Finite Group Databasebeta

← C13×#3224 #13112282

Subgroups — C13×#3224 #13112282

Order 1664.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#542C211yesmaximal, characteristic, complemented
2C13×#535C211yesmaximal, characteristic, complemented
3C13×#496C211yesmaximal, characteristic, complemented
4C13×#495C211yesmaximal, characteristic, complemented
5C13×#489C211yesmaximal, characteristic, complemented
6C13×#486C211yesmaximal, characteristic, complemented
7C13×#464C211yesmaximal, characteristic, complemented
8C13×#463C211yesmaximal, characteristic, complemented
9C13×#460C211yesmaximal, characteristic, complemented
10C13×#459C211yesmaximal, characteristic, complemented
11C13×#452C211yesmaximal, characteristic, complemented
12C13×#450C211yesmaximal, characteristic, complemented
13C13×#449C211yesmaximal, characteristic, complemented
14C13×#447C211yesmaximal, characteristic, complemented
15C13×#433C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×SD16C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic
21C2×C13×SD16C2211yescharacteristic, complemented
22C2×C13×SD16C2211yescharacteristic, complemented
23C2×C13×D8C2211yescharacteristic
24C2×C13×D8C2211yescharacteristic
25C2×C13×D8C2211yescharacteristic, complemented
26C13×C4⋊Q8C2211yescharacteristic, complemented
27C13×#127C2211yescharacteristic
28C13×#127C2211yescharacteristic
29C13×#126—21no—
30C13×#124—21no—
31C13×#124C2211yescharacteristic
32C13×#124C2211yescharacteristic
33C13×#124C2211yescharacteristic, complemented
34C13×#123—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8C2211yescharacteristic
37C13×#121—21no—
38C13×#121—21no—
39C13×#121C2211yescharacteristic
40C13×#120—21no—
41C13×#120—21no—
42C4×Q8×C13C2211yescharacteristic, complemented
43C4×D4×C13C2211yescharacteristic, complemented
44C13×#117C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic, complemented
46C13×C4⋊C8C2211yescharacteristic, complemented
47C13×#103C2211yescharacteristic, complemented
48C13×#103C2211yescharacteristic, complemented
49C13×#102C2211yescharacteristic
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic, complemented
54C13×#102C2211yescharacteristic, complemented
55C13×C22⋊C8C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×#97C2211yescharacteristic, complemented
58C4×C8×C13C2211yescharacteristic, complemented
59C24×C13—21no—
60C13×#41—41no—
61C13×#41—41no—
62C2×Q8×C13—21no—
63C2×Q8×C13C2311yescharacteristic
64C2×Q8×C13C2311yescharacteristic
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13C2311yescharacteristic
75C2×D4×C13C2311yescharacteristic
76C2×D4×C13C2311yescharacteristic
77C2×D4×C13C2311yescharacteristic
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13C2311yescharacteristic
81C13×Q16—41no—
82C13×SD16—41no—
83C13×SD16—41no—
84C13×SD16—41no—
85C13×SD16—41no—
86C13×D8—41no—
87C13×D8—41no—
88C13×D8—41no—
89C2×C8×C13C2311yescharacteristic
90C2×C8×C13C2311yescharacteristic
91C2×C8×C13C2311yescharacteristic
92C2×C8×C13C2311yescharacteristic
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4D411yescharacteristic
97C13×C4⋊C4D411yescharacteristic
98C13×C4⋊C4C2311yescharacteristic
99C13×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
108C13×C22⋊C4—21no—
109C13×C22⋊C4D411yescharacteristic
110C13×C22⋊C4D411yescharacteristic
111C42×C13—21no—
112C42×C13C2311yescharacteristic
113C42×C13C2311yescharacteristic
114#3224C1311yesmaximal, characteristic, direct product factor, Sylow
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—42no—
120C23×C13—81no—
121C23×C13—81no—
122C23×C13C2×D411yescharacteristic
