Finite Group Databasebeta

← C13×#61303 #15747642

Subgroups — C13×#61303 #15747642

Order 3328.

1840 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3480C211yesmaximal, characteristic, complemented
2Q8×C13×#41C211yesmaximal, characteristic, complemented
3C13×#3365C213yesmaximal, complemented
4C13×#3364C213yesmaximal, complemented
5C13×#3363C211yesmaximal, characteristic, complemented
6C13×#3362C211yesmaximal, characteristic, complemented
7C13×#3361C213yesmaximal, complemented
8C13×#3360C213yesmaximal, complemented
9C13×#3359C211yesmaximal, characteristic, complemented
10C13×#3358C211yesmaximal, characteristic, complemented
11C13×#3131C213yesmaximal, complemented
12C13×#3076C213yesmaximal, complemented
13C13×#3035C213yesmaximal, complemented
14C2×C8×Q8×C13C211yesmaximal, characteristic, complemented
15C4×C13×#135C213yesmaximal, complemented
16C2×C13×#135C2213yes—
17C13×#559C2213yes—
18Q82×C13C2211yescharacteristic
19C13×#557C2211yescharacteristic
20C13×#557C2213yes—
21C13×#556C2213yes—
22C13×#554—23no—
23C13×#554C2213yes—
24C13×#553—23no—
25C13×#550C2211yescharacteristic
26D4×Q8×C13—21no—
27D4×Q8×C13C2211yescharacteristic
28C13×#548—21no—
29C13×#533—23no—
30C13×#533C2213yes—
31C13×#532C2213yes—
32C13×#529—23no—
33C4×C13×#41—21no—
34C4×C13×#41C2213yes—
35C4×C13×#41C2213yes—
36C2×C4×Q8×C13—21no—
37C2×C4×Q8×C13C2211yescharacteristic
38C13×#488C2216yes—
39C13×#488C2216yes—
40C13×#487C2213yes—
41C13×#487C2213yes—
42C13×#486C2213yes—
43C13×#486C2213yes—
44C13×#479C2216yes—
45C13×#478C2216yes—
46C13×#477C2213yes—
47C13×#476C2213yes—
48C13×#475C2213yes—
49C13×#474C2213yes—
50C13×#464C2216yes—
51C13×#463C2216yes—
52C13×#462C2213yes—
53C13×#461C2213yes—
54C13×#460C2213yes—
55C13×#459C2213yes—
56C8×Q8×C13C2211yescharacteristic
57C8×Q8×C13C2211yescharacteristic
58C8×Q8×C13C2213yes—
59C8×Q8×C13C2213yes—
60C4×C13×Q16C2213yes—
61C4×C13×Q16C2213yes—
62C4×C13×SD16C2213yes—
63C4×C13×SD16C2213yes—
64C4×C13×SD16C2213yes—
65C4×C13×SD16C2213yes—
66C4×C13×D8C2213yes—
67C4×C13×D8C2213yes—
68C13×#427C2213yes—
69C2×C13×C4⋊C8C2213yes—
70C13×#416C2216yes—
71C13×#416C2213yes—
72C13×#416C2211yescharacteristic
73C2×C4×C8×C13C2213yes—
74C2×C13×#41—21no—
75C2×C13×#41C2313yes—
76C2×C13×#41C2311yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13D411yescharacteristic
79C13×#135—212no—
80C2×C13×Q16C2313yes—
81C2×C13×SD16C2313yes—
82C2×C13×SD16C2313yes—
83C2×C13×D8C2313yes—
84C22×C8×C13C2311yescharacteristic
85C22×C8×C13C2313yes—
86C13×C4⋊Q8—23no—
87C13×C4⋊Q8—23no—
88C13×C4⋊Q8C2313yes—
89C13×C4⋊Q8C2313yes—
