Finite Group Databasebeta

← C13×#19821 #15706160

Subgroups — C13×#19821 #15706160

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3364C211yesmaximal, characteristic, complemented
2C13×#3359C211yesmaximal, characteristic, complemented
3C13×#3324C211yesmaximal, characteristic
4D4×C13×SD16C211yesmaximal, characteristic
5C13×#1719C211yesmaximal, characteristic, complemented
6C13×#1699C211yesmaximal, characteristic, complemented
7C13×#1682C211yesmaximal, characteristic, complemented
8C13×#1679C211yesmaximal, characteristic, complemented
9C13×#1666C211yesmaximal, characteristic, complemented
10C13×#1650C211yesmaximal, characteristic, complemented
11C13×#1649C211yesmaximal, characteristic, complemented
12C13×#1639C211yesmaximal, characteristic
13C13×#1626C211yesmaximal, characteristic, complemented
14C13×#1583C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16C22×C13×SD16—21no—
17C13×#557C2211yescharacteristic, complemented
18C13×#556C2211yescharacteristic
19D4×Q8×C13C2211yescharacteristic
20D42×C13C2211yescharacteristic
21C13×#500C2211yescharacteristic, complemented
22C13×#492C2211yescharacteristic
23C13×#488—21no—
24C13×#487—21no—
25C13×#487C2211yescharacteristic, complemented
26C13×#487C2211yescharacteristic, complemented
27C13×#486C2211yescharacteristic
28C13×#486C2211yescharacteristic
29C13×#482—21no—
30C13×#479—21no—
31C13×#475—21no—
32C13×#475C2211yescharacteristic, complemented
33C13×#474C2211yescharacteristic
34C13×#474C2211yescharacteristic
35C13×#468—21no—
36C13×#465—21no—
37C13×#464—21no—
38C13×#462C2211yescharacteristic, complemented
39C13×#461—21no—
40C13×#461C2211yescharacteristic
41C13×#461C2211yescharacteristic
42C13×#460C2211yescharacteristic
43C13×#460C2211yescharacteristic
44C13×#450—21no—
45C13×#450—21no—
46C13×#448—21no—
47C8×Q8×C13C2211yescharacteristic, complemented
48C8×Q8×C13C2211yescharacteristic, complemented
49C4×C13×Q16—21no—
50C4×C13×SD16—21no—
51C4×C13×SD16C2211yescharacteristic
52C4×C13×SD16C2211yescharacteristic
53C13×#436C2211yescharacteristic
54C8×D4×C13C2211yescharacteristic
55C13×#418—21no—
56C13×#335C2211yescharacteristic, complemented
57C13×#334C2211yescharacteristic, complemented
58C13×#332C2211yescharacteristic, complemented
59C13×#332C2211yescharacteristic, complemented
60C13×#332C2211yescharacteristic, complemented
61C13×#331C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic, complemented
63C13×Q8⋊C8C2211yescharacteristic, complemented
64C13×D4⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic, complemented
67C22×Q8×C13—21no—
68C22×D4×C13—21no—
69C22×D4×C13—21no—
70C2×C13×Q16—21no—
71C2×C13×SD16—21no—
72C2×C13×SD16—21no—
73C2×C13×SD16—21no—
74C2×C13×SD16—21no—
75C2×C13×SD16—21no—
76C2×C13×SD16—21no—
77C2×C13×SD16—44no—
78C2×C13×SD16D411yescharacteristic
79C2×C13×SD16D411yescharacteristic
80C2×C13×M16—21no—
81C22×C8×C13—21no—
82C13×C4⋊Q8—21no—
83C13×C4⋊Q8—21no—
84C13×C4⋊Q8C2311yescharacteristic
85C13×C4⋊Q8C2311yescharacteristic
86C13×C4⋊Q8C2311yescharacteristic
87C13×#127C2311yescharacteristic
88C13×#126—41no—
89C13×#125—21no—
90C13×#125—41no—
91C13×#124—21no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—41no—
95C13×#121—21no—
96C13×#121—21no—
97C13×#120—41no—
98C4×Q8×C13—21no—
99C4×Q8×C13—21no—
100C4×Q8×C13—21no—
101C4×Q8×C13C2311yescharacteristic
102C4×Q8×C13C2311yescharacteristic
103C4×D4×C13—21no—
104C4×D4×C13C2311yescharacteristic
105C4×D4×C13C2311yescharacteristic
106C13×#117—21no—
107C13×#107—21no—
108C13×#107—21no—
109C13×#107—41no—
110C13×#106—21no—
111C13×#106D411yescharacteristic
112C13×#106D411yescharacteristic
113C13×C4⋊C8—21no—
114C13×C4⋊C8—21no—
115C13×C4⋊C8C2311yescharacteristic
