Finite Group Databasebeta

← C13×#62106 #15748445

Subgroups — C13×#62106 #15748445

Order 3328.

1782 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3518C211yesmaximal, characteristic, complemented
2C13×#3483C211yesmaximal, characteristic, complemented
3Q8×C13×Q16C211yesmaximal, characteristic, complemented
4Q8×C13×SD16C211yesmaximal, characteristic, complemented
5C13×#3362C211yesmaximal, characteristic, complemented
6C13×#3358C211yesmaximal, characteristic, complemented
7C13×#3341C213yesmaximal, complemented
8C13×#3340C213yesmaximal, complemented
9C13×#3305C213yesmaximal, complemented
10C13×#3304C213yesmaximal, complemented
11C13×#3247C213yesmaximal, complemented
12C13×#3228C213yesmaximal, complemented
13C13×#3102C213yesmaximal, complemented
14C13×#3076C213yesmaximal, complemented
15C13×#2988C211yesmaximal, characteristic, complemented
16Q82×C13C2211yescharacteristic
17Q82×C13C2211yescharacteristic
18C13×#556—23no—
19C13×#556C2213yes—
20C13×#555—23no—
21C13×#555C2213yes—
22C13×#555C2213yes—
23C13×#550—21no—
24C13×#550C2213yes—
25C13×#550C2211yescharacteristic
26D4×Q8×C13C2211yescharacteristic
27C13×#548—21no—
28C13×#542—23no—
29C13×#533C2213yes—
30C13×#532—23no—
31C13×#532C2213yes—
32C13×#529C2213yes—
33C13×#519—21no—
34C4×C13×#41—21no—
35C4×C13×#41C2213yes—
36C4×C13×#41C2211yescharacteristic
37C13×#500C2213yes—
38C13×#498C2213yes—
39C13×#486C2213yes—
40C13×#486C2213yes—
41C13×#485C2213yes—
42C13×#482C2216yes—
43C13×#482C2216yes—
44C13×#482C2213yes—
45C13×#479C2213yes—
46C13×#478C2216yes—
47C13×#478C2213yes—
48C13×#477C2213yes—
49C13×#477C2213yes—
50C13×#476C2213yes—
51C13×#476C2213yes—
52C13×#475C2213yes—
53C13×#474C2213yes—
54C13×#466C2216yes—
55C13×#465C2216yes—
56C13×#464C2211yescharacteristic
57C13×#463C2213yes—
58C13×#460C2213yes—
59C13×#459C2213yes—
60C13×#452C2213yes—
61C13×#449C2213yes—
62C8×Q8×C13C2211yescharacteristic
63C8×Q8×C13C2211yescharacteristic
64C4×C13×Q16C2213yes—
65C4×C13×SD16C2213yes—
66C4×C13×SD16C2213yes—
67C4×C13×D8C2213yes—
68C8×D4×C13C2213yes—
69C8×D4×C13C2213yes—
70C13×#431C2213yes—
71C13×#427C2216yes—
72C2×C13×C4⋊C8C2213yes—
73C13×#416C2216yes—
74C2×C13×#41—21no—
75C2×C13×#41—23no—
76C2×C13×#41D411yescharacteristic
77C2×C13×#41C2313yes—
78C22×Q8×C13—21no—
79C2×C13×Q16C2311yescharacteristic
80C2×C13×SD16C2311yescharacteristic
81C2×C13×SD16C2313yes—
82C2×C13×D8C2313yes—
83C22×C8×C13C2316yes—
84C13×C4⋊Q8—23no—
85C13×C4⋊Q8—23no—
86C13×C4⋊Q8C2313yes—
87C13×C4⋊Q8C2313yes—
88C13×C4⋊Q8C2313yes—
89C13×#127—23no—
90C13×#127C2313yes—
91C13×#126—26no—
92C13×#126—23no—
93C13×#125C2313yes—
94C13×#124—23no—
95C13×#124—26no—
96C13×#124—26no—
97C13×#124—23no—
98C13×#124C2311yescharacteristic
99C13×#123—23no—
100C13×C22⋊Q8—23no—
101C13×C22⋊Q8—23no—
102C13×C22⋊Q8—23no—
103C13×C22⋊Q8C2313yes—
104C13×#121—23no—
105C13×#121—23no—
106C13×#121—23no—
107C13×#121—23no—
108C13×#121—26no—
109C13×#121C2313yes—
110C13×#121C2316yes—
