Finite Group Databasebeta

← C13×#18460 #15704799

Subgroups — C13×#18460 #15704799

Order 3328.

936 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic, complemented
2C13×#3213C211yesmaximal, characteristic, complemented
3C13×#3211C211yesmaximal, characteristic, complemented
4C13×#2820C211yesmaximal, characteristic, complemented
5C13×#1604C212yesmaximal, complemented
6C13×#1603C212yesmaximal, complemented
7C13×#1598C212yesmaximal, complemented
8C13×#1597C212yesmaximal, complemented
9C13×#1517C211yesmaximal, characteristic, complemented
10C13×#1512C211yesmaximal, characteristic, complemented
11C13×#1470C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#562—21no—
14C13×#554—21no—
15C13×#553—21no—
16C13×#553—21no—
17C13×#547—22no—
18C13×#547—21no—
19C13×#544—21no—
20C13×#540—21no—
21C13×#539—22no—
22C13×#539C2212yes—
23C13×#537C2212yes—
24C13×#532C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C13×#496—21no—
29C13×#495—21no—
30C13×#489—21no—
31C13×#488—21no—
32C13×#464—21no—
33C13×#463—21no—
34C13×#463—22no—
35C13×#451C2211yescharacteristic
36C13×#450C2211yescharacteristic
37C13×#448C2212yes—
38C13×#448C2211yescharacteristic
39C13×#447C2212yes—
40C13×#447C2211yescharacteristic
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#399—21no—
44C13×#397—21no—
45C13×#396—22no—
46C13×#395C2212yes—
47C13×#394C2212yes—
48C13×#382C2211yescharacteristic
49C13×#328C2212yes—
50C13×#327C2212yes—
51C13×#327C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C2×C13×#41—21no—
56C2×C13×#41—22no—
57C22×Q8×C13C2311yescharacteristic
58C22×D4×C13C2311yescharacteristic
59C2×C13×Q16—21no—
60C2×C13×SD16—21no—
61C2×C13×SD16—21no—
62C2×C13×SD16—22no—
63C2×C13×D8—21no—
64C2×C13×D8—22no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8D411yescharacteristic
68C13×#127D411yescharacteristic
69C13×#126—22no—
70C13×#126—22no—
71C13×#126—21no—
72C13×#125—21no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—21no—
76C13×#125—21no—
77C13×#125—21no—
78C13×#125D411yescharacteristic
79C13×#124—21no—
80C13×#124—21no—
81C13×#124—21no—
82C13×#124—21no—
83C13×#124—21no—
84C13×#124D411yescharacteristic
85C13×#123—22no—
86C13×#123—22no—
87C13×#123—22no—
88C13×#123—22no—
89C13×#123—22no—
90C13×#123—21no—
91C13×#123—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8—22no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8C2311yescharacteristic
99C13×#121—21no—
100C13×#121—22no—
101C13×#121—21no—
102C13×#121—22no—
103C13×#121—22no—
104C13×#121—21no—
105C13×#121—22no—
106C13×#121C2311yescharacteristic
107C13×#121C2312yes—
108C4×Q8×C13D411yescharacteristic
109C4×D4×C13—22no—
110C4×D4×C13—21no—
111C4×D4×C13—21no—
112C4×D4×C13—21no—
113C4×D4×C13—22no—
114C4×D4×C13—21no—
115C4×D4×C13D411yescharacteristic
116C4×D4×C13D412yes—
117C13×#117—21no—
118C13×#117—21no—
119C2×C13×C4⋊C4—22no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—22no—
123C2×C13×C4⋊C4D412yes—
124C2×C13×C4⋊C4D411yescharacteristic
125C2×C13×C4⋊C4D411yescharacteristic
126C2×C13×C4⋊C4C2312yes—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4—22no—
131C2×C42×C13C2311yescharacteristic
132C13×C4⋊C8—21no—
133C13×C4⋊C8—21no—
134C13×#103—22no—
135C13×#103—21no—