123Q8×C13—21no—
124Q8×C13—21no—
125Q8×C13—21no—
126Q8×C13—21no—
127Q8×C13—81no—
128D4×C13—21no—
129D4×C13—21no—
130D4×C13—21no—
131D4×C13—21no—
132D4×C13—21no—
133D4×C13—21no—
134D4×C13—21no—
135D4×C13—21no—
136D4×C13—42no—
137D4×C13—42no—
138D4×C13—81no—
139D4×C13—81no—
140D4×C13—81no—
141D4×C13—81no—
142D4×C13—81no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—42no—
150C2×C4×C13—81no—
151C2×C4×C13C2×D411yescharacteristic
152C2×C4×C13C2×D411yescharacteristic
153C2×C4×C13C2×D411yescharacteristic
154C2×C4×C13C2×D411yescharacteristic
155C2×C4×C13C2×D411yescharacteristic
156C2×C4×C13C2411yescharacteristic
157C8×C13—21no—
158C8×C13—21no—
159C8×C13—21no—
160C8×C13—21no—
161#542C2×C1311yescharacteristic, complemented
162#535C2×C1311yescharacteristic, complemented
163#496C2×C1311yescharacteristic, complemented
164#495C2×C1311yescharacteristic, complemented
165#489C2×C1311yescharacteristic, complemented
166#486C2×C1311yescharacteristic, complemented
167#464C2×C1311yescharacteristic, complemented
168#463C2×C1311yescharacteristic, complemented
169#460C2×C1311yescharacteristic, complemented
170#459C2×C1311yescharacteristic, complemented
171#452C2×C1311yescharacteristic, complemented
172#450C2×C1311yescharacteristic, complemented
173#449C2×C1311yescharacteristic, complemented
174#447C2×C1311yescharacteristic, complemented
175#433C2×C1311yescharacteristic, complemented
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—84no—
192C22×C13C22×D411yescharacteristic
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13H(5,𝔽2)11yescharacteristic
203C4×C13H(5,𝔽2)11yescharacteristic
204C2×#41C22×C1311yescharacteristic
205C22×D4C22×C1311yescharacteristic
206C2×Q16C22×C1311yescharacteristic, complemented
207C2×SD16C22×C1311yescharacteristic
208C2×SD16C22×C1311yescharacteristic
209C2×SD16C22×C1311yescharacteristic, complemented
210C2×SD16C22×C1311yescharacteristic, complemented
211C2×D8C22×C1311yescharacteristic
212C2×D8C22×C1311yescharacteristic
213C2×D8C22×C1311yescharacteristic, complemented
214C4⋊Q8C22×C1311yescharacteristic, complemented
215#127C22×C1311yescharacteristic
216#127C22×C1311yescharacteristic
217#126—21no—
218#124—21no—
219#124C22×C1311yescharacteristic
220#124C22×C1311yescharacteristic
221#124C22×C1311yescharacteristic, complemented
222#123—21no—
223C22⋊Q8—21no—
224C22⋊Q8C22×C1311yescharacteristic
225#121—21no—
226#121—21no—
227#121C22×C1311yescharacteristic
228#120—21no—
229#120—21no—
230C4×Q8C22×C1311yescharacteristic, complemented
231C4×D4C22×C1311yescharacteristic, complemented
232#117C22×C1311yescharacteristic
233C4⋊C8C22×C1311yescharacteristic, complemented
234C4⋊C8C22×C1311yescharacteristic, complemented
235#103C22×C1311yescharacteristic, complemented
236#103C22×C1311yescharacteristic, complemented
237#102C22×C1311yescharacteristic
238#102C22×C1311yescharacteristic
239#102C22×C1311yescharacteristic
240#102C22×C1311yescharacteristic
241#102C22×C1311yescharacteristic, complemented
242#102C22×C1311yescharacteristic, complemented
243C22⋊C8C22×C1311yescharacteristic
244C22⋊C8C22×C1311yescharacteristic
245#97C22×C1311yescharacteristic, complemented
246C4×C8C22×C1311yescharacteristic, complemented
247C2×C13—41no—
248C2×C13—81no—
249C2×C13—81no—
250C2×C13—81no—
251C2×C13—81no—
252C2×C13#53511yescharacteristic
253C2×C13#57611yescharacteristic
254C2×C13#57711yescharacteristic
255C24—21no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×Q8C23×C1311yescharacteristic
260C2×Q8C23×C1311yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4C23×C1311yescharacteristic