111C4×Q8×C13—21no—
112C4×Q8×C13—21no—
113C4×Q8×C13—23no—
114C4×Q8×C13—23no—
115C4×Q8×C13—23no—
116C4×Q8×C13D411yescharacteristic
117C4×Q8×C13C2313yes—
118C4×Q8×C13C2313yes—
119C4×Q8×C13C2311yescharacteristic
120C4×Q8×C13C2311yescharacteristic
121C4×D4×C13—23no—
122C4×D4×C13—23no—
123C4×D4×C13—23no—
124C4×D4×C13—23no—
125C4×D4×C13—23no—
126C4×D4×C13D413yes—
127C4×D4×C13C2313yes—
128C4×D4×C13C2313yes—
129C4×D4×C13C2313yes—
130C4×D4×C13C2313yes—
131C13×#117—23no—
132C13×#117—23no—
133C13×#117—23no—
134C13×#117—23no—
135C13×#117D413yes—
136C13×#117C2316yes—
137C13×#117C2313yes—
138C2×C42×C13—23no—
139C2×C42×C13C2313yes—
140C13×#107C2313yes—
141C13×#107C2316yes—
142C13×#107C2313yes—
143C13×#106C2313yes—
144C13×#106C2316yes—
145C13×#106C2313yes—
146C13×C4⋊C8C2313yes—
147C13×C4⋊C8C2313yes—
148C13×C4⋊C8C2313yes—
149C13×C4⋊C8C2311yescharacteristic
150C13×#103C2313yes—
151C13×#103C2313yes—
152C13×#103C2311yescharacteristic
153C13×#103C2313yes—
154C13×#102C2316yes—
155C13×#102C2316yes—
156C13×#102C2311yescharacteristic
157C13×#102C2313yes—
158C13×#102C2313yes—
159C13×#102C2313yes—
160C13×C22⋊C8C2313yes—
161C13×C22⋊C8C2313yes—
162C4×C8×C13C2313yes—
163C4×C8×C13C2313yes—
164#62106C1311yesmaximal, characteristic, direct product factor, Sylow
165C13×#41—24no—
166C13×#41—26no—
167C13×#41—43no—
168C13×#41—44no—
169C13×#41—86no—
170C2×Q8×C13—23no—
171C2×Q8×C13—23no—
172C2×Q8×C13—23no—
173C2×Q8×C13—44no—
174C2×Q8×C13C2×D411yescharacteristic
175C2×Q8×C13C2411yescharacteristic
176C2×Q8×C13C2411yescharacteristic
177C2×D4×C13—23no—
178C2×D4×C13—23no—
179C2×D4×C13—26no—
180C2×D4×C13—23no—
181C2×D4×C13—23no—
182C2×D4×C13C2×D413yes—
183C2×D4×C13C2413yes—
184C2×D4×C13C2411yescharacteristic
185C22×C4×C13—23no—
186C22×C4×C13—23no—
187C22×C4×C13—23no—
188C22×C4×C13—23no—
189C22×C4×C13C2×D413yes—
190C22×C4×C13C2×D413yes—
191C22×C4×C13C2413yes—
192C13×Q16—22no—
193C13×SD16—22no—
194C13×SD16—43no—
195C13×D8—43no—
196C2×C8×C13—46no—
197C2×C8×C13C2411yescharacteristic
198C2×C8×C13C2411yescharacteristic
199C2×C8×C13C2413yes—
200C2×C8×C13C2413yes—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—23no—
203C13×C4⋊C4—23no—
204C13×C4⋊C4—23no—
205C13×C4⋊C4—23no—
206C13×C4⋊C4—23no—
207C13×C4⋊C4—23no—
208C13×C4⋊C4—23no—
209C13×C4⋊C4—23no—
210C13×C4⋊C4C2×D413yes—
211C13×C4⋊C4C2×D413yes—
212C13×C4⋊C4C2413yes—
213C13×C4⋊C4C2413yes—
214C13×C4⋊C4C2411yescharacteristic
215C13×C4⋊C4C2413yes—
216C13×C22⋊C4—23no—
217C13×C22⋊C4—26no—
218C13×C22⋊C4—23no—
219C13×C22⋊C4—23no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—26no—
222C13×C22⋊C4—23no—
223C13×C22⋊C4—23no—
224C13×C22⋊C4—21no—
225C13×C22⋊C4—23no—
226C13×C22⋊C4C2×D416yes—
227C42×C13—21no—
228C42×C13—23no—
229C42×C13—23no—
230C42×C13—26no—
231C42×C13—23no—
232C42×C13C2×D413yes—
233C42×C13C2×D413yes—
234C42×C13C2413yes—
235C42×C13C2411yescharacteristic
236#3518C2×C1311yescharacteristic, complemented
237#3483C2×C1311yescharacteristic, complemented