136C13×#103—21no—
137C13×#102—22no—
138C13×#102—21no—
139C13×#102—21no—
140C13×C22⋊C8C2311yescharacteristic
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2312yes—
143C13×#97—21no—
144C4×C8×C13—21no—
145C13×#95—21no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18460C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13—21no—
150C13×#41—81no—
151C13×#41—81no—
152C13×#41—82no—
153C13×#41—82no—
154C2×Q8×C13—22no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—21no—
158C2×Q8×C13—81no—
159C2×Q8×C13C2×D411yescharacteristic
160C2×D4×C13—21no—
161C2×D4×C13—22no—
162C2×D4×C13—22no—
163C2×D4×C13—22no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13—21no—
167C2×D4×C13—21no—
168C2×D4×C13—81no—
169C2×D4×C13C2×D411yescharacteristic
170C2×D4×C13C2×D412yes—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—21no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—21no—
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D412yes—
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2411yescharacteristic
183C13×Q16—81no—
184C13×SD16—82no—
185C13×SD16—81no—
186C13×SD16—81no—
187C13×D8—82no—
188C13×D8—81no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—22no—
207C13×C4⋊C4—22no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—81no—
210C13×C4⋊C4—82no—
211C13×C4⋊C4C2×D412yes—
212C13×C4⋊C4C2×D411yescharacteristic
213C13×C4⋊C4C2×D411yescharacteristic
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—22no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—21no—
223C13×C22⋊C4—22no—
224C13×C22⋊C4—21no—
225C13×C22⋊C4—22no—
226C13×C22⋊C4—41no—
227C13×C22⋊C4—41no—
228C13×C22⋊C4—41no—
229C13×C22⋊C4—41no—
230C13×C22⋊C4—82no—
231C13×C22⋊C4—82no—
232C42×C13—22no—
233C42×C13—21no—
234C42×C13C2×D411yescharacteristic
235C42×C13C2×D411yescharacteristic
236C42×C13C2×D411yescharacteristic
237C42×C13C2×D411yescharacteristic
238#3559C2×C1311yescharacteristic, complemented
239#3213C2×C1311yescharacteristic, complemented
240#3211C2×C1311yescharacteristic, complemented
241#2820C2×C1311yescharacteristic, complemented
242#1604C2×C1312yescomplemented
243#1603C2×C1312yescomplemented
244#1598C2×C1312yescomplemented
245#1597C2×C1312yescomplemented
246#1517C2×C1311yescharacteristic, complemented
247#1512C2×C1311yescharacteristic, complemented
248#1470C2×C1311yescharacteristic, complemented
249C23×C13—21no—
250C23×C13—22no—
251C23×C13—42no—
252C23×C13—42no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13C22×D411yescharacteristic
257Q8×C13—41no—
258Q8×C13—42no—
259Q8×C13—41no—
260Q8×C13—41no—
261Q8×C13—81no—
262Q8×C13—82no—
263D4×C13—42no—
264D4×C13—42no—
265D4×C13—41no—
266D4×C13—42no—
267D4×C13—41no—
268D4×C13—41no—
269D4×C13—42no—
270D4×C13—41no—
271D4×C13—42no—
272D4×C13—41no—
273D4×C13—81no—
274D4×C13—82no—
275D4×C13—82no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—21no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—82no—
296C2×C4×C13—82no—
297C2×C4×C13—82no—
298C2×C4×C13—82no—
299C2×C4×C13#12011yescharacteristic
300C2×C4×C13#12011yescharacteristic
301C2×C4×C13#12011yescharacteristic
302C2×C4×C13#12011yescharacteristic
303C2×C4×C13C22×D411yescharacteristic
304C2×C4×C13C22×D411yescharacteristic
