Finite Group Databasebeta

← C13×#9524 #15695863

Subgroups — C13×#9524 #15695863

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3007C211yesmaximal, characteristic
2C13×#2332C211yesmaximal, characteristic, complemented
3C13×#1789C211yesmaximal, characteristic
4C13×#1782C211yesmaximal, characteristic
5C13×#1511C211yesmaximal, characteristic, complemented
6C13×#1306C211yesmaximal, characteristic, complemented
7C13×#1284C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C2×C13×#137—21no—
10C2×C13×C22⋊Q8C2211yescharacteristic
11C13×#452—22no—
12C13×#451C412yescomplemented
13C13×#450C412yescomplemented
14C2×C13×#104—21no—
15C2×C13×#104—21no—
16C13×#417—21no—
17C2×C13×#99—21no—
18C2×C13×#99—21no—
19C13×#407C2211yescharacteristic
20C13×#407C2211yescharacteristic
21C13×#391—21no—
22C13×#388—21no—
23C13×#388—21no—
24C13×#387—21no—
25C13×#387—21no—
26C13×#381C2211yescharacteristic
27C13×#381C2211yescharacteristic
28C4×C13×C4⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C13×#328—22no—
31C2×C13×#41—21no—
32C2×C13×#41—21no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—42no—
36C2×C13×#41—42no—
37C22×Q8×C13C2×C411yescharacteristic
38C22×Q8×C13D411yescharacteristic
39C22×D4×C13—21no—
40C22×D4×C13C2×C411yescharacteristic
41C23×C4×C13—21no—
42C23×C4×C13C2311yescharacteristic
43C13×#137—42no—
44C13×#137—42no—
45C2×C13×Q16—22no—
46C2×C13×SD16—22no—
47C2×C13×M16—21no—
48C2×C13×M16—21no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8C2×C412yes—
52C13×C22⋊Q8D412yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4D411yescharacteristic
61C2×C13×C22⋊C4D411yescharacteristic
62C2×C42×C13—21no—
63C2×C42×C13—21no—
64C2×C42×C13D411yescharacteristic
65C2×C42×C13D411yescharacteristic
66C13×#104—42no—
67C13×#104—42no—
68C13×#103—22no—
69C13×#102—22no—
70C13×#99—42no—
71C13×#99—42no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8C2×C412yes—
76C13×#95—21no—
77C13×#95—21no—
78C13×#95—21no—
79C13×#95—21no—
80C13×#95—21no—
81C13×#95—21no—
82C13×#95—21no—
83C13×#95—21no—
84C13×#95—21no—
85#9524C1311yesmaximal, characteristic, direct product factor, Sylow
86C24×C13—21no—
87C24×C13C2×D411yescharacteristic
88C13×#41—22no—
89C13×#41—22no—
90C13×#41—22no—
91C13×#41—22no—
92C13×#41—41no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C13×#41—42no—
97C13×#41—42no—
98C13×#41—42no—
99C13×#41—42no—
100C2×Q8×C13—21no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13—42no—
104C2×Q8×C13—41no—
105C2×Q8×C13—41no—
106C2×Q8×C13C22⋊C412yes—
107C2×D4×C13—22no—
108C2×D4×C13—22no—
109C2×D4×C13—21no—
110C2×D4×C13—21no—
111C2×D4×C13—42no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13#4111yescharacteristic
135C22×C4×C13#4111yescharacteristic
136C13×Q16—44no—
137C13×SD16—44no—
138C13×M16—41no—
139C13×M16—41no—
140C13×M16—41no—
141C13×M16—41no—
142C2×C8×C13—22no—
143C2×C8×C13—41no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—42no—
148C13×C4⋊C4—81no—
149C13×C4⋊C4C22⋊C412yes—
150C13×C22⋊C4—22no—
151C13×C22⋊C4—22no—
152C13×C22⋊C4—42no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C42×C13—41no—
158C42×C13—41no—
159C42×C13—42no—
160C42×C13—81no—
161#3007C2×C1311yescharacteristic
162#2332C2×C1311yescharacteristic, complemented
163#1789C2×C1311yescharacteristic
164#1782C2×C1311yescharacteristic
165#1511C2×C1311yescharacteristic, complemented
166#1306C2×C1311yescharacteristic, complemented
167#1284C2×C1311yescharacteristic, complemented
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—22no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—81no—
176C23×C13—81no—
177C23×C13C4×D411yescharacteristic
178C23×C13#12011yescharacteristic
179C23×C13#12111yescharacteristic
180Q8×C13—22no—
181Q8×C13—22no—
182Q8×C13—41no—
183Q8×C13—41no—
184Q8×C13—42no—
185Q8×C13—81no—
186D4×C13—22no—
187D4×C13—22no—
188D4×C13—41no—
189D4×C13—41no—
190D4×C13—42no—
191D4×C13—42no—
192D4×C13—42no—
193D4×C13—42no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—81no—
228C2×C4×C13—81no—
229C2×C4×C13—81no—
230C2×C4×C13C2×C22⋊C411yescharacteristic
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13#12111yescharacteristic
233C2×C4×C13#12311yescharacteristic
234C8×C13—42no—
235C8×C13—81no—
236C22×#41C22×C1311yescharacteristic
237C2×#137—21no—
238C2×C22⋊Q8C22×C1311yescharacteristic
239#452—22no—
240#451C4×C1312yescomplemented
241#450C4×C1312yescomplemented
242C2×#104—21no—
243C2×#104—21no—
244#417—21no—