271C2×D4C23×C1311yescharacteristic
272C2×D4C23×C1311yescharacteristic
273C2×D4C23×C1311yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4C23×C1311yescharacteristic
277Q16—41no—
278SD16—41no—
279SD16—41no—
280SD16—41no—
281SD16—41no—
282D8—41no—
283D8—41no—
284D8—41no—
285C2×C8C23×C1311yescharacteristic
286C2×C8C23×C1311yescharacteristic
287C2×C8C23×C1311yescharacteristic
288C2×C8C23×C1311yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4D4×C1311yescharacteristic
293C4⋊C4D4×C1311yescharacteristic
294C4⋊C4C23×C1311yescharacteristic
295C4⋊C4C23×C1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4D4×C1311yescharacteristic
306C22⋊C4D4×C1311yescharacteristic
307C42—21no—
308C42C23×C1311yescharacteristic
309C42C23×C1311yescharacteristic
310C13#322411yescharacteristic, direct product factor, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—42no—
316C23—81no—
317C23—81no—
318C23C2×D4×C1311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—81no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—42no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4C2×D4×C1311yescharacteristic
348C2×C4C2×D4×C1311yescharacteristic
349C2×C4C2×D4×C1311yescharacteristic
350C2×C4C2×D4×C1311yescharacteristic
351C2×C4C2×D4×C1311yescharacteristic
352C2×C4C24×C1311yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—84no—
373C22C22×D4×C1311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4C13×H(5,𝔽2)11yescharacteristic
384C4C13×H(5,𝔽2)11yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—81no—
390C2C13×#53511yescharacteristic
391C2C13×#57611yescharacteristic
392C2C13×#57711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#542C2semidirect
2. C13×#535C2semidirect
3. C13×#496C2semidirect
4. C13×#495C2semidirect
5. C13×#489C2semidirect
6. C13×#486C2semidirect
7. C13×#464C2semidirect
8. C13×#463C2semidirect
9. C13×#460C2semidirect
10. C13×#459C2semidirect
11. C13×#452C2semidirect
12. C13×#450C2semidirect
13. C13×#449C2semidirect
14. C13×#447C2semidirect
15. C13×#433C2semidirect
18. C2×C13×Q16C22semidirect
21. C2×C13×SD16C22semidirect
22. C2×C13×SD16C22semidirect
25. C2×C13×D8C22semidirect
26. C13×C4⋊Q8C22semidirect
33. C13×#124C22semidirect
42. C4×Q8×C13C22semidirect
43. C4×D4×C13C22semidirect
45. C13×C4⋊C8C22semidirect
46. C13×C4⋊C8C22semidirect
47. C13×#103C22semidirect
48. C13×#103C22semidirect
53. C13×#102C22semidirect
54. C13×#102C22semidirect
57. C13×#97C22semidirect
58. C4×C8×C13C22semidirect
114. #3224C13direct (N × H)
161. #542C2×C13semidirect
162. #535C2×C13semidirect
163. #496C2×C13semidirect
164. #495C2×C13semidirect
165. #489C2×C13semidirect
166. #486C2×C13semidirect
167. #464C2×C13semidirect
168. #463C2×C13semidirect
169. #460C2×C13semidirect
170. #459C2×C13semidirect
171. #452C2×C13semidirect
172. #450C2×C13semidirect
173. #449C2×C13semidirect
174. #447C2×C13semidirect
175. #433C2×C13semidirect
206. C2×Q16C22×C13semidirect
209. C2×SD16C22×C13semidirect
210. C2×SD16C22×C13semidirect
213. C2×D8C22×C13semidirect
214. C4⋊Q8C22×C13semidirect
221. #124C22×C13semidirect
230. C4×Q8C22×C13semidirect
231. C4×D4C22×C13semidirect
233. C4⋊C8C22×C13semidirect
234. C4⋊C8C22×C13semidirect
235. #103C22×C13semidirect
236. #103C22×C13semidirect
241. #102C22×C13semidirect
242. #102C22×C13semidirect
245. #97C22×C13semidirect
246. C4×C8C22×C13semidirect
310. C13#3224direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5422
C13×#5352
C13×#4962
C13×#4952
C13×#4892
C13×#4862
C13×#4642
C13×#4632
C13×#4602
C13×#4592
C13×#4522
C13×#4502
C13×#4492
C13×#4472
C13×#4332
#322413