305C8×C13—42no—
306C8×C13—41no—
307C8×C13—41no—
308#563—21no—
309#562—21no—
310#554—21no—
311#553—21no—
312#553—21no—
313#547—22no—
314#547—21no—
315#544—21no—
316#540—21no—
317#539—22no—
318#539C22×C1312yes—
319#537C22×C1312yes—
320#532C22×C1311yescharacteristic
321#529C22×C1311yescharacteristic
322C2×#125C22×C1311yescharacteristic
323C2×#124C22×C1311yescharacteristic
324#496—21no—
325#495—21no—
326#489—21no—
327#488—21no—
328#464—21no—
329#463—21no—
330#463—22no—
331#451C22×C1311yescharacteristic
332#450C22×C1311yescharacteristic
333#448C22×C1312yes—
334#448C22×C1311yescharacteristic
335#447C22×C1312yes—
336#447C22×C1311yescharacteristic
337#432C22×C1311yescharacteristic
338#431C22×C1311yescharacteristic
339#399—21no—
340#397—21no—
341#396—22no—
342#395C22×C1312yes—
343#394C22×C1312yes—
344#382C22×C1311yescharacteristic
345#328C22×C1312yes—
346#327C22×C1312yes—
347#327C22×C1312yes—
348#327C22×C1312yes—
349#324C22×C1312yes—
350#324C22×C1312yes—
351C22×C13—21no—
352C22×C13—21no—
353C22×C13—42no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—41no—
359C22×C13—82no—
360C22×C13—82no—
361C22×C13—81no—
362C22×C13—81no—
363C22×C13—81no—
364C22×C13C2×#12011yescharacteristic
365C22×C13#57611yescharacteristic
366C22×C13#57711yescharacteristic
367C4×C13—21no—
368C4×C13—21no—
369C4×C13—21no—
370C4×C13—21no—
371C4×C13—21no—
372C4×C13—21no—
373C4×C13—42no—
374C4×C13—42no—
375C4×C13—41no—
376C4×C13—41no—
377C4×C13—42no—
378C4×C13—41no—
379C4×C13—82no—
380C4×C13—81no—
381C2×#41—21no—
382C2×#41—22no—
383C22×Q8C23×C1311yescharacteristic
384C22×D4C23×C1311yescharacteristic
385C2×Q16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—22no—
389C2×D8—21no—
390C2×D8—22no—
391C4⋊Q8—21no—
392C4⋊Q8—22no—
393C4⋊Q8D4×C1311yescharacteristic
394#127D4×C1311yescharacteristic
395#126—22no—
396#126—22no—
397#126—21no—
398#125—21no—
399#125—22no—
400#125—21no—
401#125—21no—
402#125—21no—
403#125—21no—
404#125D4×C1311yescharacteristic
405#124—21no—
406#124—21no—
407#124—21no—
408#124—21no—
409#124—21no—
410#124D4×C1311yescharacteristic
411#123—22no—
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416#123—21no—
417#123—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8C23×C1311yescharacteristic
425#121—21no—
426#121—22no—
427#121—21no—
428#121—22no—
429#121—22no—
430#121—21no—
431#121—22no—
432#121C23×C1311yescharacteristic
433#121C23×C1312yes—
434C4×Q8D4×C1311yescharacteristic
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—22no—
440C4×D4—21no—
441C4×D4D4×C1311yescharacteristic
442C4×D4D4×C1312yes—
443#117—21no—
444#117—21no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4D4×C1312yes—
450C2×C4⋊C4D4×C1311yescharacteristic
451C2×C4⋊C4D4×C1311yescharacteristic
452C2×C4⋊C4C23×C1312yes—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C42C23×C1311yescharacteristic
458C4⋊C8—21no—
459C4⋊C8—21no—
460#103—22no—
461#103—21no—
462#103—21no—
463#102—22no—
464#102—21no—
465#102—21no—
466C22⋊C8C23×C1311yescharacteristic
467C22⋊C8C23×C1311yescharacteristic
468C22⋊C8C23×C1312yes—
469#97—21no—
470C4×C8—21no—
471#95—21no—
472#95—22no—
473#95C23×C1312yes—
474C2×C13—21no—
475C2×C13—21no—
476C2×C13—81no—
477C2×C13—82no—
478C2×C13—161no—