238Q8×Q16C2×C1311yescharacteristic, complemented
239Q8×SD16C2×C1311yescharacteristic, complemented
240#3362C2×C1311yescharacteristic, complemented
241#3358C2×C1311yescharacteristic, complemented
242#3341C2×C1313yescomplemented
243#3340C2×C1313yescomplemented
244#3305C2×C1313yescomplemented
245#3304C2×C1313yescomplemented
246#3247C2×C1313yescomplemented
247#3228C2×C1313yescomplemented
248#3102C2×C1313yescomplemented
249#3076C2×C1313yescomplemented
250#2988C2×C1311yescharacteristic, complemented
251C23×C13—21no—
252C23×C13—23no—
253C23×C13C22×D413yes—
254Q8×C13—21no—
255Q8×C13—21no—
256Q8×C13—21no—
257Q8×C13—46no—
258Q8×C13—83no—
259Q8×C13—83no—
260Q8×C13#13514yes—
261Q8×C132−1+412yes—
262D4×C13—26no—
263D4×C13—21no—
264D4×C13—23no—
265D4×C13—21no—
266D4×C13—23no—
267D4×C13—46no—
268D4×C13—46no—
269D4×C13—83no—
270D4×C13—83no—
271D4×C13—86no—
272C2×C4×C13—21no—
273C2×C4×C13—26no—
274C2×C4×C13—23no—
275C2×C4×C13—23no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—23no—
279C2×C4×C13—23no—
280C2×C4×C13—23no—
281C2×C4×C13—43no—
282C2×C4×C13—46no—
283C2×C4×C13—46no—
284C2×C4×C13—46no—
285C2×C4×C13—46no—
286C2×C4×C13C22×D413yes—
287C2×C4×C13C22×D411yescharacteristic
288C2×C4×C13C22×D411yescharacteristic
289C2×C4×C13C22×D413yes—
290C2×C4×C13C22×D413yes—
291C2×C4×C13C2511yescharacteristic
292C8×C13—21no—
293C8×C13—21no—
294C8×C13—23no—
295C8×C13—23no—
296Q82C22×C1311yescharacteristic
297Q82C22×C1311yescharacteristic
298#556—23no—
299#556C22×C1313yes—
300#555—23no—
301#555C22×C1313yes—
302#555C22×C1313yes—
303#550—21no—
304#550C22×C1313yes—
305#550C22×C1311yescharacteristic
306D4×Q8C22×C1311yescharacteristic
307#548—21no—
308#542—23no—
309#533C22×C1313yes—
310#532—23no—
311#532C22×C1313yes—
312#529C22×C1313yes—
313#519—21no—
314C4×#41—21no—
315C4×#41C22×C1313yes—
316C4×#41C22×C1311yescharacteristic
317#500C22×C1313yes—
318#498C22×C1313yes—
319#486C22×C1313yes—
320#486C22×C1313yes—
321#485C22×C1313yes—
322#482C22×C1316yes—
323#482C22×C1313yes—
324#482C22×C1316yes—
325#479C22×C1313yes—
326#478C22×C1316yes—
327#478C22×C1313yes—
328#477C22×C1313yes—
329#477C22×C1313yes—
330#476C22×C1313yes—
331#476C22×C1313yes—
332#475C22×C1313yes—
333#474C22×C1313yes—
334#466C22×C1316yes—
335#465C22×C1316yes—
336#464C22×C1311yescharacteristic
337#463C22×C1313yes—
338#460C22×C1313yes—
339#459C22×C1313yes—
340#452C22×C1313yes—
341#449C22×C1313yes—
342C8×Q8C22×C1311yescharacteristic
343C8×Q8C22×C1311yescharacteristic
344C4×Q16C22×C1313yes—
345C4×SD16C22×C1313yes—
346C4×SD16C22×C1313yes—
347C4×D8C22×C1313yes—
348C8×D4C22×C1313yes—
349C8×D4C22×C1313yes—
350#431C22×C1313yes—
351#427C22×C1316yes—
352C2×C4⋊C8C22×C1313yes—
353#416C22×C1316yes—
354C22×C13—23no—
355C22×C13—23no—
356C22×C13—23no—
357C22×C13—43no—
358C22×C13—41no—
359C22×C13—43no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—43no—
363C22×C13C23×D411yescharacteristic
364C4×C13—21no—
