Finite Group Databasebeta

← C13×#13065 #15699404

Subgroups — C13×#13065 #15699404

Order 3328.

510 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
1C22×C13×M32C211yesmaximal, characteristic, complemented
2C13×#3050C211yesmaximal, characteristic
3C2×C13×#360C212yesmaximal, complemented
4C13×#1807C211yesmaximal, characteristic, complemented
5C13×#1386C212yesmaximal, complemented
6C2×C13×#135C2211yescharacteristic
7C23×C8×C13C2211yescharacteristic
8C13×#525—21no—
9C2×C13×M32—21no—
10C2×C13×M32—24no—
11C2×C13×M32C2212yes—
12C22×C13×C16—21no—
13C13×#467C411yescharacteristic, complemented
14C13×#467C411yescharacteristic, complemented
15C13×#466C411yescharacteristic, complemented
16C13×#466C411yescharacteristic, complemented
17C13×#465—21no—
18C13×#465—21no—
19C13×#427C2211yescharacteristic
20C2×C13×#106C2212yes—
21C13×#416—21no—
22C13×#380—21no—
23C13×#360—24no—
24C13×#340—21no—
25C2×C13×#41—21no—
26C23×C4×C13D411yescharacteristic
27C13×#135—22no—
28C13×#135—22no—
29C2×C13×Q16C2×C411yescharacteristic
30C2×C13×SD16—21no—
31C2×C13×D8C2×C411yescharacteristic
32C22×C8×C13—22no—
33C22×C8×C13—22no—
34C22×C8×C13C2×C411yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13D411yescharacteristic
37C22×C8×C13D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C22×C8×C13C2311yescharacteristic
40C13×#123—41no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#120—41no—
46C4×D4×C13—41no—
47C4×D4×C13—41no—
48C13×#117—21no—
49C2×C13×C4⋊C4—22no—
50C2×C13×C22⋊C4—41no—
51C13×M32—24no—
52C13×M32—22no—
53C13×M32D414yescomplemented
54C2×C13×C16—24no—
55C2×C13×C16—22no—
56C13×#107C2×C411yescharacteristic
57C13×#107C2×C411yescharacteristic
58C13×#106—21no—
59C13×#106—22no—
60C13×#106—22no—
61C13×#103—21no—
62C13×#103—21no—
63C13×#102—21no—
64C13×#102—21no—
65C13×#95—41no—
66#13065C1311yesmaximal, characteristic, direct product factor, Sylow
67C24×C13D811yescharacteristic
68C13×#41—42no—
69C13×#41—42no—
70C2×Q8×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—41no—
78C22×C4×C13—42no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13D811yescharacteristic
82C22×C4×C13SD1611yescharacteristic
83C22×C4×C13SD1611yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C13×Q16—22no—
86C13×SD16—41no—
87C13×SD16—41no—
88C13×D8—22no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13C22⋊C411yescharacteristic
97C2×C8×C13C22⋊C411yescharacteristic
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D412yes—
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13#4112yes—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—42no—
107C13×C4⋊C4—42no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—82no—
114C42×C13—41no—
115C13×C16—24no—
116C22×M32C2×C1311yescharacteristic, complemented
117#3050C2×C1311yescharacteristic
118C2×#360C2×C1312yescomplemented
119#1807C2×C1311yescharacteristic, complemented
120#1386C2×C1312yescomplemented
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13#10211yescharacteristic
126C23×C13#10211yescharacteristic
127C23×C13C2×D811yescharacteristic
128Q8×C13—41no—
129Q8×C13—41no—
130D4×C13—41no—
131D4×C13—41no—
132D4×C13—82no—
133D4×C13—82no—
134D4×C13—82no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—82no—
146C2×C4×C13—82no—
147C2×C4×C13—82no—
148C2×C4×C13—82no—
149C2×C4×C13#10211yescharacteristic
150C2×C4×C13#10211yescharacteristic
151C2×C4×C13C2×C22⋊C411yescharacteristic
152C2×C4×C13#12112yes—
153C2×C4×C13C2×SD1611yescharacteristic
154C2×C4×C13#13512yes—
155C8×C13—21no—
156C8×C13—21no—
157C8×C13C4×D412yes—
158C8×C13#12011yescharacteristic
159C8×C13#12311yescharacteristic
160C2×#135C22×C1311yescharacteristic
161C23×C8C22×C1311yescharacteristic
162#525—21no—
163C2×M32—21no—
164C2×M32—24no—
165C2×M32C22×C1312yes—
166C22×C16—21no—
167#467C4×C1311yescharacteristic, complemented
168#467C4×C1311yescharacteristic, complemented
169#466C4×C1311yescharacteristic, complemented
170#466C4×C1311yescharacteristic, complemented
171#465—21no—
172#465—21no—
173#427C22×C1311yescharacteristic
174C2×#106C22×C1312yes—
175#416—21no—
176#380—21no—