116C13×C4⋊C8C2311yescharacteristic
117C13×C4⋊C8C2311yescharacteristic
118C13×C4⋊C8C2311yescharacteristic
119C13×#103—21no—
120C13×#103—21no—
121C13×#103—21no—
122C13×#103—21no—
123C13×#103—21no—
124C13×#103—21no—
125C13×#103—21no—
126C13×#103—21no—
127C13×#103D411yescharacteristic
128C13×#103D411yescharacteristic
129C13×#102—21no—
130C13×#102—21no—
131C13×#102—21no—
132C13×#102—21no—
133C13×#102—21no—
134C13×#102—21no—
135C13×#102—41no—
136C13×#102D411yescharacteristic
137C13×#102D411yescharacteristic
138C13×C22⋊C8—21no—
139C13×C22⋊C8—21no—
140C4×C8×C13—21no—
141C4×C8×C13—21no—
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144C4×C8×C13C2311yescharacteristic
145#19821C1311yesmaximal, characteristic, direct product factor, Sylow
146C24×C13—41no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—41no—
151C2×Q8×C13—42no—
152C2×Q8×C13—81no—
153C2×Q8×C13C2×D411yescharacteristic
154C2×Q8×C13C2×D411yescharacteristic
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—41no—
159C2×D4×C13—41no—
160C2×D4×C13—42no—
161C2×D4×C13—42no—
162C2×D4×C13—81no—
163C2×D4×C13—81no—
164C2×D4×C13C2×D411yescharacteristic
165C2×D4×C13C2×D411yescharacteristic
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—41no—
169C13×Q16—42no—
170C13×SD16—22no—
171C13×SD16—22no—
172C13×SD16—42no—
173C13×SD16—42no—
174C13×SD16—42no—
175C13×SD16—42no—
176C13×SD16—81no—
177C13×SD16—81no—
178C13×M16—81no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13—21no—
183C2×C8×C13—21no—
184C2×C8×C13—42no—
185C2×C8×C13C2×D411yescharacteristic
186C2×C8×C13C2×D411yescharacteristic
187C2×C8×C13C2×D411yescharacteristic
188C2×C8×C13C2×D411yescharacteristic
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—41no—
198C13×C4⋊C4—41no—
199C13×C4⋊C4—41no—
200C13×C4⋊C4—41no—
201C13×C4⋊C4—41no—
202C13×C4⋊C4C2×D411yescharacteristic
203C13×C4⋊C4C2×D411yescharacteristic
204C13×C4⋊C4C2×D411yescharacteristic
205C13×C4⋊C4C2×D411yescharacteristic
206C13×C22⋊C4—21no—
207C13×C22⋊C4—21no—
208C13×C22⋊C4—41no—
209C13×C22⋊C4—41no—
210C13×C22⋊C4—41no—
211C13×C22⋊C4—41no—
212C42×C13—21no—
213C42×C13—21no—
214C42×C13—41no—
215C42×C13—41no—
216C42×C13C2411yescharacteristic
217#3364C2×C1311yescharacteristic, complemented
218#3359C2×C1311yescharacteristic, complemented
219#3324C2×C1311yescharacteristic
220D4×SD16C2×C1311yescharacteristic
221#1719C2×C1311yescharacteristic, complemented
222#1699C2×C1311yescharacteristic, complemented
223#1682C2×C1311yescharacteristic, complemented
224#1679C2×C1311yescharacteristic, complemented
225#1666C2×C1311yescharacteristic, complemented
226#1650C2×C1311yescharacteristic, complemented
227#1649C2×C1311yescharacteristic, complemented
228#1639C2×C1311yescharacteristic
229#1626C2×C1311yescharacteristic, complemented
230#1583C2×C1311yescharacteristic, complemented
231SD16⋊C8C2×C1311yescharacteristic, complemented
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—41no—
235C23×C13—82no—
236C23×C13—82no—
237C23×C13—161no—
238Q8×C13—21no—
239Q8×C13—21no—
240Q8×C13—21no—
241Q8×C13—41no—
242Q8×C13—41no—
243Q8×C13—41no—
244Q8×C13—41no—
245Q8×C13—41no—
246Q8×C13—41no—
247Q8×C13—82no—
248Q8×C13AGL(1,ℤ/8)12yes—
249D4×C13—21no—
250D4×C13—21no—
251D4×C13—21no—
252D4×C13—41no—
253D4×C13—41no—
254D4×C13—41no—
255D4×C13—41no—
256D4×C13—81no—
257D4×C13—82no—
258D4×C13—82no—
259D4×C13#13512yes—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—82no—
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C22×D411yescharacteristic
276C2×C4×C13H(5,𝔽2)11yescharacteristic
277C8×C13—21no—
278C8×C13—21no—
279C8×C13—21no—
280C8×C13—21no—
281C8×C13—41no—
282C8×C13—41no—
283C8×C13—41no—
284C8×C13—41no—
285C8×C13—41no—
286C22×SD16—21no—
