Finite Group Databasebeta

← C13×#61887 #15748226

Subgroups — C13×#61887 #15748226

Order 3328.

1740 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3523C211yesmaximal, characteristic, complemented
2C13×#3480C211yesmaximal, characteristic, complemented
3C13×#3395C211yesmaximal, characteristic, complemented
4C13×#3394C213yesmaximal, complemented
5C13×#3393C213yesmaximal, complemented
6C13×#3392C211yesmaximal, characteristic, complemented
7C13×#3365C213yesmaximal, complemented
8C13×#3364C213yesmaximal, complemented
9C13×#3359C211yesmaximal, characteristic, complemented
10C13×#3358C211yesmaximal, characteristic, complemented
11C13×#3212C213yesmaximal, complemented
12C13×#3210C213yesmaximal, complemented
13C13×#3107C213yesmaximal, complemented
14C13×#3102C213yesmaximal, complemented
15C13×#2982C211yesmaximal, characteristic, complemented
16C13×#559C2213yes—
17C13×#557C2211yescharacteristic
18C13×#557C2211yescharacteristic
19C13×#557C2213yes—
20C13×#556C2213yes—
21C13×#556C2213yes—
22C13×#553—23no—
23C13×#552—23no—
24C13×#550C2211yescharacteristic
25D4×Q8×C13—21no—
26D4×Q8×C13C2211yescharacteristic
27C13×#548—21no—
28C13×#541—23no—
29C13×#533C2213yes—
30C13×#532C2213yes—
31C13×#529—23no—
32C13×#529C2213yes—
33C13×#519—21no—
34C4×C13×#41—21no—
35C4×C13×#41C2213yes—
36C2×C4×Q8×C13C2211yescharacteristic
37C13×#495C2216yes—
38C13×#494C2213yes—
39C13×#492C2213yes—
40C13×#488C2216yes—
41C13×#487C2213yes—
42C13×#486C2213yes—
43C13×#485C2213yes—
44C13×#482C2211yescharacteristic
45C13×#479C2213yes—
46C13×#478C2213yes—
47C13×#475C2213yes—
48C13×#474C2213yes—
49C13×#464C2213yes—
50C13×#464C2216yes—
51C13×#464C2216yes—
52C13×#463C2213yes—
53C13×#462C2213yes—
54C13×#462C2213yes—
55C13×#461C2213yes—
56C13×#461C2213yes—
57C13×#460C2213yes—
58C13×#459C2213yes—
59C13×#452C2213yes—
60C13×#452C2216yes—
61C13×#449C2213yes—
62C8×Q8×C13C2211yescharacteristic
63C8×Q8×C13C2211yescharacteristic
64C8×Q8×C13C2213yes—
65C8×Q8×C13C2213yes—
66C4×C13×Q16C2213yes—
67C4×C13×Q16C2216yes—
68C4×C13×SD16C2213yes—
69C4×C13×SD16C2213yes—
70C4×C13×SD16C2216yes—
71C4×C13×D8C2213yes—
72C13×#431C2213yes—
73C13×#431C2213yes—
74C2×C13×#41—21no—
75C2×C13×#41C2313yes—
76C22×Q8×C13—21no—
77C22×Q8×C13D411yescharacteristic
78C2×C13×Q16C2316yes—
79C2×C13×Q16C2313yes—
80C2×C13×SD16C2313yes—
81C2×C13×SD16C2316yes—
82C2×C13×SD16C2313yes—
83C2×C13×D8C2313yes—
84C13×C4⋊Q8—23no—
85C13×C4⋊Q8C2313yes—
86C13×C4⋊Q8C2313yes—
87C13×C4⋊Q8C2313yes—
88C13×#127C2313yes—
89C13×#126—26no—
90C13×#126—26no—
91C13×#126—23no—
92C13×#125—23no—
93C13×#125—26no—
94C13×#125—23no—
95C13×#125—23no—
96C13×#125C2313yes—
97C13×#124—23no—
98C13×#124C2313yes—
99C13×#124C2316yes—
100C13×#123—23no—
101C13×#123—26no—
102C13×C22⋊Q8—23no—
103C13×C22⋊Q8—23no—
104C13×C22⋊Q8—23no—
105C13×C22⋊Q8—23no—
106C13×C22⋊Q8C2313yes—
107C13×#121—23no—
108C13×#121—23no—
109C13×#121—23no—