177#360—24no—
178#340—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—44no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13#36012yescomplemented
191C22×C13C2×#10211yescharacteristic
192C22×C13#46612yes—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—162no—
199C4×C13#38611yescharacteristic
200C4×C13#41611yescharacteristic
201C4×C13#46512yes—
202C2×#41—21no—
203C23×C4D4×C1311yescharacteristic
204#135—22no—
205#135—22no—
206C2×Q16C2×C4×C1311yescharacteristic
207C2×SD16—21no—
208C2×D8C2×C4×C1311yescharacteristic
209C22×C8—22no—
210C22×C8—22no—
211C22×C8C2×C4×C1311yescharacteristic
212C22×C8C2×C4×C1311yescharacteristic
213C22×C8D4×C1311yescharacteristic
214C22×C8D4×C1311yescharacteristic
215C22×C8D4×C1311yescharacteristic
216C22×C8C23×C1311yescharacteristic
217#123—41no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#121—21no—
221#121—21no—
222#120—41no—
223C4×D4—41no—
224C4×D4—41no—
225#117—21no—
226C2×C4⋊C4—22no—
227C2×C22⋊C4—41no—
228M32—24no—
229M32—22no—
230M32D4×C1314yescomplemented
231C2×C16—24no—
232C2×C16—22no—
233#107C2×C4×C1311yescharacteristic
234#107C2×C4×C1311yescharacteristic
235#106—21no—
236#106—22no—
237#106—22no—
238#103—21no—
239#103—21no—
240#102—21no—
241#102—21no—
242#95—41no—
243C2×C13—22no—
244C2×C13—22no—
245C2×C13—41no—
246C2×C13—161no—
247C2×C13#189311yescharacteristic
248C2×C13C2×#36011yescharacteristic
249C2×C13#214511yescharacteristic
250C24C13×D811yescharacteristic
251#41—42no—
252#41—42no—
253C2×Q8—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—42no—
262C22×C4C13×C22⋊C411yescharacteristic
263C22×C4C13×C22⋊C411yescharacteristic
264C22×C4C13×D811yescharacteristic
265C22×C4C13×SD1611yescharacteristic
266C22×C4C13×SD1611yescharacteristic
267C22×C4C2×D4×C1311yescharacteristic
268Q16—22no—
269SD16—41no—
270SD16—41no—
271D8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8C13×C22⋊C411yescharacteristic
280C2×C8C13×C22⋊C411yescharacteristic
281C2×C8C22×C4×C1311yescharacteristic
282C2×C8C2×D4×C1312yes—
283C2×C8C2×D4×C1311yescharacteristic
284C2×C8C13×#4112yes—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—82no—
297C42—41no—
298C16—24no—
299C13#1306511yescharacteristic, direct product factor, Sylow
300C23—22no—
301C23—22no—
302C23—41no—
303C23—41no—
304C23C13×#10211yescharacteristic
305C23C13×#10211yescharacteristic
306C23C2×C13×D811yescharacteristic
307Q8—41no—
308Q8—41no—
309D4—41no—
310D4—41no—
311D4—82no—
312D4—82no—
313D4—82no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4C13×#10211yescharacteristic
329C2×C4C13×#10211yescharacteristic
330C2×C4C2×C13×C22⋊C411yescharacteristic
331C2×C4C13×#12112yes—
332C2×C4C2×C13×SD1611yescharacteristic
333C2×C4C13×#13512yes—
334C8—21no—
335C8—21no—
336C8C4×D4×C1312yes—
337C8C13×#12011yescharacteristic
338C8C13×#12311yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22C13×#36012yescomplemented
351C22C2×C13×#10211yescharacteristic
352C22C13×#46612yes—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—162no—
359C4C13×#38611yescharacteristic
360C4C13×#41611yescharacteristic
361C4C13×#46512yes—
362C2—22no—
363C2—22no—
364C2—41no—
365C2—161no—
366C2C13×#189311yescharacteristic
367C2C2×C13×#36011yescharacteristic
368C2C13×#214511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#102
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×M32C2semidirect
3. C2×C13×#360C2semidirect
4. C13×#1807C2semidirect
5. C13×#1386C2semidirect
13. C13×#467C4semidirect
14. C13×#467C4semidirect
15. C13×#466C4semidirect
16. C13×#466C4semidirect
53. C13×M32D4semidirect
66. #13065C13direct (N × H)
116. C22×M32C2×C13semidirect
118. C2×#360C2×C13semidirect
119. #1807C2×C13semidirect
120. #1386C2×C13semidirect
167. #467C4×C13semidirect
168. #467C4×C13semidirect
169. #466C4×C13semidirect
170. #466C4×C13semidirect
190. C22×C13#360semidirect
230. M32D4×C13semidirect
299. C13#13065direct (N × H)
350. C22C13×#360semidirect

Maximal subgroups

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

subgroupindex
C22×C13×M322
C13×#30502
C2×C13×#3602
C13×#18072
C13×#13862
#1306513