Finite Group Databasebeta

← C13×#3309 #13112367

Subgroups — C13×#3309 #13112367

Order 1664.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#553C211yesmaximal, characteristic, complemented
2C13×#550C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4C13×#482C211yesmaximal, characteristic, complemented
5C13×#480C211yesmaximal, characteristic, complemented
6C13×#479C211yesmaximal, characteristic, complemented
7C13×#469C211yesmaximal, characteristic, complemented
8C13×#466C211yesmaximal, characteristic, complemented
9C13×#459C211yesmaximal, characteristic, complemented
10C13×#449C211yesmaximal, characteristic, complemented
11C13×#449C211yesmaximal, characteristic, complemented
12C13×#440C211yesmaximal, characteristic, complemented
13C13×#435C211yesmaximal, characteristic, complemented
14C13×#417C211yesmaximal, characteristic, complemented
15C13×#416C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×#41C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C2×C13×M16C2211yescharacteristic
22C22×C8×C13C2211yescharacteristic
23C13×#127—21no—
24C13×#127C2211yescharacteristic
25C13×#126—21no—
26C13×#125C2211yescharacteristic
27C13×#123—21no—
28C13×#121—21no—
29C13×#121—21no—
30C13×#121—21no—
31C13×#121C2211yescharacteristic
32C13×#121C2211yescharacteristic
33C13×#121C2211yescharacteristic
34C13×#121C2211yescharacteristic
35C4×Q8×C13C2211yescharacteristic
36C4×D4×C13—21no—
37C4×D4×C13—21no—
38C4×D4×C13C2211yescharacteristic
39C4×D4×C13C2211yescharacteristic
40C13×#117C2211yescharacteristic
41C2×C13×C4⋊C4C2211yescharacteristic
42C13×#107C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#106C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic
46C13×#103C2211yescharacteristic
47C13×#103C2211yescharacteristic
48C13×#103C2211yescharacteristic
49C13×#102C2211yescharacteristic
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×#102C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×C22⋊C8C2211yescharacteristic
58C13×#97C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C13×#41—41no—
62C13×#41—41no—
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13—21no—
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×C13D411yescharacteristic
73C2×D4×C13C2311yescharacteristic
74C2×D4×C13C2311yescharacteristic
75C2×D4×C13C2311yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13C2311yescharacteristic
81C22×C4×C13C2311yescharacteristic
82C13×SD16—22no—
83C13×D8—41no—
84C13×D8—41no—
85C13×M16—41no—
86C2×C8×C13—41no—
87C2×C8×C13C2311yescharacteristic
88C2×C8×C13C2311yescharacteristic
89C2×C8×C13C2311yescharacteristic
90C2×C8×C13C2311yescharacteristic
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⋊C4D411yescharacteristic
107C13×C22⋊C4D411yescharacteristic
108C42×C13—21no—
109C42×C13—21no—
110C42×C13C2311yescharacteristic
111#3309C1311yesmaximal, characteristic, direct product factor, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C2×D411yescharacteristic
116C23×C13C2×D411yescharacteristic
117Q8×C13—21no—
118Q8×C13#4112yes—
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—41no—
126D4×C13—42no—
127D4×C13—42no—
128D4×C13—42no—
129D4×C13—42no—
130D4×C13—81no—
131D4×C13—81no—
132D4×C13—81no—
133D4×C13—81no—
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—42no—
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#550C2×C1311yescharacteristic, complemented
158#490C2×C1311yescharacteristic, complemented
159#482C2×C1311yescharacteristic, complemented
160#480C2×C1311yescharacteristic, complemented
161#479C2×C1311yescharacteristic, complemented
162#469C2×C1311yescharacteristic, complemented
163#466C2×C1311yescharacteristic, complemented
164#459C2×C1311yescharacteristic, complemented
165#449C2×C1311yescharacteristic, complemented
166#449C2×C1311yescharacteristic, complemented
167#440C2×C1311yescharacteristic, complemented
168#435C2×C1311yescharacteristic, complemented
169#417C2×C1311yescharacteristic, complemented
170#416C2×C1311yescharacteristic, complemented
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
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—41no—
186C22×C13C22×D411yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—22no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13C2×#4111yescharacteristic
197C4×C13H(5,𝔽2)11yescharacteristic
198C2×#41C22×C1311yescharacteristic
199C2×#41C22×C1311yescharacteristic
