Finite Group Databasebeta

← C13×#62105 #15748444

Subgroups — C13×#62105 #15748444

Order 3328.

1728 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3518C211yesmaximal, characteristic, complemented
2C13×#3482C211yesmaximal, characteristic, complemented
3Q8×C13×SD16C211yesmaximal, characteristic, complemented
4Q8×C13×D8C211yesmaximal, characteristic, complemented
5C13×#3363C211yesmaximal, characteristic, complemented
6C13×#3359C211yesmaximal, characteristic, complemented
7C13×#3342C213yesmaximal, complemented
8C13×#3340C213yesmaximal, complemented
9C13×#3303C213yesmaximal, complemented
10C13×#3302C213yesmaximal, complemented
11C13×#3248C213yesmaximal, complemented
12C13×#3231C213yesmaximal, complemented
13C13×#3102C213yesmaximal, complemented
14C13×#3076C213yesmaximal, complemented
15C13×#2988C211yesmaximal, characteristic, complemented
16Q82×C13C2211yescharacteristic
17C13×#557C2211yescharacteristic
18C13×#556—23no—
19C13×#556C2213yes—
20C13×#556C2213yes—
21C13×#555C2213yes—
22C13×#552—23no—
23D4×Q8×C13C2211yescharacteristic
24D4×Q8×C13C2211yescharacteristic
25C13×#548—21no—
26C13×#548—21no—
27C13×#547C2213yes—
28C13×#542—23no—
29C13×#533C2213yes—
30C13×#533C2213yes—
31C13×#529—23no—
32C13×#529C2213yes—
33C13×#519—21no—
34C4×C13×#41C2213yes—
35C4×C13×#41C2211yescharacteristic
36C2×C4×Q8×C13—21no—
37C13×#500C2213yes—
38C13×#498C2213yes—
39C13×#487C2213yes—
40C13×#487C2213yes—
41C13×#485C2216yes—
42C13×#485C2216yes—
43C13×#485C2213yes—
44C13×#482C2213yes—
45C13×#479C2216yes—
46C13×#479C2213yes—
47C13×#478C2213yes—
48C13×#477C2213yes—
49C13×#476C2213yes—
50C13×#475C2213yes—
51C13×#475C2213yes—
52C13×#474C2213yes—
53C13×#474C2213yes—
54C13×#467C2216yes—
55C13×#465C2216yes—
56C13×#464C2213yes—
57C13×#463C2211yescharacteristic
58C13×#462C2213yes—
59C13×#461C2213yes—
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×#41D411yescharacteristic
75C2×C13×#41C2313yes—
76C22×Q8×C13—21no—
77C22×Q8×C13—21no—
78C2×C13×Q16C2313yes—
79C2×C13×SD16C2311yescharacteristic
80C2×C13×SD16C2313yes—
81C2×C13×D8C2311yescharacteristic
82C22×C8×C13C2316yes—
83C13×C4⋊Q8—23no—
84C13×C4⋊Q8C2313yes—
85C13×C4⋊Q8C2313yes—
86C13×C4⋊Q8C2313yes—
87C13×C4⋊Q8C2313yes—
88C13×#126—26no—
89C13×#126—26no—
90C13×#126—23no—
91C13×#125—23no—
92C13×#125—23no—
93C13×#125C2313yes—
94C13×#124—23no—
95C13×#124—23no—
96C13×#124—26no—
97C13×#124C2311yescharacteristic
98C13×#123—23no—
99C13×#123—26no—
100C13×C22⋊Q8—23no—
101C13×C22⋊Q8—23no—
102C13×C22⋊Q8—23no—
103C13×C22⋊Q8—23no—
104C13×C22⋊Q8—23no—
105C13×C22⋊Q8C2313yes—
106C13×C22⋊Q8C2316yes—
107C13×#121—23no—
108C13×#121—23no—
109C13×#121C2313yes—
110C4×Q8×C13—21no—
111C4×Q8×C13—21no—
112C4×Q8×C13—23no—
113C4×Q8×C13—23no—
114C4×Q8×C13—23no—
115C4×Q8×C13—23no—
116C4×Q8×C13—23no—