245C2×#99—21no—
246C2×#99—21no—
247#407C22×C1311yescharacteristic
248#407C22×C1311yescharacteristic
249#391—21no—
250#388—21no—
251#388—21no—
252#387—21no—
253#387—21no—
254#381C22×C1311yescharacteristic
255#381C22×C1311yescharacteristic
256C4×C4⋊C4—21no—
257C4×C22⋊C4C22×C1311yescharacteristic
258#328—22no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—42no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—82no—
271C22×C13—82no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13#38611yescharacteristic
275C22×C13B(4,𝔽2)11yescharacteristic
276C22×C13B(4,𝔽2)11yescharacteristic
277C4×C13—21no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—42no—
282C4×C13—42no—
283C4×C13—42no—
284C4×C13—42no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13—161no—
289C2×#41—21no—
290C2×#41—21no—
291C2×#41—21no—
292C2×#41—21no—
293C2×#41—42no—
294C2×#41—42no—
295C22×Q8C2×C4×C1311yescharacteristic
296C22×Q8D4×C1311yescharacteristic
297C22×D4—21no—
298C22×D4C2×C4×C1311yescharacteristic
299C23×C4—21no—
300C23×C4C23×C1311yescharacteristic
301#137—42no—
302#137—42no—
303C2×Q16—22no—
304C2×SD16—22no—
305C2×M16—21no—
306C2×M16—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8C2×C4×C1312yes—
310C22⋊Q8D4×C1312yes—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C1311yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4D4×C1311yescharacteristic
319C2×C22⋊C4D4×C1311yescharacteristic
320C2×C42—21no—
321C2×C42—21no—
322C2×C42D4×C1311yescharacteristic
323C2×C42D4×C1311yescharacteristic
324#104—42no—
325#104—42no—
326#103—22no—
327#102—22no—
328#99—42no—
329#99—42no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8C2×C4×C1312yes—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343C2×C13—21no—
344C2×C13—21no—
345C2×C13—41no—
346C2×C13—41no—
347C2×C13—82no—
348C2×C13#188911yescharacteristic
349C2×C13#190511yescharacteristic
350C2×C13#190611yescharacteristic
351C24—21no—
352C24C2×D4×C1311yescharacteristic
353#41—22no—
354#41—22no—
355#41—22no—
356#41—22no—
357#41—41no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—42no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—42no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8C13×C22⋊C412yes—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—42no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4C22×C4×C1311yescharacteristic
396C22×C4C2×D4×C1311yescharacteristic
397C22×C4C2×D4×C1311yescharacteristic
398C22×C4C2×D4×C1311yescharacteristic
399C22×C4C13×#4111yescharacteristic
400C22×C4C13×#4111yescharacteristic
401Q16—44no—
402SD16—44no—
403M16—41no—
404M16—41no—
405M16—41no—
406M16—41no—
407C2×C8—22no—
408C2×C8—41no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—42no—
413C4⋊C4—81no—
414C4⋊C4C13×C22⋊C412yes—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C42—41no—
423C42—41no—
424C42—42no—
425C42—81no—
426C13#952411yescharacteristic, direct product factor, Sylow
427C23—21no—
428C23—21no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—81no—
435C23—81no—
436C23C4×D4×C1311yescharacteristic
437C23C13×#12011yescharacteristic
438C23C13×#12111yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—42no—
442Q8—41no—
443Q8—41no—
444Q8—81no—
445D4—22no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4C2×C13×C22⋊C411yescharacteristic
490C2×C4C4×D4×C1311yescharacteristic
491C2×C4C13×#12111yescharacteristic
492C2×C4C13×#12311yescharacteristic
493C8—42no—
494C8—81no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22C13×#38611yescharacteristic
511C22C13×B(4,𝔽2)11yescharacteristic
512C22C13×B(4,𝔽2)11yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—81no—
522C4—81no—
523C4—81no—
524C4—161no—
525C2—21no—
526C2—21no—
527C2—41no—
528C2—41no—
529C2—82no—
530C2C13×#188911yescharacteristic
531C2C13×#190511yescharacteristic
532C2C13×#190611yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC22×C13×#41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2332C2semidirect
5. C13×#1511C2semidirect
6. C13×#1306C2semidirect
7. C13×#1284C2semidirect
12. C13×#451C4semidirect
13. C13×#450C4semidirect
85. #9524C13direct (N × H)
162. #2332C2×C13semidirect
165. #1511C2×C13semidirect
166. #1306C2×C13semidirect
167. #1284C2×C13semidirect
240. #451C4×C13semidirect
241. #450C4×C13semidirect
426. C13#9524direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30072
C13×#23322
C13×#17892
C13×#17822
C13×#15112
C13×#13062
C13×#12842
#952413