365C4×C13—23no—
366C4×C13—23no—
367C4×C13—22no—
368C4×C13—21no—
369C4×C13—43no—
370C4×C13—43no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13—43no—
374C4×C13C2×#13516yes—
375C4×C13C2×2−1+411yescharacteristic
376C4×C13#58511yescharacteristic
377C2×#41—21no—
378C2×#41—23no—
379C2×#41D4×C1311yescharacteristic
380C2×#41C23×C1313yes—
381C22×Q8—21no—
382C2×Q16C23×C1311yescharacteristic
383C2×SD16C23×C1311yescharacteristic
384C2×SD16C23×C1313yes—
385C2×D8C23×C1313yes—
386C22×C8C23×C1316yes—
387C4⋊Q8—23no—
388C4⋊Q8—23no—
389C4⋊Q8C23×C1313yes—
390C4⋊Q8C23×C1313yes—
391C4⋊Q8C23×C1313yes—
392#127—23no—
393#127C23×C1313yes—
394#126—26no—
395#126—23no—
396#125C23×C1313yes—
397#124—23no—
398#124—26no—
399#124—26no—
400#124—23no—
401#124C23×C1311yescharacteristic
402#123—23no—
403C22⋊Q8—23no—
404C22⋊Q8—23no—
405C22⋊Q8—23no—
406C22⋊Q8C23×C1313yes—
407#121—23no—
408#121—23no—
409#121—23no—
410#121—23no—
411#121—26no—
412#121C23×C1313yes—
413#121C23×C1316yes—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8—23no—
419C4×Q8D4×C1311yescharacteristic
420C4×Q8C23×C1311yescharacteristic
421C4×Q8C23×C1313yes—
422C4×Q8C23×C1313yes—
423C4×Q8C23×C1311yescharacteristic
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4D4×C1313yes—
430C4×D4C23×C1313yes—
431C4×D4C23×C1313yes—
432C4×D4C23×C1313yes—
433C4×D4C23×C1313yes—
434#117—23no—
435#117—23no—
436#117—23no—
437#117—23no—
438#117D4×C1313yes—
439#117C23×C1313yes—
440#117C23×C1316yes—
441C2×C42—23no—
442C2×C42C23×C1313yes—
443#107C23×C1313yes—
444#107C23×C1316yes—
445#107C23×C1313yes—
446#106C23×C1313yes—
447#106C23×C1316yes—
448#106C23×C1313yes—
449C4⋊C8C23×C1313yes—
450C4⋊C8C23×C1313yes—
451C4⋊C8C23×C1313yes—
452C4⋊C8C23×C1311yescharacteristic
453#103C23×C1313yes—
454#103C23×C1313yes—
455#103C23×C1311yescharacteristic
456#103C23×C1313yes—
457#102C23×C1316yes—
458#102C23×C1316yes—
459#102C23×C1311yescharacteristic
460#102C23×C1313yes—
461#102C23×C1313yes—
462#102C23×C1313yes—
463C22⋊C8C23×C1313yes—
464C22⋊C8C23×C1313yes—
465C4×C8C23×C1313yes—
466C4×C8C23×C1313yes—
467C2×C13—43no—
468C2×C13—83no—
469C2×C13—81no—
470C2×C13#348911yescharacteristic
471C2×C13C22×#13511yescharacteristic
472C2×C13#358511yescharacteristic
473#41—24no—
474#41—26no—
475#41—43no—
476#41—44no—
477#41—86no—
478C2×Q8—23no—
479C2×Q8—23no—
480C2×Q8—23no—
481C2×Q8—44no—
482C2×Q8C2×D4×C1311yescharacteristic
483C2×Q8C24×C1311yescharacteristic
484C2×Q8C24×C1311yescharacteristic
485C2×D4—23no—
486C2×D4—23no—
487C2×D4—26no—
488C2×D4—23no—
489C2×D4—23no—
490C2×D4C2×D4×C1313yes—
491C2×D4C24×C1313yes—
492C2×D4C24×C1311yescharacteristic
493C22×C4—23no—
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—23no—
497C22×C4C2×D4×C1313yes—
498C22×C4C2×D4×C1313yes—
499C22×C4C24×C1313yes—
500Q16—22no—
501SD16—22no—
502SD16—43no—
503D8—43no—
504C2×C8—46no—
505C2×C8C24×C1311yescharacteristic
506C2×C8C24×C1311yescharacteristic
507C2×C8C24×C1313yes—