90C13×C4⋊Q8C2313yes—
91C13×#127C2313yes—
92C13×#126—26no—
93C13×#125—23no—
94C13×#125—26no—
95C13×#125C2316yes—
96C13×#124—23no—
97C13×#124C2316yes—
98C13×#123—26no—
99C13×C22⋊Q8—23no—
100C13×C22⋊Q8—23no—
101C13×C22⋊Q8—23no—
102C13×C22⋊Q8—23no—
103C13×C22⋊Q8—23no—
104C13×C22⋊Q8—26no—
105C13×#121—23no—
106C13×#121—23no—
107C13×#121—23no—
108C4×Q8×C13—21no—
109C4×Q8×C13—21no—
110C4×Q8×C13—23no—
111C4×Q8×C13—23no—
112C4×Q8×C13—23no—
113C4×Q8×C13D411yescharacteristic
114C4×Q8×C13D413yes—
115C4×Q8×C13C2313yes—
116C4×Q8×C13C2313yes—
117C4×Q8×C13C2313yes—
118C4×Q8×C13C2313yes—
119C4×Q8×C13C2311yescharacteristic
120C4×Q8×C13C2313yes—
121C4×D4×C13—23no—
122C4×D4×C13—23no—
123C4×D4×C13—23no—
124C4×D4×C13—23no—
125C4×D4×C13—23no—
126C4×D4×C13—23no—
127C4×D4×C13—23no—
128C4×D4×C13C2313yes—
129C4×D4×C13C2313yes—
130C4×D4×C13C2313yes—
131C4×D4×C13C2313yes—
132C13×#117—23no—
133C13×#117—23no—
134C13×#117—23no—
135C13×#117C2313yes—
136C13×#117C2311yescharacteristic
137C2×C13×C4⋊C4—23no—
138C2×C13×C4⋊C4D413yes—
139C2×C42×C13—23no—
140C2×C42×C13—23no—
141C2×C42×C13C2313yes—
142C13×#107C2313yes—
143C13×#107C2313yes—
144C13×#106C2313yes—
145C13×#106C2313yes—
146C13×C4⋊C8C2313yes—
147C13×C4⋊C8C2313yes—
148C13×C4⋊C8C2316yes—
149C13×#103C2311yescharacteristic
150C13×#103C2311yescharacteristic
151C13×#103C2313yes—
152C13×#103C2313yes—
153C13×#103C2316yes—
154C13×#103C2316yes—
155C13×#102C2311yescharacteristic
156C13×#102C2311yescharacteristic
157C13×#102C2313yes—
158C13×#102C2313yes—
159C13×#102C2316yes—
160C13×#102C2316yes—
161C4×C8×C13C2313yes—
162C4×C8×C13C2313yes—
163C4×C8×C13C2313yes—
164C4×C8×C13C2313yes—
165#61303C1311yesmaximal, characteristic, direct product factor, Sylow
166C13×#41—22no—
167C13×#41—26no—
168C13×#41—26no—
169C13×#41—44no—
170C13×#41#4114yescomplemented
171C2×Q8×C13—24no—
172C2×Q8×C13—23no—
173C2×Q8×C13—23no—
174C2×Q8×C13—44no—
175C2×Q8×C13C2×D413yes—
176C2×Q8×C13C2×D411yescharacteristic
177C2×Q8×C13C2413yes—
178C2×Q8×C13C2411yescharacteristic
179C2×D4×C13—21no—
180C2×D4×C13—23no—
181C2×D4×C13—23no—
182C2×D4×C13—23no—
183C2×D4×C13C2413yes—
184C2×D4×C13C2411yescharacteristic
185C22×C4×C13—21no—
186C22×C4×C13—23no—
187C22×C4×C13—23no—
188C22×C4×C13—23no—
189C22×C4×C13—23no—
190C22×C4×C13—23no—
191C22×C4×C13C2×D413yes—
192C22×C4×C13C2×D413yes—
193C22×C4×C13C2411yescharacteristic
194C13×Q16—26no—
195C13×SD16—26no—
196C13×SD16—26no—
197C13×D8—26no—
198C2×C8×C13—26no—
199C2×C8×C13—22no—
200C2×C8×C13C2411yescharacteristic
201C2×C8×C13C2411yescharacteristic
202C2×C8×C13C2413yes—