110C13×#121C2311yescharacteristic
111C4×Q8×C13—21no—
112C4×Q8×C13—21no—
113C4×Q8×C13—23no—
114C4×Q8×C13—23no—
115C4×Q8×C13D411yescharacteristic
116C4×Q8×C13D413yes—
117C4×Q8×C13C2313yes—
118C4×Q8×C13C2313yes—
119C4×Q8×C13C2316yes—
120C4×Q8×C13C2313yes—
121C4×Q8×C13C2311yescharacteristic
122C4×Q8×C13C2313yes—
123C4×D4×C13—23no—
124C4×D4×C13—23no—
125C4×D4×C13—23no—
126C4×D4×C13—23no—
127C4×D4×C13—23no—
128C4×D4×C13—23no—
129C4×D4×C13C2313yes—
130C4×D4×C13C2313yes—
131C4×D4×C13C2313yes—
132C13×#117—23no—
133C13×#117—23no—
134C13×#117—23no—
135C13×#117—23no—
136C13×#117—23no—
137C13×#117C2311yescharacteristic
138C2×C13×C4⋊C4D413yes—
139C2×C42×C13—23no—
140C2×C42×C13C2313yes—
141C13×#107C2313yes—
142C13×#107C2311yescharacteristic
143C13×#106C2313yes—
144C13×#106C2311yescharacteristic
145C13×C4⋊C8C2313yes—
146C13×C4⋊C8C2313yes—
147C13×C4⋊C8C2313yes—
148C13×C4⋊C8C2313yes—
149C13×#103C2313yes—
150C13×#103C2313yes—
151C13×#103C2313yes—
152C13×#103C2313yes—
153C13×#103C2316yes—
154C13×#102C2311yescharacteristic
155C13×#102C2313yes—
156C13×#102C2311yescharacteristic
157C13×#102C2313yes—
158C13×#102C2316yes—
159C13×C22⋊C8C2313yes—
160C13×C22⋊C8C2311yescharacteristic
161C4×C8×C13C2313yes—
162C4×C8×C13C2313yes—
163C4×C8×C13C2316yes—
164#61887C1311yesmaximal, characteristic, direct product factor, Sylow
165C13×#41—43no—
166C13×#41—43no—
167C13×#41—44no—
168C2×Q8×C13—24no—
169C2×Q8×C13—23no—
170C2×Q8×C13—44no—
171C2×Q8×C13C2×D413yes—
172C2×Q8×C13C2×D411yescharacteristic
173C2×Q8×C13C2413yes—
174C2×Q8×C13C2413yes—
175C2×D4×C13—21no—
176C2×D4×C13—23no—
177C2×D4×C13—23no—
178C2×D4×C13—23no—
179C2×D4×C13C2413yes—
180C2×D4×C13C2411yescharacteristic
181C22×C4×C13—23no—
182C22×C4×C13—23no—
183C22×C4×C13—23no—
184C22×C4×C13—23no—
185C22×C4×C13C2×D413yes—
186C22×C4×C13C2×D413yes—
187C22×C4×C13C2411yescharacteristic
188C13×Q16—46no—
189C13×Q16—43no—
190C13×SD16—43no—
191C13×SD16—43no—
192C13×SD16—46no—
193C13×D8—43no—
194C2×C8×C13C2411yescharacteristic
195C2×C8×C13C2413yes—
196C2×C8×C13C2411yescharacteristic
197C2×C8×C13C2413yes—
198C13×C4⋊C4—23no—
199C13×C4⋊C4—23no—
200C13×C4⋊C4—23no—
201C13×C4⋊C4—23no—
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—26no—
209C13×C4⋊C4—23no—
210C13×C4⋊C4C2×D413yes—
211C13×C4⋊C4C2×D413yes—
212C13×C4⋊C4C2×D416yes—
213C13×C4⋊C4C2413yes—
214C13×C4⋊C4C2411yescharacteristic
215C13×C4⋊C4C2411yescharacteristic
216C13×C4⋊C4C2411yescharacteristic
217C13×C22⋊C4—23no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—23no—
221C13×C22⋊C4—26no—
222C13×C22⋊C4—23no—
223C13×C22⋊C4—23no—
224C13×C22⋊C4—26no—
225C13×C22⋊C4—23no—
226C13×C22⋊C4—23no—
227C42×C13—21no—
228C42×C13—23no—
229C42×C13—23no—
230C42×C13—26no—
231C42×C13—23no—
232C42×C13C2×D413yes—
233C42×C13C2×D413yes—
234C42×C13C2413yes—
235C42×C13C2413yes—
236#3523C2×C1311yescharacteristic, complemented
237#3480C2×C1311yescharacteristic, complemented
