Finite Group Databasebeta

← C13×#3314 #13112372

Subgroups — C13×#3314 #13112372

Order 1664.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#554C211yesmaximal, characteristic, complemented
2C13×#546C211yesmaximal, characteristic
3C13×#489C211yesmaximal, characteristic, complemented
4C13×#484C211yesmaximal, characteristic, complemented
5C13×#480C211yesmaximal, characteristic, complemented
6C13×#474C211yesmaximal, characteristic, complemented
7C13×#468C211yesmaximal, characteristic, complemented
8C13×#467C211yesmaximal, characteristic, complemented
9C13×#464C211yesmaximal, characteristic, complemented
10C13×#452C211yesmaximal, characteristic, complemented
11C13×#450C211yesmaximal, characteristic, complemented
12C13×#440C211yesmaximal, characteristic, complemented
13C13×#435C211yesmaximal, characteristic, complemented
14C13×#417C211yesmaximal, characteristic, complemented
15C2×C13×#102C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×SD16C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic
21C2×C13×M16C2211yescharacteristic, complemented
22C22×C8×C13C2211yescharacteristic
23C13×C4⋊Q8C2211yescharacteristic, complemented
24C13×#125—21no—
25C13×#124C2211yescharacteristic
26C13×#123—21no—
27C13×C22⋊Q8—21no—
28C13×C22⋊Q8—21no—
29C13×C22⋊Q8C2211yescharacteristic
30C13×C22⋊Q8C2211yescharacteristic
31C13×C22⋊Q8C2211yescharacteristic, complemented
32C13×#121—21no—
33C13×#121C2211yescharacteristic
34C13×#120—21no—
35C4×Q8×C13C2211yescharacteristic, complemented
36C4×D4×C13—21no—
37C4×D4×C13C2211yescharacteristic
38C4×D4×C13C2211yescharacteristic
39C2×C13×C4⋊C4C2211yescharacteristic
40C2×C13×C4⋊C4C2211yescharacteristic, complemented
41C2×C13×C22⋊C4—21no—
42C13×#107C2211yescharacteristic, complemented
43C13×#107C2211yescharacteristic, complemented
44C13×#107C2211yescharacteristic, complemented
45C13×C4⋊C8C2211yescharacteristic, complemented
46C13×#103C2211yescharacteristic, complemented
47C13×#103C2211yescharacteristic, complemented
48C13×#103C2211yescharacteristic, complemented
49C13×#103C2211yescharacteristic, complemented
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×#102C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×C22⋊C8C2211yescharacteristic, complemented
58C13×#97C2211yescharacteristic, complemented
59C24×C13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13—21no—
63C2×Q8×C13C2311yescharacteristic
64C2×Q8×C13C2311yescharacteristic
65C2×D4×C13—22no—
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
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13C2311yescharacteristic
78C22×C4×C13C2311yescharacteristic
79C13×Q16—41no—
80C13×SD16—22no—
81C13×SD16—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⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4D411yescharacteristic
96C13×C4⋊C4C2311yescharacteristic
97C13×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
108C13×C22⋊C4D411yescharacteristic
109C42×C13—21no—
110C42×C13C2311yescharacteristic
111#3314C1311yesmaximal, characteristic, direct product factor, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—81no—
117C23×C13C2×D411yescharacteristic
118C23×C13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121Q8×C13—21no—
122Q8×C13—21no—
123Q8×C13—81no—
124D4×C13—22no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—42no—
129D4×C13—42no—
130D4×C13—81no—
131D4×C13#4112yes—
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—21no—