203C2×C8×C13C2413yes—
204C13×C4⋊C4—26no—
205C13×C4⋊C4—23no—
206C13×C4⋊C4—23no—
207C13×C4⋊C4—23no—
208C13×C4⋊C4—23no—
209C13×C4⋊C4—23no—
210C13×C4⋊C4—23no—
211C13×C4⋊C4—23no—
212C13×C4⋊C4—23no—
213C13×C4⋊C4—26no—
214C13×C4⋊C4C2×D413yes—
215C13×C4⋊C4C2×D413yes—
216C13×C4⋊C4C2×D416yes—
217C13×C4⋊C4C2413yes—
218C13×C4⋊C4C2413yes—
219C13×C4⋊C4C2411yescharacteristic
220C13×C4⋊C4C2411yescharacteristic
221C13×C22⋊C4—21no—
222C13×C22⋊C4—23no—
223C13×C22⋊C4—26no—
224C13×C22⋊C4—23no—
225C13×C22⋊C4—23no—
226C13×C22⋊C4—23no—
227C13×C22⋊C4—23no—
228C13×C22⋊C4—26no—
229C42×C13—23no—
230C42×C13—23no—
231C42×C13—23no—
232C42×C13—23no—
233C42×C13—21no—
234C42×C13—23no—
235C42×C13C2×D413yes—
236C42×C13C2×D413yes—
237C42×C13C2413yes—
238C42×C13C2413yes—
239#3480C2×C1311yescharacteristic, complemented
240Q8×#41C2×C1311yescharacteristic, complemented
241#3365C2×C1313yescomplemented
242#3364C2×C1313yescomplemented
243#3363C2×C1311yescharacteristic, complemented
244#3362C2×C1311yescharacteristic, complemented
245#3361C2×C1313yescomplemented
246#3360C2×C1313yescomplemented
247#3359C2×C1311yescharacteristic, complemented
248#3358C2×C1311yescharacteristic, complemented
249#3131C2×C1313yescomplemented
250#3076C2×C1313yescomplemented
251#3035C2×C1313yescomplemented
252C2×C8×Q8C2×C1311yescharacteristic, complemented
253C4×#135C2×C1313yescomplemented
254C23×C13—21no—
255C23×C13—23no—
256C23×C13C22×D411yescharacteristic
257Q8×C13—26no—
258Q8×C13—21no—
259Q8×C13—23no—
260Q8×C13—23no—
261Q8×C13—46no—
262Q8×C13—83no—
263Q8×C13#13514yescomplemented
264Q8×C13C2×#4112yes—
265D4×C13—24no—
266D4×C13—23no—
267D4×C13—21no—
268D4×C13—23no—
269D4×C13—46no—
270D4×C13—46no—
271D4×C13—83no—
272D4×C13C2×#4112yes—
273C2×C4×C13—21no—
274C2×C4×C13—24no—
275C2×C4×C13—26no—
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—83no—
286C2×C4×C13—83no—
287C2×C4×C13C22×D413yes—
288C2×C4×C13C22×D413yes—
289C2×C4×C13C22×D413yes—
290C2×C4×C13C22×D413yes—
291C2×C4×C13C22×D411yescharacteristic
292C2×C4×C13C2×#4112yes—
293C2×C4×C132−1+412yes—
294C2×C4×C13C2511yescharacteristic
295C8×C13—23no—
296C8×C13—23no—
297C8×C13—21no—
298C8×C13—21no—
299C2×#135C22×C1313yes—
300#559C22×C1313yes—
301Q82C22×C1311yescharacteristic
302#557C22×C1311yescharacteristic
303#557C22×C1313yes—
304#556C22×C1313yes—
305#554—23no—
306#554C22×C1313yes—
307#553—23no—
308#550C22×C1311yescharacteristic
309D4×Q8—21no—
310D4×Q8C22×C1311yescharacteristic
311#548—21no—
312#533—23no—
313#533C22×C1313yes—
314#532C22×C1313yes—
315#529—23no—
316C4×#41—21no—
317C4×#41C22×C1313yes—
