Finite Group Databasebeta

← C13×#18400 #15704739

Subgroups — C13×#18400 #15704739

Order 3328.

978 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3493C211yesmaximal, characteristic, complemented
2C13×#3211C212yesmaximal, complemented
3C13×#2610C211yesmaximal, characteristic, complemented
4C13×#1606C212yesmaximal, complemented
5C13×#1605C211yesmaximal, characteristic, complemented
6C13×#1604C211yesmaximal, characteristic, complemented
7C13×#1600C212yesmaximal, complemented
8C13×#1599C211yesmaximal, characteristic, complemented
9C13×#1598C211yesmaximal, characteristic, complemented
10C13×#1500C212yesmaximal, complemented
11C13×#1458C211yesmaximal, characteristic, complemented
12C13×#556—22no—
13C13×#555—22no—
14C13×#553—22no—
15C13×#552—22no—
16C13×#544C2211yescharacteristic
17C13×#538—21no—
18C13×#538C2212yes—
19C13×#537C2211yescharacteristic
20C13×#529—21no—
21C13×#529C2212yes—
22C2×C13×#124C2211yescharacteristic
23C13×#525—21no—
24C13×#520—21no—
25C2×C13×#117C2211yescharacteristic
26C13×#495—22no—
27C13×#488—22no—
28C13×#464—22no—
29C13×#463—22no—
30C13×#451C2212yes—
31C13×#450C2212yes—
32C13×#448C2212yes—
33C13×#447C2212yes—
34C13×#431C2212yes—
35C13×#395C2211yescharacteristic
36C13×#394C2211yescharacteristic
37C13×#393C2211yescharacteristic
38C13×#392C2211yescharacteristic
39C13×#390—21no—
40C13×#388—21no—
41C13×#388—21no—
42C13×#386—21no—
43C13×#376C2211yescharacteristic
44C13×#328C2212yes—
45C13×#328C2212yes—
46C13×#327C2212yes—
47C13×#327C2212yes—
48C13×#324C2211yescharacteristic
49C13×#324C2211yescharacteristic
50C13×#323C2212yes—
51C2×C13×#41—21no—
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13—21no—
54C22×D4×C13C2311yescharacteristic
55C23×C4×C13D411yescharacteristic
56C2×C13×Q16—22no—
57C2×C13×SD16—22no—
58C2×C13×SD16—22no—
59C2×C13×D8—22no—
60C13×C4⋊Q8—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—22no—
65C13×#125—21no—
66C13×#125—22no—
67C13×#125D412yescomplemented
68C13×#124—21no—
69C13×#124—22no—
70C13×#124—22no—
71C13×#124—22no—
72C13×#124—22no—
73C13×#124D412yescomplemented
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×C22⋊Q8—21no—
78C13×C22⋊Q8—21no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8C2312yes—
82C13×#121—21no—
83C13×#121—21no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#121—22no—
87C13×#121—21no—
88C13×#121C2312yes—
89C13×#120—22no—
90C4×Q8×C13—22no—
91C4×Q8×C13—21no—
92C4×Q8×C13D412yescomplemented
93C4×D4×C13—22no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C4×D4×C13—21no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C4×D4×C13D412yescomplemented
100C13×#117—22no—
101C13×#117—22no—
102C13×#117—21no—
103C13×#117—22no—
104C13×#117—22no—
105C13×#117—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4D411yescharacteristic
117C2×C13×C22⋊C4C2311yescharacteristic
118C2×C42×C13—21no—
119C2×C42×C13D411yescharacteristic
120C2×C42×C13C2311yescharacteristic
121C13×C4⋊C8—22no—
122C13×#103—22no—
123C13×#103—22no—
124C13×#102—22no—
125C13×#102—22no—
126C13×C22⋊C8C2312yes—
127C13×C22⋊C8C2312yes—
128C4×C8×C13—22no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95C2311yescharacteristic
133C13×#95C2311yescharacteristic
134#18400C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13—21no—
136C24×C13C2×D411yescharacteristic
137C13×#41—42no—
138C13×#41—42no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—22no—
142C2×Q8×C13—81no—
143C2×Q8×C13C2×D412yes—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—22no—
150C2×D4×C13—42no—
151C2×D4×C13—42no—
152C2×D4×C13—81no—
153C2×D4×C13—81no—
154C2×D4×C13C2×D412yes—
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—41no—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2411yescharacteristic
171C13×Q16—82no—
172C13×SD16—82no—
173C13×SD16—82no—
174C13×D8—82no—
175C2×C8×C13—22no—
176C2×C8×C13—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—81no—
190C13×C4⋊C4C2×D412yes—