117C4×Q8×C13D411yescharacteristic
118C4×Q8×C13C2313yes—
119C4×Q8×C13C2313yes—
120C4×Q8×C13C2313yes—
121C4×Q8×C13C2311yescharacteristic
122C4×D4×C13—23no—
123C4×D4×C13—23no—
124C4×D4×C13—23no—
125C4×D4×C13D413yes—
126C4×D4×C13C2313yes—
127C4×D4×C13C2313yes—
128C4×D4×C13C2311yescharacteristic
129C4×D4×C13C2313yes—
130C13×#117—23no—
131C13×#117—23no—
132C13×#117—23no—
133C13×#117—23no—
134C13×#117D413yes—
135C13×#117C2316yes—
136C13×#117C2313yes—
137C2×C13×C4⋊C4—23no—
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×#103C2316yes—
151C13×#103C2316yes—
152C13×#103C2313yes—
153C13×#103C2313yes—
154C13×#103C2311yescharacteristic
155C13×#103C2313yes—
156C13×#102C2313yes—
157C13×#102C2313yes—
158C13×#102C2313yes—
159C13×#102C2311yescharacteristic
160C13×C22⋊C8C2313yes—
161C13×C22⋊C8C2313yes—
162C4×C8×C13C2313yes—
163C4×C8×C13C2313yes—
164#62105C1311yesmaximal, characteristic, direct product factor, Sylow
165C13×#41—24no—
166C13×#41—26no—
167C13×#41—43no—
168C2×Q8×C13—23no—
169C2×Q8×C13—23no—
170C2×Q8×C13—23no—
171C2×Q8×C13—44no—
172C2×Q8×C13—44no—
173C2×Q8×C13C2×D411yescharacteristic
174C2×Q8×C13C2413yes—
175C2×Q8×C13C2411yescharacteristic
176C2×D4×C13—23no—
177C2×D4×C13—23no—
178C2×D4×C13C2×D413yes—
179C2×D4×C13C2411yescharacteristic
180C2×D4×C13C2411yescharacteristic
181C22×C4×C13—21no—
182C22×C4×C13—23no—
183C22×C4×C13—23no—
184C22×C4×C13—23no—
185C22×C4×C13C2×D413yes—
186C22×C4×C13C2×D413yes—
187C22×C4×C13C2413yes—
188C13×Q16—43no—
189C13×SD16—22no—
190C13×SD16—43no—
191C13×D8—22no—
192C2×C8×C13—46no—
193C2×C8×C13C2411yescharacteristic
194C2×C8×C13C2411yescharacteristic
195C2×C8×C13C2413yes—
196C2×C8×C13C2413yes—
197C13×C4⋊C4—23no—
198C13×C4⋊C4—26no—
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—23no—
209C13×C4⋊C4C2×D413yes—
210C13×C4⋊C4C2×D413yes—
211C13×C4⋊C4C2413yes—
212C13×C4⋊C4C2413yes—
213C13×C4⋊C4C2411yescharacteristic
214C13×C4⋊C4C2413yes—
215C13×C22⋊C4—26no—
216C13×C22⋊C4—23no—
217C13×C22⋊C4—26no—
218C13×C22⋊C4—23no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—23no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—23no—
223C13×C22⋊C4—21no—
224C13×C22⋊C4—23no—
225C13×C22⋊C4C2×D416yes—
226C42×C13—23no—
227C42×C13—23no—
228C42×C13—23no—
229C42×C13—26no—
230C42×C13—23no—
231C42×C13C2×D413yes—
232C42×C13C2×D413yes—
233C42×C13C2413yes—
234C42×C13C2411yescharacteristic
235#3518C2×C1311yescharacteristic, complemented
236#3482C2×C1311yescharacteristic, complemented
237Q8×SD16C2×C1311yescharacteristic, complemented
238Q8×D8C2×C1311yescharacteristic, complemented
239#3363C2×C1311yescharacteristic, complemented
240#3359C2×C1311yescharacteristic, complemented
241#3342C2×C1313yescomplemented
242#3340C2×C1313yescomplemented
243#3303C2×C1313yescomplemented