318C4×#41C22×C1313yes—
319C2×C4×Q8—21no—
320C2×C4×Q8C22×C1311yescharacteristic
321#488C22×C1316yes—
322#488C22×C1316yes—
323#487C22×C1313yes—
324#487C22×C1313yes—
325#486C22×C1313yes—
326#486C22×C1313yes—
327#479C22×C1316yes—
328#478C22×C1316yes—
329#477C22×C1313yes—
330#476C22×C1313yes—
331#475C22×C1313yes—
332#474C22×C1313yes—
333#464C22×C1316yes—
334#463C22×C1316yes—
335#462C22×C1313yes—
336#461C22×C1313yes—
337#460C22×C1313yes—
338#459C22×C1313yes—
339C8×Q8C22×C1311yescharacteristic
340C8×Q8C22×C1311yescharacteristic
341C8×Q8C22×C1313yes—
342C8×Q8C22×C1313yes—
343C4×Q16C22×C1313yes—
344C4×Q16C22×C1313yes—
345C4×SD16C22×C1313yes—
346C4×SD16C22×C1313yes—
347C4×SD16C22×C1313yes—
348C4×SD16C22×C1313yes—
349C4×D8C22×C1313yes—
350C4×D8C22×C1313yes—
351#427C22×C1313yes—
352C2×C4⋊C8C22×C1313yes—
353#416C22×C1316yes—
354#416C22×C1313yes—
355#416C22×C1311yescharacteristic
356C2×C4×C8C22×C1313yes—
357C22×C13—21no—
358C22×C13—21no—
359C22×C13—22no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—43no—
363C22×C13—43no—
364C22×C13—43no—
365C22×C13#54812yes—
366C22×C13C23×D411yescharacteristic
367C4×C13—23no—
368C4×C13—23no—
369C4×C13—22no—
370C4×C13—23no—
371C4×C13—41no—
372C4×C13—43no—
373C4×C13—43no—
374C4×C13—41no—
375C4×C13—43no—
376C4×C13#54812yes—
377C4×C13C2×#13516yes—
378C4×C13C22×#4111yescharacteristic
379C4×C13C2×2−1+411yescharacteristic
380C2×#41—21no—
381C2×#41C23×C1313yes—
382C2×#41C23×C1311yescharacteristic
383C22×Q8—21no—
384C22×Q8D4×C1311yescharacteristic
385#135—212no—
386C2×Q16C23×C1313yes—
387C2×SD16C23×C1313yes—
388C2×SD16C23×C1313yes—
389C2×D8C23×C1313yes—
390C22×C8C23×C1313yes—
391C22×C8C23×C1311yescharacteristic
392C4⋊Q8—23no—
393C4⋊Q8—23no—
394C4⋊Q8C23×C1313yes—
395C4⋊Q8C23×C1313yes—
396C4⋊Q8C23×C1313yes—
397#127C23×C1313yes—
398#126—26no—
399#125—23no—
400#125—26no—
401#125C23×C1316yes—
402#124—23no—
403#124C23×C1316yes—
404#123—26no—
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407C22⋊Q8—23no—
408C22⋊Q8—23no—
409C22⋊Q8—23no—
410C22⋊Q8—26no—
411#121—23no—
412#121—23no—
413#121—23no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8—23no—
419C4×Q8D4×C1311yescharacteristic
420C4×Q8D4×C1313yes—
421C4×Q8C23×C1313yes—
422C4×Q8C23×C1313yes—
423C4×Q8C23×C1313yes—
424C4×Q8C23×C1313yes—
425C4×Q8C23×C1311yescharacteristic
426C4×Q8C23×C1313yes—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4—23no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4C23×C1313yes—
435C4×D4C23×C1313yes—
436C4×D4C23×C1313yes—
437C4×D4C23×C1313yes—
438#117—23no—
439#117—23no—