191C13×C4⋊C4C2×D412yes—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—42no—
204C13×C22⋊C4—41no—
205C13×C22⋊C4—41no—
206C13×C22⋊C4—42no—
207C13×C22⋊C4—42no—
208C13×C22⋊C4—81no—
209C13×C22⋊C4—81no—
210C42×C13—22no—
211C42×C13—22no—
212C42×C13—21no—
213C42×C13—21no—
214C42×C13—22no—
215C42×C13—42no—
216C42×C13C2×D412yes—
217C42×C13C2×D412yes—
218#3493C2×C1311yescharacteristic, complemented
219#3211C2×C1312yescomplemented
220#2610C2×C1311yescharacteristic, complemented
221#1606C2×C1312yescomplemented
222#1605C2×C1311yescharacteristic, complemented
223#1604C2×C1311yescharacteristic, complemented
224#1600C2×C1312yescomplemented
225#1599C2×C1311yescharacteristic, complemented
226#1598C2×C1311yescharacteristic, complemented
227#1500C2×C1312yescomplemented
228#1458C2×C1311yescharacteristic, complemented
229C23×C13—21no—
230C23×C13—22no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13C22×D411yescharacteristic
243Q8×C13—42no—
244Q8×C13—42no—
245Q8×C13—42no—
246Q8×C13—42no—
247Q8×C13—81no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—42no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—42no—
254D4×C13—82no—
255D4×C13—81no—
256D4×C13—82no—
257D4×C13—84no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—42no—
271C2×C4×C13—42no—
272C2×C4×C13—44no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—82no—
284C2×C4×C13—82no—
285C2×C4×C13#12011yescharacteristic
286C2×C4×C13#12011yescharacteristic
287C2×C4×C13#12012yes—
288C2×C4×C13#13512yes—
289C2×C4×C13C22×D412yes—
290C8×C13—42no—
291C8×C13—42no—
292#556—22no—
293#555—22no—
294#553—22no—
295#552—22no—
296#544C22×C1311yescharacteristic
297#538—21no—
298#538C22×C1312yes—
299#537C22×C1311yescharacteristic
300#529—21no—
301#529C22×C1312yes—
302C2×#124C22×C1311yescharacteristic
303#525—21no—
304#520—21no—
305C2×#117C22×C1311yescharacteristic
306#495—22no—
307#488—22no—
308#464—22no—
309#463—22no—
310#451C22×C1312yes—
311#450C22×C1312yes—
312#448C22×C1312yes—
313#447C22×C1312yes—
314#431C22×C1312yes—
315#395C22×C1311yescharacteristic
316#394C22×C1311yescharacteristic
317#393C22×C1311yescharacteristic
318#392C22×C1311yescharacteristic
319#390—21no—
320#388—21no—
321#388—21no—
322#386—21no—
323#376C22×C1311yescharacteristic
324#328C22×C1312yes—
325#328C22×C1312yes—
326#327C22×C1312yes—
327#327C22×C1312yes—
328#324C22×C1311yescharacteristic
329#324C22×C1311yescharacteristic
330#323C22×C1312yes—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—42no—
334C22×C13—41no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13—41no—
338C22×C13—42no—
339C22×C13—41no—
340C22×C13—81no—
341C22×C13—81no—
342C22×C13—81no—
343C22×C13—81no—
344C22×C13—81no—
345C22×C13—81no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13C2×#12011yescharacteristic
349C22×C13C2×#13511yescharacteristic
350C22×C13#57511yescharacteristic
351C4×C13—22no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—22no—
355C4×C13—22no—
356C4×C13—42no—
357C4×C13—42no—
358C4×C13—41no—
359C4×C13—42no—
360C4×C13—41no—
361C4×C13—42no—
362C4×C13—81no—
363C4×C13—81no—
364C2×#41—21no—
365C22×Q8C23×C1311yescharacteristic
366C22×D4—21no—
367C22×D4C23×C1311yescharacteristic
368C23×C4D4×C1311yescharacteristic
369C2×Q16—22no—
370C2×SD16—22no—
371C2×SD16—22no—
372C2×D8—22no—
373C4⋊Q8—22no—
374#126—22no—
375#126—22no—
376#126—22no—
377#126—22no—
378#125—21no—
379#125—22no—
380#125D4×C1312yescomplemented
381#124—21no—
382#124—22no—
383#124—22no—
384#124—22no—
385#124—22no—
386#124D4×C1312yescomplemented
387#123—22no—
388#123—22no—
389#123—22no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—22no—
394C22⋊Q8C23×C1312yes—
395#121—21no—
396#121—21no—
397#121—22no—
398#121—22no—
399#121—22no—
400#121—21no—
401#121C23×C1312yes—
402#120—22no—
403C4×Q8—22no—
404C4×Q8—21no—
405C4×Q8D4×C1312yescomplemented
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4D4×C1312yescomplemented
413#117—22no—
414#117—22no—
415#117—21no—
416#117—22no—