238#3395C2×C1311yescharacteristic, complemented
239#3394C2×C1313yescomplemented
240#3393C2×C1313yescomplemented
241#3392C2×C1311yescharacteristic, complemented
242#3365C2×C1313yescomplemented
243#3364C2×C1313yescomplemented
244#3359C2×C1311yescharacteristic, complemented
245#3358C2×C1311yescharacteristic, complemented
246#3212C2×C1313yescomplemented
247#3210C2×C1313yescomplemented
248#3107C2×C1313yescomplemented
249#3102C2×C1313yescomplemented
250#2982C2×C1311yescharacteristic, complemented
251C23×C13—21no—
252C23×C13—23no—
253C23×C13C22×D411yescharacteristic
254Q8×C13—26no—
255Q8×C13—23no—
256Q8×C13—23no—
257Q8×C13—23no—
258Q8×C13—23no—
259Q8×C13—46no—
260Q8×C13#13514yes—
261D4×C13—21no—
262D4×C13—23no—
263D4×C13—21no—
264D4×C13—23no—
265D4×C13—42no—
266D4×C13—46no—
267D4×C13—46no—
268D4×C13—83no—
269C2×C4×C13—26no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—23no—
275C2×C4×C13—21no—
276C2×C4×C13—23no—
277C2×C4×C13—23no—
278C2×C4×C13—43no—
279C2×C4×C13—46no—
280C2×C4×C13—46no—
281C2×C4×C13—46no—
282C2×C4×C13—83no—
283C2×C4×C13C22×D413yes—
284C2×C4×C13C22×D411yescharacteristic
285C2×C4×C13C22×D413yes—
286C2×C4×C13C22×D413yes—
287C2×C4×C13C22×D413yes—
288C2×C4×C13C2511yescharacteristic
289C8×C13—23no—
290C8×C13—21no—
291C8×C13—23no—
292C8×C13—21no—
293#559C22×C1313yes—
294#557C22×C1311yescharacteristic
295#557C22×C1311yescharacteristic
296#557C22×C1313yes—
297#556C22×C1313yes—
298#556C22×C1313yes—
299#553—23no—
300#552—23no—
301#550C22×C1311yescharacteristic
302D4×Q8—21no—
303D4×Q8C22×C1311yescharacteristic
304#548—21no—
305#541—23no—
306#533C22×C1313yes—
307#532C22×C1313yes—
308#529—23no—
309#529C22×C1313yes—
310#519—21no—
311C4×#41—21no—
312C4×#41C22×C1313yes—
313C2×C4×Q8C22×C1311yescharacteristic
314#495C22×C1316yes—
315#494C22×C1313yes—
316#492C22×C1313yes—
317#488C22×C1316yes—
318#487C22×C1313yes—
319#486C22×C1313yes—
320#485C22×C1313yes—
321#482C22×C1311yescharacteristic
322#479C22×C1313yes—
323#478C22×C1313yes—
324#475C22×C1313yes—
325#474C22×C1313yes—
326#464C22×C1313yes—
327#464C22×C1316yes—
328#464C22×C1316yes—
329#463C22×C1313yes—
330#462C22×C1313yes—
331#462C22×C1313yes—
332#461C22×C1313yes—
333#461C22×C1313yes—
334#460C22×C1313yes—
335#459C22×C1313yes—
336#452C22×C1313yes—
337#452C22×C1316yes—
338#449C22×C1313yes—
339C8×Q8C22×C1311yescharacteristic
340C8×Q8C22×C1311yescharacteristic
341C8×Q8C22×C1313yes—
342C8×Q8C22×C1313yes—
343C4×Q16C22×C1313yes—
344C4×Q16C22×C1316yes—
345C4×SD16C22×C1313yes—
346C4×SD16C22×C1313yes—
347C4×SD16C22×C1316yes—
348C4×D8C22×C1313yes—
349#431C22×C1313yes—
350#431C22×C1313yes—
351C22×C13—21no—
352C22×C13—21no—
353C22×C13—21no—
354C22×C13—43no—
355C22×C13—41no—
356C22×C13—43no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—43no—
360C22×C13C23×D411yescharacteristic
361C4×C13—23no—
362C4×C13—23no—
363C4×C13—21no—