244#3302C2×C1313yescomplemented
245#3248C2×C1313yescomplemented
246#3231C2×C1313yescomplemented
247#3102C2×C1313yescomplemented
248#3076C2×C1313yescomplemented
249#2988C2×C1311yescharacteristic, complemented
250C23×C13—21no—
251C23×C13—21no—
252C23×C13C22×D413yes—
253Q8×C13—21no—
254Q8×C13—23no—
255Q8×C13—23no—
256Q8×C13—21no—
257Q8×C13—46no—
258Q8×C13—46no—
259Q8×C13—83no—
260Q8×C13#13514yes—
261D4×C13—26no—
262D4×C13—21no—
263D4×C13—21no—
264D4×C13—21no—
265D4×C13—46no—
266D4×C13—83no—
267D4×C132−1+412yes—
268C2×C4×C13—26no—
269C2×C4×C13—23no—
270C2×C4×C13—23no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—23no—
274C2×C4×C13—23no—
275C2×C4×C13—23no—
276C2×C4×C13—23no—
277C2×C4×C13—43no—
278C2×C4×C13—46no—
279C2×C4×C13—42no—
280C2×C4×C13—46no—
281C2×C4×C13—46no—
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C22×D413yes—
284C2×C4×C13C22×D411yescharacteristic
285C2×C4×C13C22×D413yes—
286C2×C4×C13C22×D413yes—
287C2×C4×C13C2511yescharacteristic
288C8×C13—21no—
289C8×C13—21no—
290C8×C13—23no—
291C8×C13—23no—
292Q82C22×C1311yescharacteristic
293#557C22×C1311yescharacteristic
294#556—23no—
295#556C22×C1313yes—
296#556C22×C1313yes—
297#555C22×C1313yes—
298#552—23no—
299D4×Q8C22×C1311yescharacteristic
300D4×Q8C22×C1311yescharacteristic
301#548—21no—
302#548—21no—
303#547C22×C1313yes—
304#542—23no—
305#533C22×C1313yes—
306#533C22×C1313yes—
307#529—23no—
308#529C22×C1313yes—
309#519—21no—
310C4×#41C22×C1313yes—
311C4×#41C22×C1311yescharacteristic
312C2×C4×Q8—21no—
313#500C22×C1313yes—
314#498C22×C1313yes—
315#487C22×C1313yes—
316#487C22×C1313yes—
317#485C22×C1316yes—
318#485C22×C1313yes—
319#485C22×C1316yes—
320#482C22×C1313yes—
321#479C22×C1316yes—
322#479C22×C1313yes—
323#478C22×C1313yes—
324#477C22×C1313yes—
325#476C22×C1313yes—
326#475C22×C1313yes—
327#475C22×C1313yes—
328#474C22×C1313yes—
329#474C22×C1313yes—
330#467C22×C1316yes—
331#465C22×C1316yes—
332#464C22×C1313yes—
333#463C22×C1311yescharacteristic
334#462C22×C1313yes—
335#461C22×C1313yes—
336#452C22×C1313yes—
337#449C22×C1313yes—
338C8×Q8C22×C1311yescharacteristic
339C8×Q8C22×C1311yescharacteristic
340C4×Q16C22×C1313yes—
341C4×SD16C22×C1313yes—
342C4×SD16C22×C1313yes—
343C4×D8C22×C1313yes—
344C8×D4C22×C1313yes—
345C8×D4C22×C1313yes—
346#431C22×C1313yes—
347#427C22×C1316yes—
348C2×C4⋊C8C22×C1313yes—
349#416C22×C1316yes—
350C22×C13—23no—
351C22×C13—23no—
352C22×C13—22no—
353C22×C13—23no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13C23×D411yescharacteristic
360C4×C13—21no—
361C4×C13—23no—
362C4×C13—23no—
363C4×C13—21no—
364C4×C13—41no—
365C4×C13—43no—
366C4×C13—43no—
367C4×C13—41no—
368C4×C13—43no—
369C4×C13—43no—
370C4×C13C2×#13516yes—
371C4×C13C2×2−1+411yescharacteristic
372C4×C13#58511yescharacteristic