440#117—23no—
441#117C23×C1311yescharacteristic
442#117C23×C1313yes—
443C2×C4⋊C4—23no—
444C2×C4⋊C4D4×C1313yes—
445C2×C42—23no—
446C2×C42—23no—
447C2×C42C23×C1313yes—
448#107C23×C1313yes—
449#107C23×C1313yes—
450#106C23×C1313yes—
451#106C23×C1313yes—
452C4⋊C8C23×C1313yes—
453C4⋊C8C23×C1313yes—
454C4⋊C8C23×C1316yes—
455#103C23×C1311yescharacteristic
456#103C23×C1311yescharacteristic
457#103C23×C1313yes—
458#103C23×C1313yes—
459#103C23×C1316yes—
460#103C23×C1316yes—
461#102C23×C1311yescharacteristic
462#102C23×C1311yescharacteristic
463#102C23×C1313yes—
464#102C23×C1313yes—
465#102C23×C1316yes—
466#102C23×C1316yes—
467C4×C8C23×C1313yes—
468C4×C8C23×C1313yes—
469C4×C8C23×C1313yes—
470C4×C8C23×C1313yes—
471C2×C13—22no—
472C2×C13—42no—
473C2×C13—83no—
474C2×C13C2×#54811yescharacteristic
475C2×C13C22×#13511yescharacteristic
476C2×C13#358411yescharacteristic
477#41—22no—
478#41—26no—
479#41—26no—
480#41—44no—
481#41C13×#4114yescomplemented
482C2×Q8—24no—
483C2×Q8—23no—
484C2×Q8—23no—
485C2×Q8—44no—
486C2×Q8C2×D4×C1313yes—
487C2×Q8C2×D4×C1311yescharacteristic
488C2×Q8C24×C1313yes—
489C2×Q8C24×C1311yescharacteristic
490C2×D4—21no—
491C2×D4—23no—
492C2×D4—23no—
493C2×D4—23no—
494C2×D4C24×C1313yes—
495C2×D4C24×C1311yescharacteristic
496C22×C4—21no—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—23no—
500C22×C4—23no—
501C22×C4—23no—
502C22×C4C2×D4×C1313yes—
503C22×C4C2×D4×C1313yes—
504C22×C4C24×C1311yescharacteristic
505Q16—26no—
506SD16—26no—
507SD16—26no—
508D8—26no—
509C2×C8—26no—
510C2×C8—22no—
511C2×C8C24×C1311yescharacteristic
512C2×C8C24×C1311yescharacteristic
513C2×C8C24×C1313yes—
514C2×C8C24×C1313yes—
515C4⋊C4—26no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—23no—
520C4⋊C4—23no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4—23no—
524C4⋊C4—26no—
525C4⋊C4C2×D4×C1313yes—
526C4⋊C4C2×D4×C1313yes—
527C4⋊C4C2×D4×C1316yes—
528C4⋊C4C24×C1313yes—
529C4⋊C4C24×C1313yes—
530C4⋊C4C24×C1311yescharacteristic
531C4⋊C4C24×C1311yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—23no—
534C22⋊C4—26no—
535C22⋊C4—23no—
536C22⋊C4—23no—
537C22⋊C4—23no—
538C22⋊C4—23no—
539C22⋊C4—26no—
540C42—21no—
541C42—23no—
542C42—23no—
543C42—23no—
544C42—23no—
545C42—23no—
546C42C2×D4×C1313yes—
547C42C2×D4×C1313yes—
548C42C24×C1313yes—
549C42C24×C1313yes—
550C13#6130311yescharacteristic, direct product factor, Sylow
551C23—21no—
552C23—23no—
553C23C22×D4×C1311yescharacteristic
554Q8—26no—
555Q8—21no—
556Q8—23no—
557Q8—23no—
558Q8—46no—
559Q8—83no—
560Q8C13×#13514yescomplemented