142C2×C4×C13—42no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13C2×D411yescharacteristic
147C2×C4×C13C2×D411yescharacteristic
148C2×C4×C13C2×D411yescharacteristic
149C2×C4×C13C2×D411yescharacteristic
150C2×C4×C13C2411yescharacteristic
151C8×C13—21no—
152C8×C13—21no—
153C8×C13—21no—
154C8×C13—21no—
155#554C2×C1311yescharacteristic, complemented
156#546C2×C1311yescharacteristic
157#489C2×C1311yescharacteristic, complemented
158#484C2×C1311yescharacteristic, complemented
159#480C2×C1311yescharacteristic, complemented
160#474C2×C1311yescharacteristic, complemented
161#468C2×C1311yescharacteristic, complemented
162#467C2×C1311yescharacteristic, complemented
163#464C2×C1311yescharacteristic, complemented
164#452C2×C1311yescharacteristic, complemented
165#450C2×C1311yescharacteristic, complemented
166#440C2×C1311yescharacteristic, complemented
167#435C2×C1311yescharacteristic, complemented
168#417C2×C1311yescharacteristic, complemented
169C2×#102C2×C1311yescharacteristic, complemented
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—22no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—84no—
182C22×C13#13712yes—
183C22×C13C22×D411yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13C2×#4111yescharacteristic
195C4×C13H(5,𝔽2)11yescharacteristic
196C2×#41C22×C1311yescharacteristic
197C22×D4C22×C1311yescharacteristic
198C2×Q16C22×C1311yescharacteristic, complemented
199C2×SD16C22×C1311yescharacteristic
200C2×SD16C22×C1311yescharacteristic
201C2×M16C22×C1311yescharacteristic, complemented
202C22×C8C22×C1311yescharacteristic
203C4⋊Q8C22×C1311yescharacteristic, complemented
204#125—21no—
205#124C22×C1311yescharacteristic
206#123—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C22⋊Q8C22×C1311yescharacteristic
210C22⋊Q8C22×C1311yescharacteristic
211C22⋊Q8C22×C1311yescharacteristic, complemented
212#121—21no—
213#121C22×C1311yescharacteristic
214#120—21no—
215C4×Q8C22×C1311yescharacteristic, complemented
216C4×D4—21no—
217C4×D4C22×C1311yescharacteristic
218C4×D4C22×C1311yescharacteristic
219C2×C4⋊C4C22×C1311yescharacteristic
220C2×C4⋊C4C22×C1311yescharacteristic, complemented
221C2×C22⋊C4—21no—
222#107C22×C1311yescharacteristic, complemented
223#107C22×C1311yescharacteristic, complemented
224#107C22×C1311yescharacteristic, complemented
225C4⋊C8C22×C1311yescharacteristic, complemented
226#103C22×C1311yescharacteristic, complemented
227#103C22×C1311yescharacteristic, complemented
228#103C22×C1311yescharacteristic, complemented
229#103C22×C1311yescharacteristic, complemented
230#102C22×C1311yescharacteristic
231#102C22×C1311yescharacteristic
232#102C22×C1311yescharacteristic
233#102C22×C1311yescharacteristic
234#102C22×C1311yescharacteristic
235#102C22×C1311yescharacteristic
236C22⋊C8C22×C1311yescharacteristic
237C22⋊C8C22×C1311yescharacteristic, complemented
238#97C22×C1311yescharacteristic, complemented
239C2×C13—22no—
240C2×C13—41no—
241C2×C13—42no—
242C2×C13—81no—
243C2×C13#54611yescharacteristic
244C2×C13C2×#13711yescharacteristic
245C2×C13#57611yescharacteristic
246C24—21no—
247#41—22no—
248#41—41no—
249C2×Q8—21no—
250C2×Q8C23×C1311yescharacteristic
251C2×Q8C23×C1311yescharacteristic
252C2×D4—22no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4D4×C1311yescharacteristic
258C2×D4C23×C1311yescharacteristic
259C2×D4C23×C1311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4C23×C1311yescharacteristic