373C2×#41D4×C1311yescharacteristic
374C2×#41C23×C1313yes—
375C22×Q8—21no—
376C22×Q8—21no—
377C2×Q16C23×C1313yes—
378C2×SD16C23×C1311yescharacteristic
379C2×SD16C23×C1313yes—
380C2×D8C23×C1311yescharacteristic
381C22×C8C23×C1316yes—
382C4⋊Q8—23no—
383C4⋊Q8C23×C1313yes—
384C4⋊Q8C23×C1313yes—
385C4⋊Q8C23×C1313yes—
386C4⋊Q8C23×C1313yes—
387#126—26no—
388#126—26no—
389#126—23no—
390#125—23no—
391#125—23no—
392#125C23×C1313yes—
393#124—23no—
394#124—23no—
395#124—26no—
396#124C23×C1311yescharacteristic
397#123—23no—
398#123—26no—
399C22⋊Q8—23no—
400C22⋊Q8—23no—
401C22⋊Q8—23no—
402C22⋊Q8—23no—
403C22⋊Q8—23no—
404C22⋊Q8C23×C1313yes—
405C22⋊Q8C23×C1316yes—
406#121—23no—
407#121—23no—
408#121C23×C1313yes—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—23no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8—23no—
416C4×Q8D4×C1311yescharacteristic
417C4×Q8C23×C1313yes—
418C4×Q8C23×C1313yes—
419C4×Q8C23×C1313yes—
420C4×Q8C23×C1311yescharacteristic
421C4×D4—23no—
422C4×D4—23no—
423C4×D4—23no—
424C4×D4D4×C1313yes—
425C4×D4C23×C1311yescharacteristic
426C4×D4C23×C1313yes—
427C4×D4C23×C1313yes—
428C4×D4C23×C1313yes—
429#117—23no—
430#117—23no—
431#117—23no—
432#117—23no—
433#117D4×C1313yes—
434#117C23×C1313yes—
435#117C23×C1316yes—
436C2×C4⋊C4—23no—
437C2×C42—23no—
438C2×C42C23×C1313yes—
439#107C23×C1313yes—
440#107C23×C1316yes—
441#107C23×C1313yes—
442#106C23×C1313yes—
443#106C23×C1316yes—
444#106C23×C1313yes—
445C4⋊C8C23×C1313yes—
446C4⋊C8C23×C1313yes—
447C4⋊C8C23×C1313yes—
448C4⋊C8C23×C1311yescharacteristic
449#103C23×C1316yes—
450#103C23×C1316yes—
451#103C23×C1313yes—
452#103C23×C1313yes—
453#103C23×C1311yescharacteristic
454#103C23×C1313yes—
455#102C23×C1313yes—
456#102C23×C1313yes—
457#102C23×C1313yes—
458#102C23×C1311yescharacteristic
459C22⋊C8C23×C1313yes—
460C22⋊C8C23×C1313yes—
461C4×C8C23×C1313yes—
462C4×C8C23×C1313yes—
463C2×C13—43no—
464C2×C13—42no—
465C2×C13—81no—
466C2×C13#348911yescharacteristic
467C2×C13C22×#13511yescharacteristic
468C2×C13#358611yescharacteristic
469#41—24no—
470#41—26no—
471#41—43no—
472C2×Q8—23no—
473C2×Q8—23no—
474C2×Q8—23no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8C2×D4×C1311yescharacteristic
478C2×Q8C24×C1313yes—
479C2×Q8C24×C1311yescharacteristic
480C2×D4—23no—
481C2×D4—23no—
482C2×D4C2×D4×C1313yes—
483C2×D4C24×C1311yescharacteristic
484C2×D4C24×C1311yescharacteristic
485C22×C4—21no—
486C22×C4—23no—
487C22×C4—23no—
488C22×C4—23no—
489C22×C4C2×D4×C1313yes—
490C22×C4C2×D4×C1313yes—
491C22×C4C24×C1313yes—
492Q16—43no—
493SD16—22no—
494SD16—43no—
495D8—22no—
496C2×C8—46no—
497C2×C8C24×C1311yescharacteristic
498C2×C8C24×C1311yescharacteristic
499C2×C8C24×C1313yes—
500C2×C8C24×C1313yes—
501C4⋊C4—23no—
502C4⋊C4—26no—
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⋊C4C2×D4×C1313yes—