479C2×C13#301211yescharacteristic
480C2×C13#302011yescharacteristic
481C2×C13#302711yescharacteristic
482C24—21no—
483#41—81no—
484#41—81no—
485#41—82no—
486#41—82no—
487C2×Q8—22no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—81no—
492C2×Q8C2×D4×C1311yescharacteristic
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—81no—
502C2×D4C2×D4×C1311yescharacteristic
503C2×D4C2×D4×C1312yes—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4C2×D4×C1312yes—
512C22×C4C2×D4×C1311yescharacteristic
513C22×C4C2×D4×C1312yes—
514C22×C4C2×D4×C1311yescharacteristic
515C22×C4C24×C1311yescharacteristic
516Q16—81no—
517SD16—82no—
518SD16—81no—
519SD16—81no—
520D8—82no—
521D8—81no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—82no—
544C4⋊C4C2×D4×C1312yes—
545C4⋊C4C2×D4×C1311yescharacteristic
546C4⋊C4C2×D4×C1311yescharacteristic
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—82no—
564C22⋊C4—82no—
565C42—22no—
566C42—21no—
567C42C2×D4×C1311yescharacteristic
568C42C2×D4×C1311yescharacteristic
569C42C2×D4×C1311yescharacteristic
570C42C2×D4×C1311yescharacteristic
571C13#1846011yescharacteristic, direct product factor, Sylow
572C23—21no—
573C23—22no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C22×D4×C1311yescharacteristic
580Q8—41no—
581Q8—42no—
582Q8—41no—
583Q8—41no—
584Q8—81no—
585Q8—82no—
586D4—42no—
587D4—41no—
588D4—42no—
589D4—42no—
590D4—41no—
591D4—41no—
592D4—42no—
593D4—41no—
594D4—42no—
595D4—41no—
596D4—81no—
597D4—82no—
598D4—82no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4C13×#12011yescharacteristic
623C2×C4C13×#12011yescharacteristic
624C2×C4C13×#12011yescharacteristic
625C2×C4C13×#12011yescharacteristic
626C2×C4C22×D4×C1311yescharacteristic
627C2×C4C22×D4×C1311yescharacteristic
628C8—42no—
629C8—41no—
630C8—41no—
631C22—21no—
632C22—21no—
633C22—42no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—82no—
640C22—82no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22C2×C13×#12011yescharacteristic
645C22C13×#57611yescharacteristic
646C22C13×#57711yescharacteristic
647C4—21no—
648C4—21no—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—42no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—82no—
660C4—81no—
661C2—21no—
662C2—21no—
663C2—81no—
664C2—82no—
665C2—161no—
666C2C13×#301211yescharacteristic
667C2C13×#302011yescharacteristic
668C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3559C2semidirect
2. C13×#3213C2semidirect
3. C13×#3211C2semidirect
4. C13×#2820C2semidirect
5. C13×#1604C2semidirect
6. C13×#1603C2semidirect
7. C13×#1598C2semidirect
8. C13×#1597C2semidirect
9. C13×#1517C2semidirect
10. C13×#1512C2semidirect
11. C13×#1470C2semidirect
148. #18460C13direct (N × H)
238. #3559C2×C13semidirect
239. #3213C2×C13semidirect
240. #3211C2×C13semidirect
241. #2820C2×C13semidirect
242. #1604C2×C13semidirect
243. #1603C2×C13semidirect
244. #1598C2×C13semidirect
245. #1597C2×C13semidirect
246. #1517C2×C13semidirect
247. #1512C2×C13semidirect
248. #1470C2×C13semidirect
571. C13#18460direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#32132
C13×#32112
C13×#28202
C13×#16042
C13×#16032
C13×#15982
C13×#15972
C13×#15172
C13×#15122
C13×#14702
#1846013