364C4×C13—23no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13—43no—
368C4×C13—43no—
369C4×C13—41no—
370C4×C13—43no—
371C4×C13C2×#13516yes—
372C4×C13#58511yescharacteristic
373C4×C13#58511yescharacteristic
374C2×#41—21no—
375C2×#41C23×C1313yes—
376C22×Q8—21no—
377C22×Q8D4×C1311yescharacteristic
378C2×Q16C23×C1316yes—
379C2×Q16C23×C1313yes—
380C2×SD16C23×C1313yes—
381C2×SD16C23×C1316yes—
382C2×SD16C23×C1313yes—
383C2×D8C23×C1313yes—
384C4⋊Q8—23no—
385C4⋊Q8C23×C1313yes—
386C4⋊Q8C23×C1313yes—
387C4⋊Q8C23×C1313yes—
388#127C23×C1313yes—
389#126—26no—
390#126—26no—
391#126—23no—
392#125—23no—
393#125—26no—
394#125—23no—
395#125—23no—
396#125C23×C1313yes—
397#124—23no—
398#124C23×C1313yes—
399#124C23×C1316yes—
400#123—23no—
401#123—26no—
402C22⋊Q8—23no—
403C22⋊Q8—23no—
404C22⋊Q8—23no—
405C22⋊Q8—23no—
406C22⋊Q8C23×C1313yes—
407#121—23no—
408#121—23no—
409#121—23no—
410#121C23×C1311yescharacteristic
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8D4×C1311yescharacteristic
416C4×Q8D4×C1313yes—
417C4×Q8C23×C1313yes—
418C4×Q8C23×C1313yes—
419C4×Q8C23×C1313yes—
420C4×Q8C23×C1316yes—
421C4×Q8C23×C1311yescharacteristic
422C4×Q8C23×C1313yes—
423C4×D4—23no—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4C23×C1313yes—
430C4×D4C23×C1313yes—
431C4×D4C23×C1313yes—
432#117—23no—
433#117—23no—
434#117—23no—
435#117—23no—
436#117—23no—
437#117C23×C1311yescharacteristic
438C2×C4⋊C4D4×C1313yes—
439C2×C42—23no—
440C2×C42C23×C1313yes—
441#107C23×C1313yes—
442#107C23×C1311yescharacteristic
443#106C23×C1313yes—
444#106C23×C1311yescharacteristic
445C4⋊C8C23×C1313yes—
446C4⋊C8C23×C1313yes—
447C4⋊C8C23×C1313yes—
448C4⋊C8C23×C1313yes—
449#103C23×C1313yes—
450#103C23×C1313yes—
451#103C23×C1313yes—
452#103C23×C1313yes—
453#103C23×C1316yes—
454#102C23×C1311yescharacteristic
455#102C23×C1313yes—
456#102C23×C1311yescharacteristic
457#102C23×C1313yes—
458#102C23×C1316yes—
459C22⋊C8C23×C1313yes—
460C22⋊C8C23×C1311yescharacteristic
461C4×C8C23×C1313yes—
462C4×C8C23×C1313yes—
463C4×C8C23×C1316yes—
464C2×C13—41no—
465C2×C13—83no—
466C2×C13—81no—
467C2×C13#348711yescharacteristic
468C2×C13C22×#13511yescharacteristic
469C2×C13#358611yescharacteristic
470#41—43no—
471#41—43no—
472#41—44no—
473C2×Q8—24no—
474C2×Q8—23no—
475C2×Q8—44no—
476C2×Q8C2×D4×C1313yes—
477C2×Q8C2×D4×C1311yescharacteristic
478C2×Q8C24×C1313yes—
479C2×Q8C24×C1313yes—
480C2×D4—21no—
481C2×D4—23no—
482C2×D4—23no—
483C2×D4—23no—
484C2×D4C24×C1313yes—
485C2×D4C24×C1311yescharacteristic
486C22×C4—23no—
487C22×C4—23no—
488C22×C4—23no—
489C22×C4—23no—
490C22×C4C2×D4×C1313yes—
491C22×C4C2×D4×C1313yes—
492C22×C4C24×C1311yescharacteristic
493Q16—46no—
494Q16—43no—
495SD16—43no—
496SD16—43no—
497SD16—46no—
498D8—43no—
499C2×C8C24×C1311yescharacteristic
500C2×C8C24×C1313yes—
501C2×C8C24×C1311yescharacteristic
502C2×C8C24×C1313yes—
503C4⋊C4—23no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—26no—