514C4⋊C4C2×D4×C1313yes—
515C4⋊C4C24×C1313yes—
516C4⋊C4C24×C1313yes—
517C4⋊C4C24×C1311yescharacteristic
518C4⋊C4C24×C1313yes—
519C22⋊C4—26no—
520C22⋊C4—23no—
521C22⋊C4—26no—
522C22⋊C4—23no—
523C22⋊C4—21no—
524C22⋊C4—23no—
525C22⋊C4—21no—
526C22⋊C4—23no—
527C22⋊C4—21no—
528C22⋊C4—23no—
529C22⋊C4C2×D4×C1316yes—
530C42—23no—
531C42—23no—
532C42—23no—
533C42—26no—
534C42—23no—
535C42C2×D4×C1313yes—
536C42C2×D4×C1313yes—
537C42C24×C1313yes—
538C42C24×C1311yescharacteristic
539C13#6210511yescharacteristic, direct product factor, Sylow
540C23—21no—
541C23—21no—
542C23C22×D4×C1313yes—
543Q8—21no—
544Q8—23no—
545Q8—23no—
546Q8—21no—
547Q8—46no—
548Q8—46no—
549Q8—83no—
550Q8C13×#13514yes—
551D4—26no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—46no—
556D4—83no—
557D4C13×2−1+412yes—
558C2×C4—26no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—43no—
568C2×C4—46no—
569C2×C4—42no—
570C2×C4—46no—
571C2×C4—46no—
572C2×C4C22×D4×C1311yescharacteristic
573C2×C4C22×D4×C1313yes—
574C2×C4C22×D4×C1311yescharacteristic
575C2×C4C22×D4×C1313yes—
576C2×C4C22×D4×C1313yes—
577C2×C4C25×C1311yescharacteristic
578C8—21no—
579C8—21no—
580C8—23no—
581C8—23no—
582C22—23no—
583C22—23no—
584C22—23no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C23×D4×C1311yescharacteristic
592C4—21no—
593C4—21no—
594C4—23no—
595C4—23no—
596C4—43no—
597C4—43no—
598C4—41no—
599C4—43no—
600C4—43no—
601C4—41no—
602C4C2×C13×#13516yes—
603C4C2×C13×2−1+411yescharacteristic
604C4C13×#58511yescharacteristic
605C2—43no—
606C2—42no—
607C2—81no—
608C2C13×#348911yescharacteristic
609C2C22×C13×#13511yescharacteristic
610C2C13×#358611yescharacteristic
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×#3482C2semidirect
3. Q8×C13×SD16C2semidirect
4. Q8×C13×D8C2semidirect
5. C13×#3363C2semidirect
6. C13×#3359C2semidirect
7. C13×#3342C2semidirect
8. C13×#3340C2semidirect
9. C13×#3303C2semidirect
10. C13×#3302C2semidirect
11. C13×#3248C2semidirect
12. C13×#3231C2semidirect
13. C13×#3102C2semidirect
14. C13×#3076C2semidirect
15. C13×#2988C2semidirect
164. #62105C13direct (N × H)
235. #3518C2×C13semidirect
236. #3482C2×C13semidirect
237. Q8×SD16C2×C13semidirect
238. Q8×D8C2×C13semidirect
239. #3363C2×C13semidirect
240. #3359C2×C13semidirect
241. #3342C2×C13semidirect
242. #3340C2×C13semidirect
243. #3303C2×C13semidirect
244. #3302C2×C13semidirect
245. #3248C2×C13semidirect
246. #3231C2×C13semidirect
247. #3102C2×C13semidirect
248. #3076C2×C13semidirect
249. #2988C2×C13semidirect
539. C13#62105direct (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×#34822
Q8×C13×SD162
Q8×C13×D82
C13×#33632
C13×#33592
C13×#33422
C13×#33402
C13×#33032
C13×#33022
C13×#32482
C13×#32312
C13×#31022
C13×#30762
C13×#29882
#6210513