Finite Group Databasebeta

← C13×#18426 #15704765

Subgroups — C13×#18426 #15704765

Order 3328.

1168 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3558C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic, complemented
3C13×#3205C211yesmaximal, characteristic, complemented
4C13×#2657C211yesmaximal, characteristic, complemented
5C13×#1600C214yesmaximal, complemented
6C13×#1595C214yesmaximal, complemented
7C13×#1505C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1469C211yesmaximal, characteristic, complemented
10C13×#562—21no—
11C13×H(3,𝔽4)—21no—
12C13×#559—21no—
13C13×#548—21no—
14C13×#546—21no—
15C13×#546—22no—
16D42×C13—21no—
17C13×#542—21no—
18C13×#538—22no—
19C13×#538C2212yes—
20C13×#535—21no—
21C13×#534C2212yes—
22C13×#532C2211yescharacteristic
23C2×C13×#127—21no—
24C2×C13×#127C2211yescharacteristic, complemented
25C13×#529C2211yescharacteristic
26C2×C13×#124—21no—
27C2×C13×#124C2211yescharacteristic
28C13×#496—21no—
29C13×#493—21no—
30C13×#490—21no—
31C13×#486—21no—
32C13×#460—21no—
33C13×#459—22no—
34C13×#459—21no—
35C13×#450C2212yescomplemented
36C13×#447C2212yes—
37C13×#447C2214yescomplemented
38C13×#432C2211yescharacteristic, complemented
39C13×#431C2211yescharacteristic, complemented
40C13×#392—22no—
41C13×#392C2214yescomplemented
42C13×#376C2211yescharacteristic, complemented
43C13×#328C2212yescomplemented
44C13×#327C2212yes—
45C13×#327C2214yescomplemented
46C13×#323C2214yescomplemented
47C2×C13×#41—21no—
48C2×C13×#41—21no—
49C22×Q8×C13D411yescharacteristic
50C22×D4×C13—21no—
51C22×D4×C13—22no—
52C22×D4×C13—24no—
53C22×D4×C13—21no—
54C22×D4×C13—21no—
55C22×D4×C13D411yescharacteristic
56C22×D4×C13C2312yes—
57C2×C13×SD16—22no—
58C2×C13×D8—22no—
59C2×C13×D8—24no—
60C13×C4⋊Q8D411yescharacteristic, complemented
61C13×#127—21no—
62C13×#127—21no—
63C13×#127—21no—
64C13×#127—21no—
65C13×#127—21no—
66C13×#127—44no—
67C13×#127D411yescharacteristic, complemented
68C13×#126—22no—
69C13×#126—21no—
70C13×#125D411yescharacteristic, complemented
71C13×#124—21no—
72C13×#124—22no—
73C13×#124—22no—
74C13×#124—22no—
75C13×#124—21no—
76C13×#124—21no—
77C13×#124—21no—
78C13×#124—21no—
79C13×#124—21no—
80C13×#124—44no—
81C13×#124D411yescharacteristic, complemented
82C13×#123—22no—
83C13×#123—21no—
84C13×#123—22no—
85C13×#123—22no—
86C13×#123—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8C2311yescharacteristic
91C13×#121—22no—
92C13×#121—22no—
93C13×#121—22no—
94C13×#121—21no—
95C13×#121—22no—
96C13×#121—21no—
97C13×#121—22no—
98C13×#121C2311yescharacteristic
99C13×#121C2312yes—
100C13×#120—22no—
101C13×#120—22no—
102C13×#120—22no—
103C13×#120—22no—
104C13×#120—22no—
105C4×Q8×C13—21no—
106C4×Q8×C13D411yescharacteristic, complemented
107C4×D4×C13—22no—
108C4×D4×C13—21no—
109C4×D4×C13—21no—
110C4×D4×C13—22no—
111C4×D4×C13—21no—
112C4×D4×C13D411yescharacteristic, complemented
113C4×D4×C13D412yescomplemented
114C13×#117—21no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4D412yes—
118C2×C13×C22⋊C4C2312yes—
119C2×C42×C13—21no—
120C2×C42×C13C2311yescharacteristic
121C13×C4⋊C8—21no—
122C13×C4⋊C8—21no—
123C13×#102—22no—
124C13×#102—24no—
125C13×#102—22no—
126C13×C22⋊C8C2312yes—
127C13×C22⋊C8C2312yes—
128C13×#97—21no—
129C4×C8×C13—21no—
130C13×#95—21no—
131C13×#95C2312yes—
132#18426C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—22no—
134C24×C13—22no—
135C24×C13C2×D412yes—
136C13×#41—82no—
137C13×#41—82no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—42no—
142C2×Q8×C13C2×D411yescharacteristic
143C2×D4×C13—22no—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—22no—
155C2×D4×C13—22no—
156C2×D4×C13—42no—
157C2×D4×C13—42no—
158C2×D4×C13—42no—
159C2×D4×C13—48no—
160C2×D4×C13—41no—
161C2×D4×C13—41no—
162C2×D4×C13—41no—
163C2×D4×C13—41no—
164C2×D4×C13—82no—
165C2×D4×C13—82no—
166C2×D4×C13—82no—
167C2×D4×C13—84no—
168C2×D4×C13—84no—
169C2×D4×C13—84no—
170C2×D4×C13C2×D411yescharacteristic
171C2×D4×C13C2×D412yes—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—21no—
176C22×C4×C13—22no—
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2411yescharacteristic
181C13×SD16—82no—
182C13×D8—84no—
183C13×D8—82no—
184C2×C8×C13—22no—
185C2×C8×C13—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4C2×D412yes—
