Finite Group Databasebeta

← C13×#18461 #15704800

Subgroups — C13×#18461 #15704800

Order 3328.

880 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic, complemented
2C13×#3215C211yesmaximal, characteristic, complemented
3C13×#3211C211yesmaximal, characteristic
4C13×#2820C211yesmaximal, characteristic, complemented
5C13×#1605C212yesmaximal, complemented
6C13×#1603C212yesmaximal, complemented
7C13×#1599C212yesmaximal, complemented
8C13×#1597C212yesmaximal
9C13×#1518C211yesmaximal, characteristic, complemented
10C13×#1512C211yesmaximal, characteristic, complemented
11C13×#1470C211yesmaximal, characteristic, complemented
12C13×#564—21no—
13C13×#563—21no—
14C13×#557—21no—
15C13×#554—21no—
16C13×#552—21no—
17C13×#552—22no—
18C13×#552—21no—
19C13×#544—21no—
20C13×#544C2212yes—
21C13×#541—21no—
22C13×#541—22no—
23C13×#539C2212yes—
24C13×#533C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C13×#497—21no—
29C13×#495—21no—
30C13×#489—21no—
31C13×#488—21no—
32C13×#464—21no—
33C13×#464—22no—
34C13×#463—21no—
35C13×#451C2212yes—
36C13×#451C2211yescharacteristic
37C13×#450C2212yes—
38C13×#450C2211yescharacteristic
39C13×#448C2211yescharacteristic
40C13×#447C2211yescharacteristic
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#399—21no—
44C13×#397—21no—
45C13×#396—22no—
46C13×#395C2212yes—
47C13×#394C2212yes—
48C13×#382C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C22×Q8×C13C2311yescharacteristic
56C22×D4×C13C2311yescharacteristic
57C2×C13×Q16—21no—
58C2×C13×Q16—22no—
59C2×C13×SD16—21no—
60C2×C13×SD16—22no—
61C2×C13×SD16—21no—
62C2×C13×D8—21no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8D411yescharacteristic
67C13×C4⋊Q8D411yescharacteristic
68C13×#126—22no—
69C13×#126—22no—
70C13×#126—22no—
71C13×#126—22no—
72C13×#126—21no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#125—22no—
76C13×#125—22no—
77C13×#125—21no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#125—22no—
81C13×#125—22no—
82C13×#125—21no—
83C13×#125—21no—
84C13×#125—21no—
85C13×#125—21no—
86C13×#125—21no—
87C13×#125D411yescharacteristic
88C13×#124—21no—
89C13×#124—21no—
90C13×#124—21no—
91C13×#124—21no—
92C13×#124D411yescharacteristic
93C13×#123—22no—
94C13×#123—21no—
95C13×#123—22no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—21no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8—22no—
100C13×C22⋊Q8—22no—
101C13×C22⋊Q8—21no—
102C13×C22⋊Q8—22no—
103C13×C22⋊Q8C2311yescharacteristic
104C13×C22⋊Q8C2312yes—
105C13×#121C2311yescharacteristic
106C4×Q8×C13—21no—
107C4×Q8×C13—22no—
108C4×Q8×C13—21no—
109C4×Q8×C13—21no—
110C4×Q8×C13D411yescharacteristic
111C4×Q8×C13D412yes—
112C4×D4×C13—21no—
113C4×D4×C13—22no—
114C4×D4×C13D411yescharacteristic
115C13×#117—22no—
116C13×#117—21no—
117C13×#117—21no—
118C13×#117—22no—
119C13×#117—21no—
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—21no—
135C13×#103—21no—
136C13×#103—22no—
137C13×#102—21no—
138C13×#102—21no—
139C13×#102—22no—
140C13×C22⋊C8C2312yes—
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2311yescharacteristic
143C13×#97—21no—
144C4×C8×C13—21no—
145C13×#95—21no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18461C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13—21no—
150C2×Q8×C13—22no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—81no—
155C2×Q8×C13C2×D412yes—
156C2×Q8×C13C2×D411yescharacteristic
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—81no—
161C2×D4×C13C2×D411yescharacteristic
162C22×C4×C13—22no—
163C22×C4×C13—21no—
164C22×C4×C13—22no—
165C22×C4×C13—21no—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2411yescharacteristic
171C13×Q16—81no—
172C13×Q16—82no—
173C13×SD16—81no—
174C13×SD16—81no—
175C13×SD16—82no—
176C13×D8—81no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—81no—
206C13×C4⋊C4—82no—
207C13×C4⋊C4C2×D411yescharacteristic