287#557C22×C1311yescharacteristic, complemented
288#556C22×C1311yescharacteristic
289D4×Q8C22×C1311yescharacteristic
290D42C22×C1311yescharacteristic
291#500C22×C1311yescharacteristic, complemented
292#492C22×C1311yescharacteristic
293#488—21no—
294#487—21no—
295#487C22×C1311yescharacteristic, complemented
296#487C22×C1311yescharacteristic, complemented
297#486C22×C1311yescharacteristic
298#486C22×C1311yescharacteristic
299#482—21no—
300#479—21no—
301#475—21no—
302#475C22×C1311yescharacteristic, complemented
303#474C22×C1311yescharacteristic
304#474C22×C1311yescharacteristic
305#468—21no—
306#465—21no—
307#464—21no—
308#462C22×C1311yescharacteristic, complemented
309#461—21no—
310#461C22×C1311yescharacteristic
311#461C22×C1311yescharacteristic
312#460C22×C1311yescharacteristic
313#460C22×C1311yescharacteristic
314#450—21no—
315#450—21no—
316#448—21no—
317C8×Q8C22×C1311yescharacteristic, complemented
318C8×Q8C22×C1311yescharacteristic, complemented
319C4×Q16—21no—
320C4×SD16—21no—
321C4×SD16C22×C1311yescharacteristic
322C4×SD16C22×C1311yescharacteristic
323#436C22×C1311yescharacteristic
324C8×D4C22×C1311yescharacteristic
325#418—21no—
326#335C22×C1311yescharacteristic, complemented
327#334C22×C1311yescharacteristic, complemented
328#332C22×C1311yescharacteristic, complemented
329#332C22×C1311yescharacteristic, complemented
330#332C22×C1311yescharacteristic, complemented
331#331C22×C1311yescharacteristic
332Q8⋊C8C22×C1311yescharacteristic, complemented
333Q8⋊C8C22×C1311yescharacteristic, complemented
334D4⋊C8C22×C1311yescharacteristic
335D4⋊C8C22×C1311yescharacteristic
336#322C22×C1311yescharacteristic, complemented
337C22×C13—22no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—81no—
344C22×C13—81no—
345C22×C13—81no—
346C22×C13—164no—
347C22×C13D4211yescharacteristic
348C4×C13—22no—
349C4×C13—21no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—81no—
356C4×C13—81no—
357C4×C13—81no—
358C4×C13C2×#13511yescharacteristic
359C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
360C4×C13#57711yescharacteristic
361C4×C13#57711yescharacteristic
362C22×Q8—21no—
363C22×D4—21no—
364C22×D4—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—44no—
373C2×SD16D4×C1311yescharacteristic
374C2×SD16D4×C1311yescharacteristic
375C2×M16—21no—
376C22×C8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—21no—
379C4⋊Q8C23×C1311yescharacteristic
380C4⋊Q8C23×C1311yescharacteristic
381C4⋊Q8C23×C1311yescharacteristic
382#127C23×C1311yescharacteristic
383#126—41no—
384#125—21no—
385#125—41no—
386#124—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—41no—
390#121—21no—
391#121—21no—
392#120—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8C23×C1311yescharacteristic
397C4×Q8C23×C1311yescharacteristic
398C4×D4—21no—
399C4×D4C23×C1311yescharacteristic
400C4×D4C23×C1311yescharacteristic
401#117—21no—
402#107—21no—
403#107—21no—
404#107—41no—
405#106—21no—
406#106D4×C1311yescharacteristic
407#106D4×C1311yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C1311yescharacteristic
411C4⋊C8C23×C1311yescharacteristic
412C4⋊C8C23×C1311yescharacteristic
413C4⋊C8C23×C1311yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103D4×C1311yescharacteristic
423#103D4×C1311yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—41no—
431#102D4×C1311yescharacteristic
432#102D4×C1311yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C1311yescharacteristic
438C4×C8C23×C1311yescharacteristic
439C4×C8C23×C1311yescharacteristic
440C2×C13—42no—
441C2×C13—81no—
442C2×C13—161no—
443C2×C13#326511yescharacteristic
444C2×C13#328211yescharacteristic
445C2×C13#328911yescharacteristic