514C4⋊C4—23no—
515C4⋊C4C2×D4×C1313yes—
516C4⋊C4C2×D4×C1313yes—
517C4⋊C4C2×D4×C1316yes—
518C4⋊C4C24×C1313yes—
519C4⋊C4C24×C1311yescharacteristic
520C4⋊C4C24×C1311yescharacteristic
521C4⋊C4C24×C1311yescharacteristic
522C22⋊C4—23no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—23no—
526C22⋊C4—26no—
527C22⋊C4—23no—
528C22⋊C4—23no—
529C22⋊C4—26no—
530C22⋊C4—23no—
531C22⋊C4—23no—
532C42—21no—
533C42—23no—
534C42—23no—
535C42—26no—
536C42—23no—
537C42C2×D4×C1313yes—
538C42C2×D4×C1313yes—
539C42C24×C1313yes—
540C42C24×C1313yes—
541C13#6188711yescharacteristic, direct product factor, Sylow
542C23—21no—
543C23—23no—
544C23C22×D4×C1311yescharacteristic
545Q8—26no—
546Q8—23no—
547Q8—23no—
548Q8—23no—
549Q8—23no—
550Q8—46no—
551Q8C13×#13514yes—
552D4—21no—
553D4—23no—
554D4—21no—
555D4—23no—
556D4—42no—
557D4—46no—
558D4—46no—
559D4—83no—
560C2×C4—26no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—23no—
566C2×C4—21no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—43no—
570C2×C4—46no—
571C2×C4—46no—
572C2×C4—46no—
573C2×C4—83no—
574C2×C4C22×D4×C1313yes—
575C2×C4C22×D4×C1311yescharacteristic
576C2×C4C22×D4×C1313yes—
577C2×C4C22×D4×C1313yes—
578C2×C4C22×D4×C1313yes—
579C2×C4C25×C1311yescharacteristic
580C8—23no—
581C8—21no—
582C8—23no—
583C8—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—43no—
589C22—43no—
590C22—41no—
591C22—43no—
592C22—41no—
593C22C23×D4×C1311yescharacteristic
594C4—23no—
595C4—23no—
596C4—23no—
597C4—21no—
598C4—41no—
599C4—43no—
600C4—41no—
601C4—41no—
602C4—43no—
603C4—43no—
604C4C2×C13×#13516yes—
605C4C13×#58511yescharacteristic
606C4C13×#58511yescharacteristic
607C2—41no—
608C2—81no—
609C2—83no—
610C2C13×#348711yescharacteristic
611C2C22×C13×#13511yescharacteristic
612C2C13×#358611yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3523C2semidirect
2. C13×#3480C2semidirect
3. C13×#3395C2semidirect
4. C13×#3394C2semidirect
5. C13×#3393C2semidirect
6. C13×#3392C2semidirect
7. C13×#3365C2semidirect
8. C13×#3364C2semidirect
9. C13×#3359C2semidirect
10. C13×#3358C2semidirect
11. C13×#3212C2semidirect
12. C13×#3210C2semidirect
13. C13×#3107C2semidirect
14. C13×#3102C2semidirect
15. C13×#2982C2semidirect
164. #61887C13direct (N × H)
236. #3523C2×C13semidirect
237. #3480C2×C13semidirect
238. #3395C2×C13semidirect
239. #3394C2×C13semidirect
240. #3393C2×C13semidirect
241. #3392C2×C13semidirect
242. #3365C2×C13semidirect
243. #3364C2×C13semidirect
244. #3359C2×C13semidirect
245. #3358C2×C13semidirect
246. #3212C2×C13semidirect
247. #3210C2×C13semidirect
248. #3107C2×C13semidirect
249. #3102C2×C13semidirect
250. #2982C2×C13semidirect
541. C13#61887direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35232
C13×#34802
C13×#33952
C13×#33942
C13×#33932
C13×#33922
C13×#33652
C13×#33642
C13×#33592
C13×#33582
C13×#32122
C13×#32102
C13×#31072
C13×#31022
C13×#29822
#6188713