic
224C2×C22⋊C4—21no—
225#107C22×C1311yescharacteristic, complemented
226#107C22×C1311yescharacteristic, complemented
227#106C22×C1311yescharacteristic, complemented
228C4⋊C8C22×C1311yescharacteristic, complemented
229#103C22×C1311yescharacteristic, complemented
230#103C22×C1311yescharacteristic, complemented
231#103C22×C1311yescharacteristic, complemented
232#102C22×C1311yescharacteristic
233#102C22×C1311yescharacteristic
234#102C22×C1311yescharacteristic
235#102C22×C1311yescharacteristic
236#102C22×C1311yescharacteristic
237#102C22×C1311yescharacteristic
238#102C22×C1311yescharacteristic, complemented
239C22⋊C8C22×C1311yescharacteristic
240C22⋊C8C22×C1311yescharacteristic, complemented
241C4×C8C22×C1311yescharacteristic, complemented
242C2×C13—22no—
243C2×C13—41no—
244C2×C13—42no—
245C2×C13—81no—
246C2×C13—81no—
247C2×C13#54611yescharacteristic
248C2×C13C2×#13511yescharacteristic
249C2×C13#57611yescharacteristic
250C24—21no—
251#41—22no—
252#41—41no—
253C2×Q8C23×C1311yescharacteristic
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4D4×C1311yescharacteristic
262C2×D4C23×C1311yescharacteristic
263C2×D4C23×C1311yescharacteristic
264C2×D4C23×C1311yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C23×C1311yescharacteristic
270C22×C4C23×C1311yescharacteristic
271SD16—41no—
272D8—22no—
273D8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8C23×C1311yescharacteristic
277C2×C8C23×C1311yescharacteristic
278C2×C8C23×C1311yescharacteristic
279C2×C8C23×C1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4D4×C1311yescharacteristic
285C4⋊C4C23×C1311yescharacteristic
286C4⋊C4C23×C1311yescharacteristic
287C4⋊C4C23×C1311yescharacteristic
288C4⋊C4C23×C1311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4D4×C1311yescharacteristic
299C22⋊C4D4×C1311yescharacteristic
300C42—21no—
301C42C23×C1311yescharacteristic
302C13#329711yescharacteristic, direct product factor, Sylow
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23C2×D4×C1311yescharacteristic
310C23C2×D4×C1311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—42no—
321D4—42no—
322D4—81no—
323D4—81no—
324D4C13×#4112yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4C2×D4×C1311yescharacteristic
339C2×C4C2×D4×C1311yescharacteristic
340C2×C4C2×D4×C1311yescharacteristic
341C2×C4C2×D4×C1311yescharacteristic
342C2×C4C24×C1311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22C13×#13512yes—
363C22C22×D4×C1311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4C2×C13×#4111yescharacteristic
374C4C13×H(5,𝔽2)11yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—81no—
380C2C13×#54611yescharacteristic
381C2C2×C13×#13511yescharacteristic
382C2C13×#57611yescharacteristic
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×#553C2semidirect
2. C13×#546C2semidirect
3. C13×#488C2semidirect
4. C13×#484C2semidirect
5. C13×#482C2semidirect
6. C13×#478C2semidirect
7. C13×#466C2semidirect
8. C13×#465C2semidirect
9. C13×#463C2semidirect
10. C13×#449C2semidirect
11. C13×#447C2semidirect
12. C4×C13×D8C2semidirect
13. C8×D4×C13C2semidirect
14. C13×#416C2semidirect
15. C2×C13×#102C2semidirect
18. C2×C13×SD16C22semidirect
22. C22×C8×C13C22semidirect
24. C13×#125C22semidirect
33. C13×#121C22semidirect
38. C4×D4×C13C22semidirect
39. C13×#117C22semidirect
42. C13×#107C22semidirect
43. C13×#107C22semidirect
44. C13×#106C22semidirect
45. C13×C4⋊C8C22semidirect
46. C13×#103C22semidirect
47. C13×#103C22semidirect
48. C13×#103C22semidirect
55. C13×#102C22semidirect
57. C13×C22⋊C8C22semidirect
58. C4×C8×C13C22semidirect
111. #3297C13direct (N × H)
156. #553C2×C13semidirect
157. #546C2×C13semidirect
158. #488C2×C13semidirect
159. #484C2×C13semidirect
160. #482C2×C13semidirect
161. #478C2×C13semidirect
162. #466C2×C13semidirect
163. #465C2×C13semidirect
164. #463C2×C13semidirect
165. #449C2×C13semidirect
166. #447C2×C13semidirect
167. C4×D8C2×C13semidirect
168. C8×D4C2×C13semidirect
169. #416C2×C13semidirect
170. C2×#102C2×C13semidirect
201. C2×SD16C22×C13semidirect
205. C22×C8C22×C13semidirect
207. #125C22×C13semidirect
216. #121C22×C13semidirect
221. C4×D4C22×C13semidirect
222. #117C22×C13semidirect
225. #107C22×C13semidirect
226. #107C22×C13semidirect
227. #106C22×C13semidirect
228. C4⋊C8C22×C13semidirect
229. #103C22×C13semidirect
230. #103C22×C13semidirect
231. #103C22×C13semidirect
238. #102C22×C13semidirect
240. C22⋊C8C22×C13semidirect
241. C4×C8C22×C13semidirect
302. C13#3297direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5532
C13×#5462
C13×#4882
C13×#4842
C13×#4822
C13×#4782
C13×#4662
C13×#4652
C13×#4632
C13×#4492
C13×#4472
C4×C13×D82
C8×D4×C132
C13×#4162
C2×C13×#1022
#329713