265C22×C4C23×C1311yescharacteristic
266Q16—41no—
267SD16—22no—
268SD16—41no—
269M16—41no—
270C2×C8—41no—
271C2×C8C23×C1311yescharacteristic
272C2×C8C23×C1311yescharacteristic
273C2×C8C23×C1311yescharacteristic
274C2×C8C23×C1311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4D4×C1311yescharacteristic
283C4⋊C4C23×C1311yescharacteristic
284C4⋊C4C23×C1311yescharacteristic
285C4⋊C4C23×C1311yescharacteristic
286C4⋊C4C23×C1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4D4×C1311yescharacteristic
295C22⋊C4D4×C1311yescharacteristic
296C42—21no—
297C42C23×C1311yescharacteristic
298C13#331411yescharacteristic, direct product factor, Sylow
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×D4×C1311yescharacteristic
305C23C2×D4×C1311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—81no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4C13×#4112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4C2×D4×C1311yescharacteristic
334C2×C4C2×D4×C1311yescharacteristic
335C2×C4C2×D4×C1311yescharacteristic
336C2×C4C2×D4×C1311yescharacteristic
337C2×C4C24×C1311yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22C13×#13712yes—
355C22C22×D4×C1311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4C2×C13×#4111yescharacteristic
367C4C13×H(5,𝔽2)11yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2C13×#54611yescharacteristic
373C2C2×C13×#13711yescharacteristic
374C2C13×#57611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
prime radicalC13×#546C2
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×#554C2semidirect
3. C13×#489C2semidirect
4. C13×#484C2semidirect
5. C13×#480C2semidirect
6. C13×#474C2semidirect
7. C13×#468C2semidirect
8. C13×#467C2semidirect
9. C13×#464C2semidirect
10. C13×#452C2semidirect
11. C13×#450C2semidirect
12. C13×#440C2semidirect
13. C13×#435C2semidirect
14. C13×#417C2semidirect
15. C2×C13×#102C2semidirect
18. C2×C13×Q16C22semidirect
21. C2×C13×M16C22semidirect
23. C13×C4⋊Q8C22semidirect
31. C13×C22⋊Q8C22semidirect
35. C4×Q8×C13C22semidirect
40. C2×C13×C4⋊C4C22semidirect
42. C13×#107C22semidirect
43. C13×#107C22semidirect
44. C13×#107C22semidirect
45. C13×C4⋊C8C22semidirect
46. C13×#103C22semidirect
47. C13×#103C22semidirect
48. C13×#103C22semidirect
49. C13×#103C22semidirect
57. C13×C22⋊C8C22semidirect
58. C13×#97C22semidirect
111. #3314C13direct (N × H)
155. #554C2×C13semidirect
157. #489C2×C13semidirect
158. #484C2×C13semidirect
159. #480C2×C13semidirect
160. #474C2×C13semidirect
161. #468C2×C13semidirect
162. #467C2×C13semidirect
163. #464C2×C13semidirect
164. #452C2×C13semidirect
165. #450C2×C13semidirect
166. #440C2×C13semidirect
167. #435C2×C13semidirect
168. #417C2×C13semidirect
169. C2×#102C2×C13semidirect
198. C2×Q16C22×C13semidirect
201. C2×M16C22×C13semidirect
203. C4⋊Q8C22×C13semidirect
211. C22⋊Q8C22×C13semidirect
215. C4×Q8C22×C13semidirect
220. C2×C4⋊C4C22×C13semidirect
222. #107C22×C13semidirect
223. #107C22×C13semidirect
224. #107C22×C13semidirect
225. C4⋊C8C22×C13semidirect
226. #103C22×C13semidirect
227. #103C22×C13semidirect
228. #103C22×C13semidirect
229. #103C22×C13semidirect
237. C22⋊C8C22×C13semidirect
238. #97C22×C13semidirect
298. C13#3314direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5542
C13×#5462
C13×#4892
C13×#4842
C13×#4802
C13×#4742
C13×#4682
C13×#4672
C13×#4642
C13×#4522
C13×#4502
C13×#4402
C13×#4352
C13×#4172
C2×C13×#1022
#331413