200C2×SD16C22×C1311yescharacteristic
201C2×D8C22×C1311yescharacteristic
202C2×D8C22×C1311yescharacteristic
203C2×M16C22×C1311yescharacteristic
204C22×C8C22×C1311yescharacteristic
205#127—21no—
206#127C22×C1311yescharacteristic
207#126—21no—
208#125C22×C1311yescharacteristic
209#123—21no—
210#121—21no—
211#121—21no—
212#121—21no—
213#121C22×C1311yescharacteristic
214#121C22×C1311yescharacteristic
215#121C22×C1311yescharacteristic
216#121C22×C1311yescharacteristic
217C4×Q8C22×C1311yescharacteristic
218C4×D4—21no—
219C4×D4—21no—
220C4×D4C22×C1311yescharacteristic
221C4×D4C22×C1311yescharacteristic
222#117C22×C1311yescharacteristic
223C2×C4⋊C4C22×C1311yescharacteristic
224#107C22×C1311yescharacteristic
225#107C22×C1311yescharacteristic
226#106C22×C1311yescharacteristic
227C4⋊C8C22×C1311yescharacteristic
228#103C22×C1311yescharacteristic
229#103C22×C1311yescharacteristic
230#103C22×C1311yescharacteristic
231#102C22×C1311yescharacteristic
232#102C22×C1311yescharacteristic
233#102C22×C1311yescharacteristic
234#102C22×C1311yescharacteristic
235#102C22×C1311yescharacteristic
236#102C22×C1311yescharacteristic
237#102C22×C1311yescharacteristic
238C22⋊C8C22×C1311yescharacteristic
239C22⋊C8C22×C1311yescharacteristic
240#97C22×C1311yescharacteristic
241C2×C13—41no—
242C2×C13—41no—
243C2×C13—81no—
244C2×C13—81no—
245C2×C13—81no—
246C2×C13#54611yescharacteristic
247C2×C13#57511yescharacteristic
248C2×C13#57611yescharacteristic
249#41—22no—
250#41—22no—
251#41—41no—
252#41—41no—
253C2×Q8C23×C1311yescharacteristic
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4D4×C1311yescharacteristic
263C2×D4C23×C1311yescharacteristic
264C2×D4C23×C1311yescharacteristic
265C2×D4C23×C1311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4C23×C1311yescharacteristic
271C22×C4C23×C1311yescharacteristic
272SD16—22no—
273D8—41no—
274D8—41no—
275M16—41no—
276C2×C8—41no—
277C2×C8C23×C1311yescharacteristic
278C2×C8C23×C1311yescharacteristic
279C2×C8C23×C1311yescharacteristic
280C2×C8C23×C1311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4D4×C1311yescharacteristic
286C4⋊C4C23×C1311yescharacteristic
287C4⋊C4C23×C1311yescharacteristic
288C4⋊C4C23×C1311yescharacteristic
289C4⋊C4C23×C1311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4D4×C1311yescharacteristic
297C22⋊C4D4×C1311yescharacteristic
298C42—21no—
299C42—21no—
300C42C23×C1311yescharacteristic
301C13#330911yescharacteristic, direct product factor, Sylow
302C23—21no—
303C23—21no—
304C23—21no—
305C23C2×D4×C1311yescharacteristic
306C23C2×D4×C1311yescharacteristic
307Q8—21no—
308Q8C13×#4112yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—41no—
316D4—42no—
317D4—42no—
318D4—42no—
319D4—42no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
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—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C2×D4×C1311yescharacteristic
338C2×C4C2×D4×C1311yescharacteristic
339C2×C4C2×D4×C1311yescharacteristic
340C2×C4C2×D4×C1311yescharacteristic
341C2×C4C24×C1311yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×D4×C1311yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4C2×C13×#4111yescharacteristic
372C4C13×H(5,𝔽2)11yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—81no—
378C2C13×#54611yescharacteristic
379C2C13×#57511yescharacteristic
380C2C13×#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×#550C2semidirect
3. C13×#490C2semidirect
4. C13×#482C2semidirect
5. C13×#480C2semidirect
6. C13×#479C2semidirect
7. C13×#469C2semidirect
8. C13×#466C2semidirect
9. C13×#459C2semidirect
10. C13×#449C2semidirect
11. C13×#449C2semidirect
12. C13×#440C2semidirect
13. C13×#435C2semidirect
14. C13×#417C2semidirect
15. C13×#416C2semidirect
111. #3309C13direct (N × H)
156. #553C2×C13semidirect
157. #550C2×C13semidirect
158. #490C2×C13semidirect
159. #482C2×C13semidirect
160. #480C2×C13semidirect
161. #479C2×C13semidirect
162. #469C2×C13semidirect
163. #466C2×C13semidirect
164. #459C2×C13semidirect
165. #449C2×C13semidirect
166. #449C2×C13semidirect
167. #440C2×C13semidirect
168. #435C2×C13semidirect
169. #417C2×C13semidirect
170. #416C2×C13semidirect
301. C13#3309direct (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×#5502
C13×#4902
C13×#4822
C13×#4802
C13×#4792
C13×#4692
C13×#4662
C13×#4592
C13×#4492
C13×#4402
C13×#4352
C13×#4172
C13×#4162
#330913