508C2×C8C24×C1313yes—
509C4⋊C4—21no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4C2×D4×C1313yes—
519C4⋊C4C2×D4×C1313yes—
520C4⋊C4C24×C1313yes—
521C4⋊C4C24×C1313yes—
522C4⋊C4C24×C1311yescharacteristic
523C4⋊C4C24×C1313yes—
524C22⋊C4—23no—
525C22⋊C4—26no—
526C22⋊C4—23no—
527C22⋊C4—23no—
528C22⋊C4—21no—
529C22⋊C4—26no—
530C22⋊C4—23no—
531C22⋊C4—23no—
532C22⋊C4—21no—
533C22⋊C4—23no—
534C22⋊C4C2×D4×C1316yes—
535C42—21no—
536C42—23no—
537C42—23no—
538C42—26no—
539C42—23no—
540C42C2×D4×C1313yes—
541C42C2×D4×C1313yes—
542C42C24×C1313yes—
543C42C24×C1311yescharacteristic
544C13#6210611yescharacteristic, direct product factor, Sylow
545C23—21no—
546C23—23no—
547C23C22×D4×C1313yes—
548Q8—21no—
549Q8—21no—
550Q8—21no—
551Q8—46no—
552Q8—83no—
553Q8—83no—
554Q8C13×#13514yes—
555Q8C13×2−1+412yes—
556D4—26no—
557D4—21no—
558D4—23no—
559D4—21no—
560D4—23no—
561D4—46no—
562D4—46no—
563D4—83no—
564D4—83no—
565D4—86no—
566C2×C4—21no—
567C2×C4—26no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—43no—
576C2×C4—46no—
577C2×C4—46no—
578C2×C4—46no—
579C2×C4—46no—
580C2×C4C22×D4×C1313yes—
581C2×C4C22×D4×C1311yescharacteristic
582C2×C4C22×D4×C1311yescharacteristic
583C2×C4C22×D4×C1313yes—
584C2×C4C22×D4×C1313yes—
585C2×C4C25×C1311yescharacteristic
586C8—21no—
587C8—21no—
588C8—23no—
589C8—23no—
590C22—23no—
591C22—23no—
592C22—23no—
593C22—41no—
594C22—43no—
595C22—43no—
596C22—41no—
597C22—43no—
598C22—41no—
599C22C23×D4×C1311yescharacteristic
600C4—21no—
601C4—21no—
602C4—23no—
603C4—23no—
604C4—22no—
605C4—41no—
606C4—43no—
607C4—43no—
608C4—43no—
609C4—41no—
610C4C2×C13×#13516yes—
611C4C2×C13×2−1+411yescharacteristic
612C4C13×#58511yescharacteristic
613C2—43no—
614C2—81no—
615C2—83no—
616C2C13×#348911yescharacteristic
617C2C22×C13×#13511yescharacteristic
618C2C13×#358511yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3518C2semidirect
2. C13×#3483C2semidirect
3. Q8×C13×Q16C2semidirect
4. Q8×C13×SD16C2semidirect
5. C13×#3362C2semidirect
6. C13×#3358C2semidirect
7. C13×#3341C2semidirect
8. C13×#3340C2semidirect
9. C13×#3305C2semidirect
10. C13×#3304C2semidirect
11. C13×#3247C2semidirect
12. C13×#3228C2semidirect
13. C13×#3102C2semidirect
14. C13×#3076C2semidirect
15. C13×#2988C2semidirect
164. #62106C13direct (N × H)
236. #3518C2×C13semidirect
237. #3483C2×C13semidirect
238. Q8×Q16C2×C13semidirect
239. Q8×SD16C2×C13semidirect
240. #3362C2×C13semidirect
241. #3358C2×C13semidirect
242. #3341C2×C13semidirect
243. #3340C2×C13semidirect
244. #3305C2×C13semidirect
245. #3304C2×C13semidirect
246. #3247C2×C13semidirect
247. #3228C2×C13semidirect
248. #3102C2×C13semidirect
249. #3076C2×C13semidirect
250. #2988C2×C13semidirect
544. C13#62106direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35182
C13×#34832
Q8×C13×Q162
Q8×C13×SD162
C13×#33622
C13×#33582
C13×#33412
C13×#33402
C13×#33052
C13×#33042
C13×#32472
C13×#32282
C13×#31022
C13×#30762
C13×#29882
#6210613