Finite Group Databasebeta

← C13×#10196 #15696535

Subgroups — C13×#10196 #15696535

Order 3328.

546 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3245C211yesmaximal, characteristic
2C13×#3206C211yesmaximal, characteristic, complemented
3C13×#3141C211yesmaximal, characteristic, complemented
4C13×#1987C211yesmaximal, characteristic, complemented
5C13×#1980C211yesmaximal, characteristic, complemented
6C13×#1502C211yesmaximal, characteristic, complemented
7C13×#1283C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C13×#492—21no—
12C13×#489—22no—
13C13×#487—21no—
14C13×#487—21no—
15C13×#486—21no—
16C13×#474—21no—
17C13×#474—21no—
18C13×#466—22no—
19C13×#461—22no—
20C13×#459—21no—
21C13×#459—21no—
22C13×#448—22no—
23C13×#431C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#104—22no—
26C13×#417—22no—
27C4×C13×M16C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C13×#340—22no—
30C13×#327—22no—
31C2×C13×#41—21no—
32C2×C13×#41—21no—
33C22×Q8×C13—21no—
34C2×C13×SD16—24no—
35C2×C13×D8—22no—
36C2×C13×M16D412yes—
37C22×C8×C13D412yes—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8D412yes—
42C13×C4⋊Q8D411yescharacteristic
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#127D411yescharacteristic
46C13×#124—21no—
47C13×#124—21no—
48C13×#121—21no—
49C13×#121—21no—
50C13×#121—21no—
51C13×#121—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C4×D4×C13—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C42×C13—21no—
60C2×C42×C13C2311yescharacteristic
61C13×#107—22no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#104—44no—
66C13×#103—24no—
67C13×#103—24no—
68C13×#102—24no—
69C13×#102—22no—
70C13×#102—22no—
71C13×C22⋊C8D412yes—
72C13×#97—21no—
73C4×C8×C13—21no—
74C4×C8×C13—21no—
75C13×#95—21no—
76#10196C1311yesmaximal, characteristic, direct product factor, Sylow
77C13×#41—42no—
78C13×#41—42no—
79C13×#41—42no—
80C13×#41—42no—
81C2×Q8×C13—21no—
82C2×Q8×C13—22no—
83C2×Q8×C13—21no—
84C2×Q8×C13—41no—
85C2×Q8×C13—82no—
86C2×D4×C13—21no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C13×SD16—84no—
102C13×D8—82no—
103C13×M16—22no—
104C13×M16—22no—
105C2×C8×C13—22no—
106C2×C8×C13—22no—
107C2×C8×C13—22no—
108C2×C8×C13—42no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C42×C13—42no—
124C42×C13C2×D411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13#4111yescharacteristic
128#3245C2×C1311yescharacteristic
129#3206C2×C1311yescharacteristic, complemented
130#3141C2×C1311yescharacteristic, complemented
131#1987C2×C1311yescharacteristic, complemented
132#1980C2×C1311yescharacteristic, complemented
133#1502C2×C1311yescharacteristic, complemented
134#1283C2×C1311yescharacteristic, complemented
135C23×C13—41no—
136C23×C13—41no—
137C23×C13#12711yescharacteristic
138Q8×C13—44no—
139Q8×C13—42no—
140Q8×C13—42no—
141Q8×C13—82no—
142D4×C13—42no—
143D4×C13—42no—
144D4×C13—41no—
145D4×C13—41no—
146D4×C13—41no—
147D4×C13—41no—
148D4×C13—42no—
149D4×C13—81no—
150D4×C13—81no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—81no—
162C2×C4×C13—82no—
163C2×C4×C13—81no—
164C2×C4×C13—82no—
165C2×C4×C13—82no—
166C2×C4×C13#12011yescharacteristic
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12011yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#13512yes—
173C2×C4×C13AGL(1,ℤ/8)12yes—
174C8×C13—42no—
175C8×C13—42no—
176C8×C13—42no—
177#532C22×C1311yescharacteristic
178#532C22×C1311yescharacteristic
179C2×C4⋊Q8C22×C1311yescharacteristic
180#492—21no—
181#489—22no—
182#487—21no—
183#487—21no—
184#486—21no—
185#474—21no—
186#474—21no—
187#466—22no—
188#461—22no—
189#459—21no—
190#459—21no—
191#448—22no—
192#431C22×C1311yescharacteristic
193C2×C4⋊C8C22×C1311yescharacteristic
194C2×#104—22no—