417#117—22no—
418#117—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4D4×C1311yescharacteristic
422C2×C4⋊C4C23×C1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4D4×C1311yescharacteristic
430C2×C22⋊C4C23×C1311yescharacteristic
431C2×C42—21no—
432C2×C42D4×C1311yescharacteristic
433C2×C42C23×C1311yescharacteristic
434C4⋊C8—22no—
435#103—22no—
436#103—22no—
437#102—22no—
438#102—22no—
439C22⋊C8C23×C1312yes—
440C22⋊C8C23×C1312yes—
441C4×C8—22no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95C23×C1311yescharacteristic
446#95C23×C1311yescharacteristic
447C2×C13—21no—
448C2×C13—21no—
449C2×C13—82no—
450C2×C13—81no—
451C2×C13—161no—
452C2×C13#300211yescharacteristic
453C2×C13#301811yescharacteristic
454C2×C13#302711yescharacteristic
455C24—21no—
456C24C2×D4×C1311yescharacteristic
457#41—42no—
458#41—42no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—81no—
463C2×Q8C2×D4×C1312yes—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—81no—
473C2×D4—81no—
474C2×D4C2×D4×C1312yes—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4C2×D4×C1311yescharacteristic
486C22×C4C2×D4×C1311yescharacteristic
487C22×C4C2×D4×C1311yescharacteristic
488C22×C4C2×D4×C1311yescharacteristic
489C22×C4C2×D4×C1311yescharacteristic
490C22×C4C24×C1311yescharacteristic
491Q16—82no—
492SD16—82no—
493SD16—82no—
494D8—82no—
495C2×C8—22no—
496C2×C8—22no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—81no—
510C4⋊C4C2×D4×C1312yes—
511C4⋊C4C2×D4×C1312yes—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—42no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—81no—
529C22⋊C4—81no—
530C42—22no—
531C42—22no—
532C42—21no—
533C42—21no—
534C42—22no—
535C42—42no—
536C42C2×D4×C1312yes—
537C42C2×D4×C1312yes—
538C13#1840011yescharacteristic, direct product factor, Sylow
539C23—21no—
540C23—22no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C22×D4×C1311yescharacteristic
553Q8—42no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—81no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—82no—
565D4—81no—
566D4—82no—
567D4—84no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—44no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4C13×#12012yes—
596C2×C4C13×#12011yescharacteristic
597C2×C4C13×#12011yescharacteristic
598C2×C4C13×#13512yes—
599C2×C4C22×D4×C1312yes—
600C8—42no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—42no—
605C22—42no—
606C22—41no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C2×C13×#12011yescharacteristic
620C22C2×C13×#13511yescharacteristic
621C22C13×#57511yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—21no—
626C4—21no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—42no—
632C4—42no—
633C4—81no—
634C4—81no—
635C2—21no—
636C2—21no—
637C2—81no—
638C2—82no—
639C2—161no—
640C2C13×#300211yescharacteristic
641C2C13×#301811yescharacteristic
642C2C13×#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×#3493C2semidirect
2. C13×#3211C2semidirect
3. C13×#2610C2semidirect
4. C13×#1606C2semidirect
5. C13×#1605C2semidirect
6. C13×#1604C2semidirect
7. C13×#1600C2semidirect
8. C13×#1599C2semidirect
9. C13×#1598C2semidirect
10. C13×#1500C2semidirect
11. C13×#1458C2semidirect
67. C13×#125D4semidirect
73. C13×#124D4semidirect
92. C4×Q8×C13D4semidirect
99. C4×D4×C13D4semidirect
134. #18400C13direct (N × H)
218. #3493C2×C13semidirect
219. #3211C2×C13semidirect
220. #2610C2×C13semidirect
221. #1606C2×C13semidirect
222. #1605C2×C13semidirect
223. #1604C2×C13semidirect
224. #1600C2×C13semidirect
225. #1599C2×C13semidirect
226. #1598C2×C13semidirect
227. #1500C2×C13semidirect
228. #1458C2×C13semidirect
380. #125D4×C13semidirect
386. #124D4×C13semidirect
405. C4×Q8D4×C13semidirect
412. C4×D4D4×C13semidirect
538. C13#18400direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34932
C13×#32112
C13×#26102
C13×#16062
C13×#16052
C13×#16042
C13×#16002
C13×#15992
C13×#15982
C13×#15002
C13×#14582
#1840013