194C13×C4⋊C4C2×D411yescharacteristic
195C13×C4⋊C4C2×D411yescharacteristic
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—21no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—21no—
206C13×C22⋊C4—21no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—21no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—48no—
213C42×C13—24no—
214C42×C13—22no—
215C42×C13—21no—
216C42×C13C2×D411yescharacteristic
217C42×C13C2×D411yescharacteristic
218C42×C13C2×D411yescharacteristic
219C42×C13C2×D411yescharacteristic
220#3558C2×C1311yescharacteristic, complemented
221#3217C2×C1311yescharacteristic, complemented
222#3205C2×C1311yescharacteristic, complemented
223#2657C2×C1311yescharacteristic, complemented
224#1600C2×C1314yescomplemented
225#1595C2×C1314yescomplemented
226#1505C2×C1311yescharacteristic, complemented
227#1500C2×C1311yescharacteristic, complemented
228#1469C2×C1311yescharacteristic, complemented
229C23×C13—22no—
230C23×C13—21no—
231C23×C13—22no—
232C23×C13—24no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—42no—
236C23×C13—42no—
237C23×C13—44no—
238C23×C13—42no—
239C23×C13—44no—
240C23×C13—82no—
241C23×C13—82no—
242C23×C13—82no—
243C23×C13C22×D411yescharacteristic
244Q8×C13—41no—
245Q8×C13—42no—
246Q8×C13—81no—
247Q8×C13—81no—
248D4×C13—42no—
249D4×C13—41no—
250D4×C13—44no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—42no—
254D4×C13—44no—
255D4×C13—42no—
256D4×C13—42no—
257D4×C13—81no—
258D4×C13—81no—
259D4×C13—82no—
260D4×C13—82no—
261D4×C13—82no—
262D4×C13—82no—
263D4×C13—82no—
264D4×C13—82no—
265D4×C13—82no—
266D4×C13—82no—
267D4×C13—816no—
268D4×C13—82no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—24no—
272C2×C4×C13—21no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—41no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—82no—
283C2×C4×C13—82no—
284C2×C4×C13—82no—
285C2×C4×C13#12011yescharacteristic
286C2×C4×C13#12011yescharacteristic
287C2×C4×C13#12011yescharacteristic
288C2×C4×C13#12011yescharacteristic
289C2×C4×C13C22×D411yescharacteristic
290C2×C4×C13C22×D411yescharacteristic
291C8×C13—42no—
292C8×C13—42no—
293#562—21no—
294H(3,𝔽4)—21no—
295#559—21no—
296#548—21no—
297#546—21no—
298#546—22no—
299D42—21no—
300#542—21no—
301#538—22no—
302#538C22×C1312yes—
303#535—21no—
304#534C22×C1312yes—
305#532C22×C1311yescharacteristic
306C2×#127—21no—
307C2×#127C22×C1311yescharacteristic, complemented
308#529C22×C1311yescharacteristic
309C2×#124—21no—
310C2×#124C22×C1311yescharacteristic
311#496—21no—
312#493—21no—
313#490—21no—
314#486—21no—
315#460—21no—
316#459—22no—
317#459—21no—
318#450C22×C1312yescomplemented
319#447C22×C1312yes—
320#447C22×C1314yescomplemented
321#432C22×C1311yescharacteristic, complemented
322#431C22×C1311yescharacteristic, complemented
323#392—22no—
324#392C22×C1314yescomplemented
325#376C22×C1311yescharacteristic, complemented
326#328C22×C1312yescomplemented
327#327C22×C1312yes—
328#327C22×C1314yescomplemented
329#323C22×C1314yescomplemented
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—42no—
337C22×C13—42no—
338C22×C13—42no—
339C22×C13—41no—
340C22×C13—42no—
341C22×C13—84no—
342C22×C13—84no—
343C22×C13—84no—
344C22×C13—82no—
345C22×C13—82no—
346C22×C13—82no—
347C22×C13—164no—
348C22×C13C2×#12011yescharacteristic
349C22×C13#57612yes—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—44no—
356C4×C13—41no—
357C4×C13—42no—
358C4×C13—41no—
359C4×C13—42no—
360C4×C13—41no—
361C4×C13#45312yes—
362C2×#41—21no—
363C2×#41—21no—
364C22×Q8D4×C1311yescharacteristic
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—24no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4D4×C1311yescharacteristic
371C22×D4C23×C1312yes—
372C2×SD16—22no—
373C2×D8—22no—
374C2×D8—24no—
375C4⋊Q8D4×C1311yescharacteristic, complemented
376#127—21no—
377#127—21no—
378#127—21no—
379#127—21no—
380#127—21no—
381#127—44no—
382#127D4×C1311yescharacteristic, complemented
383#126—22no—
384#126—21no—
385#125D4×C1311yescharacteristic, complemented
386#124—21no—
387#124—22no—
388#124—22no—
389#124—22no—
390#124—21no—
391#124—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#124—44no—
396#124D4×C1311yescharacteristic, complemented
397#123—22no—
398#123—21no—