561Q8C2×C13×#4112yes—
562D4—24no—
563D4—23no—
564D4—21no—
565D4—23no—
566D4—46no—
567D4—46no—
568D4—83no—
569D4C2×C13×#4112yes—
570C2×C4—21no—
571C2×C4—24no—
572C2×C4—26no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—23no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—43no—
579C2×C4—46no—
580C2×C4—46no—
581C2×C4—46no—
582C2×C4—83no—
583C2×C4—83no—
584C2×C4C22×D4×C1313yes—
585C2×C4C22×D4×C1313yes—
586C2×C4C22×D4×C1313yes—
587C2×C4C22×D4×C1311yescharacteristic
588C2×C4C22×D4×C1313yes—
589C2×C4C2×C13×#4112yes—
590C2×C4C13×2−1+412yes—
591C2×C4C25×C1311yescharacteristic
592C8—23no—
593C8—23no—
594C8—21no—
595C8—21no—
596C22—21no—
597C22—21no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—43no—
602C22—43no—
603C22—43no—
604C22C13×#54812yes—
605C22C23×D4×C1311yescharacteristic
606C4—23no—
607C4—23no—
608C4—23no—
609C4—22no—
610C4—41no—
611C4—43no—
612C4—41no—
613C4—43no—
614C4—43no—
615C4C13×#54812yes—
616C4C2×C13×#13516yes—
617C4C22×C13×#4111yescharacteristic
618C4C2×C13×2−1+411yescharacteristic
619C2—22no—
620C2—42no—
621C2—83no—
622C2C2×C13×#54811yescharacteristic
623C2C22×C13×#13511yescharacteristic
624C2C13×#358411yescharacteristic
subgroupG/H
centerC2×C4×C13C22×D4
commutator, Frattini, cosocleC2×C4C25×C13
socleC22×C13C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3480C2semidirect
2. Q8×C13×#41C2semidirect
3. C13×#3365C2semidirect
4. C13×#3364C2semidirect
5. C13×#3363C2semidirect
6. C13×#3362C2semidirect
7. C13×#3361C2semidirect
8. C13×#3360C2semidirect
9. C13×#3359C2semidirect
10. C13×#3358C2semidirect
11. C13×#3131C2semidirect
12. C13×#3076C2semidirect
13. C13×#3035C2semidirect
14. C2×C8×Q8×C13C2semidirect
15. C4×C13×#135C2semidirect
165. #61303C13direct (N × H)
170. C13×#41#41semidirect
239. #3480C2×C13semidirect
240. Q8×#41C2×C13semidirect
241. #3365C2×C13semidirect
242. #3364C2×C13semidirect
243. #3363C2×C13semidirect
244. #3362C2×C13semidirect
245. #3361C2×C13semidirect
246. #3360C2×C13semidirect
247. #3359C2×C13semidirect
248. #3358C2×C13semidirect
249. #3131C2×C13semidirect
250. #3076C2×C13semidirect
251. #3035C2×C13semidirect
252. C2×C8×Q8C2×C13semidirect
253. C4×#135C2×C13semidirect
263. Q8×C13#135semidirect
481. #41C13×#41semidirect
550. C13#61303direct (N × H)
560. Q8C13×#135semidirect

Maximal subgroups

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

subgroupindex
C13×#34802
Q8×C13×#412
C13×#33652
C13×#33642
C13×#33632
C13×#33622
C13×#33612
C13×#33602
C13×#33592
C13×#33582
C13×#31312
C13×#30762
C13×#30352
C2×C8×Q8×C132
C4×C13×#1352
#6130313