446C24—41no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—41no—
451C2×Q8—42no—
452C2×Q8—81no—
453C2×Q8C2×D4×C1311yescharacteristic
454C2×Q8C2×D4×C1311yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4C2×D4×C1311yescharacteristic
465C2×D4C2×D4×C1311yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469Q16—42no—
470SD16—22no—
471SD16—22no—
472SD16—42no—
473SD16—42no—
474SD16—42no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478M16—81no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8C2×D4×C1311yescharacteristic
486C2×C8C2×D4×C1311yescharacteristic
487C2×C8C2×D4×C1311yescharacteristic
488C2×C8C2×D4×C1311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C1311yescharacteristic
503C4⋊C4C2×D4×C1311yescharacteristic
504C4⋊C4C2×D4×C1311yescharacteristic
505C4⋊C4C2×D4×C1311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C42—21no—
513C42—21no—
514C42—41no—
515C42—41no—
516C42C24×C1311yescharacteristic
517C13#1982111yescharacteristic, direct product factor, Sylow
518C23—21no—
519C23—21no—
520C23—41no—
521C23—82no—
522C23—82no—
523C23—161no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—82no—
534Q8C13×AGL(1,ℤ/8)12yes—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4C13×#13512yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4C22×D4×C1311yescharacteristic
561C2×C4C22×D4×C1311yescharacteristic
562C2×C4C13×H(5,𝔽2)11yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—164no—
582C22D42×C1311yescharacteristic
583C4—22no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C2×C13×#13511yescharacteristic
594C4C2×C13×AGL(1,ℤ/8)11yescharacteristic
595C4C13×#57711yescharacteristic
596C4C13×#57711yescharacteristic
597C2—42no—
598C2—81no—
599C2—161no—
600C2C13×#326511yescharacteristic
601C2C13×#328211yescharacteristic
602C2C13×#328911yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalD42×C13C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3364C2semidirect
2. C13×#3359C2semidirect
5. C13×#1719C2semidirect
6. C13×#1699C2semidirect
7. C13×#1682C2semidirect
8. C13×#1679C2semidirect
9. C13×#1666C2semidirect
10. C13×#1650C2semidirect
11. C13×#1649C2semidirect
13. C13×#1626C2semidirect
14. C13×#1583C2semidirect
15. C13×SD16⋊C8C2semidirect
17. C13×#557C22semidirect
21. C13×#500C22semidirect
25. C13×#487C22semidirect
26. C13×#487C22semidirect
32. C13×#475C22semidirect
38. C13×#462C22semidirect
47. C8×Q8×C13C22semidirect
48. C8×Q8×C13C22semidirect
56. C13×#335C22semidirect
57. C13×#334C22semidirect
58. C13×#332C22semidirect
59. C13×#332C22semidirect
60. C13×#332C22semidirect
62. C13×Q8⋊C8C22semidirect
63. C13×Q8⋊C8C22semidirect
66. C13×#322C22semidirect
145. #19821C13direct (N × H)
217. #3364C2×C13semidirect
218. #3359C2×C13semidirect
221. #1719C2×C13semidirect
222. #1699C2×C13semidirect
223. #1682C2×C13semidirect
224. #1679C2×C13semidirect
225. #1666C2×C13semidirect
226. #1650C2×C13semidirect
227. #1649C2×C13semidirect
229. #1626C2×C13semidirect
230. #1583C2×C13semidirect
231. SD16⋊C8C2×C13semidirect
287. #557C22×C13semidirect
291. #500C22×C13semidirect
295. #487C22×C13semidirect
296. #487C22×C13semidirect
302. #475C22×C13semidirect
308. #462C22×C13semidirect
317. C8×Q8C22×C13semidirect
318. C8×Q8C22×C13semidirect
326. #335C22×C13semidirect
327. #334C22×C13semidirect
328. #332C22×C13semidirect
329. #332C22×C13semidirect
330. #332C22×C13semidirect
332. Q8⋊C8C22×C13semidirect
333. Q8⋊C8C22×C13semidirect
336. #322C22×C13semidirect
517. C13#19821direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33642
C13×#33592
C13×#33242
D4×C13×SD162
C13×#17192
C13×#16992
C13×#16822
C13×#16792
C13×#16662
C13×#16502
C13×#16492
C13×#16392
C13×#16262
C13×#15832
C13×SD16⋊C82
#1982113