195#417—22no—
196C4×M16C22×C1311yescharacteristic
197C4×C4⋊C4C22×C1311yescharacteristic
198#340—22no—
199#327—22no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13#39211yescharacteristic
209C22×C13#49511yescharacteristic
210C22×C13#49611yescharacteristic
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—82no—
215C4×C13—82no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13#44912yes—
219C4×C13#45511yescharacteristic
220C4×C13#45611yescharacteristic
221C4×C13#46312yes—
222C2×#41—21no—
223C2×#41—21no—
224C22×Q8—21no—
225C2×SD16—24no—
226C2×D8—22no—
227C2×M16D4×C1312yes—
228C22×C8D4×C1312yes—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8D4×C1312yes—
233C4⋊Q8D4×C1311yescharacteristic
234C4⋊Q8D4×C1311yescharacteristic
235#127D4×C1311yescharacteristic
236#127D4×C1311yescharacteristic
237#124—21no—
238#124—21no—
239#121—21no—
240#121—21no—
241#121—21no—
242#121—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42C23×C1311yescharacteristic
252#107—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256#104—44no—
257#103—24no—
258#103—24no—
259#102—24no—
260#102—22no—
261#102—22no—
262C22⋊C8D4×C1312yes—
263#97—21no—
264C4×C8—21no—
265C4×C8—21no—
266#95—21no—
267C2×C13—21no—
268C2×C13—21no—
269C2×C13—161no—
270C2×C13—161no—
271C2×C13#200711yescharacteristic
272C2×C13#200811yescharacteristic
273C2×C13#201211yescharacteristic
274#41—42no—
275#41—42no—
276#41—42no—
277#41—42no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—21no—
281C2×Q8—41no—
282C2×Q8—82no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4C2×D4×C1311yescharacteristic
296C22×C4C2×D4×C1311yescharacteristic
297C22×C4C2×D4×C1311yescharacteristic
298SD16—84no—
299D8—82no—
300M16—22no—
301M16—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—42no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42—42no—
321C42C2×D4×C1311yescharacteristic
322C42C2×D4×C1311yescharacteristic
323C42C2×D4×C1311yescharacteristic
324C42C13×#4111yescharacteristic
325C13#1019611yescharacteristic, direct product factor, Sylow
326C23—41no—
327C23—41no—
328C23C13×#12711yescharacteristic
329Q8—44no—
330Q8—42no—
331Q8—42no—
332Q8—82no—
333D4—42no—
334D4—42no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—42no—
340D4—81no—
341D4—81no—
342D4—81no—
343D4—81no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4C13×#12011yescharacteristic
358C2×C4C13×#12011yescharacteristic
359C2×C4C13×#12011yescharacteristic
360C2×C4C13×#12111yescharacteristic
361C2×C4C13×#12111yescharacteristic
362C2×C4C13×#12111yescharacteristic
363C2×C4C13×#13512yes—
364C2×C4C13×AGL(1,ℤ/8)12yes—
365C8—42no—
366C8—42no—
367C8—42no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22C13×#39211yescharacteristic
377C22C13×#49511yescharacteristic
378C22C13×#49611yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—82no—
384C4—81no—
385C4—81no—
386C4C13×#44912yes—
387C4C13×#45511yescharacteristic
388C4C13×#45611yescharacteristic
389C4C13×#46312yes—
390C2—21no—
391C2—21no—
392C2—161no—
393C2—161no—
394C2C13×#200711yescharacteristic
395C2C13×#200811yescharacteristic
396C2C13×#201211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3245C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3206C2semidirect
3. C13×#3141C2semidirect
4. C13×#1987C2semidirect
5. C13×#1980C2semidirect
6. C13×#1502C2semidirect
7. C13×#1283C2semidirect
76. #10196C13direct (N × H)
129. #3206C2×C13semidirect
130. #3141C2×C13semidirect
131. #1987C2×C13semidirect
132. #1980C2×C13semidirect
133. #1502C2×C13semidirect
134. #1283C2×C13semidirect
325. C13#10196direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32452
C13×#32062
C13×#31412
C13×#19872
C13×#19802
C13×#15022
C13×#12832
#1019613