208C13×C4⋊C4C2×D411yescharacteristic
209C13×C4⋊C4C2×D412yes—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—21no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—41no—
220C13×C22⋊C4—41no—
221C13×C22⋊C4—41no—
222C13×C22⋊C4—41no—
223C13×C22⋊C4—82no—
224C13×C22⋊C4—82no—
225C42×C13—22no—
226C42×C13—22no—
227C42×C13—22no—
228C42×C13—22no—
229C42×C13—21no—
230C42×C13C2×D411yescharacteristic
231C42×C13C2×D411yescharacteristic
232C42×C13C2×D411yescharacteristic
233C42×C13C2×D411yescharacteristic
234#3563C2×C1311yescharacteristic, complemented
235#3215C2×C1311yescharacteristic, complemented
236#3211C2×C1311yescharacteristic
237#2820C2×C1311yescharacteristic, complemented
238#1605C2×C1312yescomplemented
239#1603C2×C1312yescomplemented
240#1599C2×C1312yescomplemented
241#1597C2×C1312yes—
242#1518C2×C1311yescharacteristic, complemented
243#1512C2×C1311yescharacteristic, complemented
244#1470C2×C1311yescharacteristic, complemented
245C23×C13—21no—
246C23×C13—42no—
247C23×C13—42no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13C22×D411yescharacteristic
252Q8×C13—42no—
253Q8×C13—41no—
254Q8×C13—42no—
255Q8×C13—41no—
256Q8×C13—41no—
257Q8×C13—42no—
258Q8×C13—82no—
259D4×C13—41no—
260D4×C13—41no—
261D4×C13—41no—
262D4×C13—42no—
263D4×C13—41no—
264D4×C13—41no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—22no—
271C2×C4×C13—21no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—41no—
284C2×C4×C13—42no—
285C2×C4×C13—82no—
286C2×C4×C13#12011yescharacteristic
287C2×C4×C13#12011yescharacteristic
288C2×C4×C13#12011yescharacteristic
289C2×C4×C13#12011yescharacteristic
290C2×C4×C13C22×D411yescharacteristic
291C2×C4×C13C22×D411yescharacteristic
292C8×C13—41no—
293C8×C13—41no—
294C8×C13—42no—
295#564—21no—
296#563—21no—
297#557—21no—
298#554—21no—
299#552—21no—
300#552—22no—
301#552—21no—
302#544—21no—
303#544C22×C1312yes—
304#541—21no—
305#541—22no—
306#539C22×C1312yes—
307#533C22×C1311yescharacteristic
308#529C22×C1311yescharacteristic
309C2×#125C22×C1311yescharacteristic
310C2×#124C22×C1311yescharacteristic
311#497—21no—
312#495—21no—
313#489—21no—
314#488—21no—
315#464—21no—
316#464—22no—
317#463—21no—
318#451C22×C1312yes—
319#451C22×C1311yescharacteristic
320#450C22×C1312yes—
321#450C22×C1311yescharacteristic
322#448C22×C1311yescharacteristic
323#447C22×C1311yescharacteristic
324#432C22×C1311yescharacteristic
325#431C22×C1311yescharacteristic
326#399—21no—
327#397—21no—
328#396—22no—
329#395C22×C1312yes—
330#394C22×C1312yes—
331#382C22×C1311yescharacteristic
332#328C22×C1312yes—
333#328C22×C1312yes—
334#328C22×C1312yes—
335#327C22×C1312yes—
336#324C22×C1312yes—
337#324C22×C1312yes—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—82no—
344C22×C13—82no—
345C22×C13—81no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13C2×#12011yescharacteristic
349C22×C13#57711yescharacteristic
350C22×C13#57811yescharacteristic
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—42no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—42no—
361C4×C13—42no—
362C4×C13—42no—
363C4×C13—41no—
364C4×C13—82no—
365C4×C13—81no—
366C22×Q8C23×C1311yescharacteristic
367C22×D4C23×C1311yescharacteristic
368C2×Q16—21no—
369C2×Q16—22no—
370C2×SD16—21no—
371C2×SD16—22no—
372C2×SD16—21no—
373C2×D8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8D4×C1311yescharacteristic
378C4⋊Q8D4×C1311yescharacteristic
379#126—22no—
380#126—22no—
381#126—22no—
382#126—22no—
383#126—21no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—21no—
389#125—22no—
390#125—22no—
391#125—22no—
392#125—22no—
393#125—21no—
394#125—21no—
395#125—21no—
396#125—21no—
397#125—21no—
398#125D4×C1311yescharacteristic
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#124D4×C1311yescharacteristic
404#123—22no—
405#123—21no—
406#123—22no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8C23×C1311yescharacteristic
415C22⋊Q8C23×C1312yes—
416#121C23×C1311yescharacteristic
417C4×Q8—21no—
418C4×Q8—22no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8D4×C1311yescharacteristic
422C4×Q8D4×C1312yes—
423C4×D4—21no—
424C4×D4—22no—
425C4×D4D4×C1311yescharacteristic
426#117—22no—
427#117—21no—
428#117—21no—
429#117—22no—
430#117—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4D4×C1312yes—
435C2×C4⋊C4D4×C1311yescharacteristic
436C2×C4⋊C4D4×C1311yescharacteristic
437C2×C4⋊C4C23×C1312yes—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C42C23×C1311yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445#103—21no—
446#103—21no—
447#103—22no—
448#102—21no—
449#102—21no—
450#102—22no—
451C22⋊C8C23×C1312yes—
452C22⋊C8C23×C1311yescharacteristic
453C22⋊C8C23×C1311yescharacteristic
454#97—21no—
455C4×C8—21no—
456#95—21no—
457#95—22no—
458#95C23×C1312yes—
459C2×C13—21no—
460C2×C13—21no—
461C2×C13—81no—
462C2×C13—161no—
463C2×C13#301311yescharacteristic
464C2×C13#302011yescharacteristic
465C2×C13#302711yescharacteristic
466C24—21no—
467C2×Q8—22no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—81no—
472C2×Q8C2×D4×C1312yes—
473C2×Q8C2×D4×C1311yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—81no—
478C2×D4C2×D4×C1311yescharacteristic
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4C2×D4×C1312yes—
484C22×C4C2×D4×C1311yescharacteristic
485C22×C4C2×D4×C1312yes—
486C22×C4C2×D4×C1311yescharacteristic
487C22×C4C24×C1311yescharacteristic
488Q16—81no—
489Q16—82no—
490SD16—81no—
491SD16—81no—
492SD16—82no—
493D8—81no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—81no—
523C4⋊C4—82no—
524C4⋊C4C2×D4×C1311yescharacteristic
525C4⋊C4C2×D4×C1311yescharacteristic
526C4⋊C4C2×D4×C1312yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—82no—
541C22⋊C4—82no—
542C42—22no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—21no—
547C42C2×D4×C1311yescharacteristic
548C42C2×D4×C1311yescharacteristic
549C42C2×D4×C1311yescharacteristic
550C42C2×D4×C1311yescharacteristic
551C13#1846111yescharacteristic, direct product factor, Sylow
552C23—21no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23C22×D4×C1311yescharacteristic
559Q8—41no—
560Q8—42no—
561Q8—42no—
562Q8—41no—
563Q8—41no—
564Q8—42no—
565Q8—82no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—42no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—82no—
593C2×C4C13×#12011yescharacteristic
594C2×C4C13×#12011yescharacteristic
595C2×C4C13×#12011yescharacteristic
596C2×C4C13×#12011yescharacteristic
597C2×C4C22×D4×C1311yescharacteristic
598C2×C4C22×D4×C1311yescharacteristic
599C8—41no—
600C8—41no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—82no—
608C22—82no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22C2×C13×#12011yescharacteristic
613C22C13×#57711yescharacteristic
614C22C13×#57811yescharacteristic
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—41no—
628C4—82no—
629C4—81no—
630C2—21no—
631C2—21no—
632C2—81no—
633C2—161no—
634C2C13×#301311yescharacteristic
635C2C13×#302011yescharacteristic
636C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#447C22
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×#3563C2semidirect
2. C13×#3215C2semidirect
4. C13×#2820C2semidirect
5. C13×#1605C2semidirect
6. C13×#1603C2semidirect
7. C13×#1599C2semidirect
9. C13×#1518C2semidirect
10. C13×#1512C2semidirect
11. C13×#1470C2semidirect
148. #18461C13direct (N × H)
234. #3563C2×C13semidirect
235. #3215C2×C13semidirect
237. #2820C2×C13semidirect
238. #1605C2×C13semidirect
239. #1603C2×C13semidirect
240. #1599C2×C13semidirect
242. #1518C2×C13semidirect
243. #1512C2×C13semidirect
244. #1470C2×C13semidirect
551. C13#18461direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#32152
C13×#32112
C13×#28202
C13×#16052
C13×#16032
C13×#15992
C13×#15972
C13×#15182
C13×#15122
C13×#14702
#1846113