399#123—22no—
400#123—22no—
401#123—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8C23×C1311yescharacteristic
406#121—22no—
407#121—22no—
408#121—22no—
409#121—21no—
410#121—22no—
411#121—21no—
412#121—22no—
413#121C23×C1311yescharacteristic
414#121C23×C1312yes—
415#120—22no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420C4×Q8—21no—
421C4×Q8D4×C1311yescharacteristic, complemented
422C4×D4—22no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—22no—
426C4×D4—21no—
427C4×D4D4×C1311yescharacteristic, complemented
428C4×D4D4×C1312yescomplemented
429#117—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4D4×C1312yes—
433C2×C22⋊C4C23×C1312yes—
434C2×C42—21no—
435C2×C42C23×C1311yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—21no—
438#102—22no—
439#102—24no—
440#102—22no—
441C22⋊C8C23×C1312yes—
442C22⋊C8C23×C1312yes—
443#97—21no—
444C4×C8—21no—
445#95—21no—
446#95C23×C1312yes—
447C2×C13—22no—
448C2×C13—82no—
449C2×C13—82no—
450C2×C13—81no—
451C2×C13—162no—
452C2×C13#300811yescharacteristic
453C2×C13C2×#45311yescharacteristic
454C2×C13#302711yescharacteristic
455C24—22no—
456C24—22no—
457C24C2×D4×C1312yes—
458#41—82no—
459#41—82no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—42no—
464C2×Q8C2×D4×C1311yescharacteristic
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—48no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—82no—
487C2×D4—82no—
488C2×D4—82no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—84no—
492C2×D4C2×D4×C1311yescharacteristic
493C2×D4C2×D4×C1312yes—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4C2×D4×C1311yescharacteristic
500C22×C4C2×D4×C1311yescharacteristic
501C22×C4C2×D4×C1312yes—
502C22×C4C24×C1311yescharacteristic
503SD16—82no—
504D8—84no—
505D8—82no—
506C2×C8—22no—
507C2×C8—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4C2×D4×C1312yes—
516C4⋊C4C2×D4×C1311yescharacteristic
517C4⋊C4C2×D4×C1311yescharacteristic
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—48no—
535C42—24no—
536C42—22no—
537C42—21no—
538C42C2×D4×C1311yescharacteristic
539C42C2×D4×C1311yescharacteristic
540C42C2×D4×C1311yescharacteristic
541C42C2×D4×C1311yescharacteristic
542C13#1842611yescharacteristic, direct product factor, Sylow
543C23—22no—
544C23—21no—
545C23—22no—
546C23—24no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—44no—
552C23—42no—
553C23—44no—
554C23—82no—
555C23—82no—
556C23—82no—
557C23C22×D4×C1311yescharacteristic
558Q8—41no—
559Q8—42no—
560Q8—81no—
561Q8—81no—
562D4—42no—
563D4—41no—
564D4—44no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—44no—
569D4—42no—
570D4—42no—
571D4—81no—
572D4—81no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579D4—82no—
580D4—82no—
581D4—816no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4C13×#12011yescharacteristic
600C2×C4C13×#12011yescharacteristic
601C2×C4C13×#12011yescharacteristic
602C2×C4C13×#12011yescharacteristic
603C2×C4C22×D4×C1311yescharacteristic
604C2×C4C22×D4×C1311yescharacteristic
605C8—42no—
606C8—42no—
607C22—21no—
608C22—21no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—42no—
618C22—84no—
619C22—84no—
620C22—84no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—164no—
625C22C2×C13×#12011yescharacteristic
626C22C13×#57612yes—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—41no—
638C4C13×#45312yes—
639C2—22no—
640C2—82no—
641C2—81no—
642C2—82no—
643C2—162no—
644C2C13×#300811yescharacteristic
645C2C2×C13×#45311yescharacteristic
646C2C13×#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×#3558C2semidirect
2. C13×#3217C2semidirect
3. C13×#3205C2semidirect
4. C13×#2657C2semidirect
5. C13×#1600C2semidirect
6. C13×#1595C2semidirect
7. C13×#1505C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
24. C2×C13×#127C22semidirect
35. C13×#450C22semidirect
37. C13×#447C22semidirect
38. C13×#432C22semidirect
39. C13×#431C22semidirect
41. C13×#392C22semidirect
42. C13×#376C22semidirect
43. C13×#328C22semidirect
45. C13×#327C22semidirect
46. C13×#323C22semidirect
60. C13×C4⋊Q8D4semidirect
67. C13×#127D4semidirect
70. C13×#125D4semidirect
81. C13×#124D4semidirect
106. C4×Q8×C13D4semidirect
112. C4×D4×C13D4semidirect
113. C4×D4×C13D4semidirect
132. #18426C13direct (N × H)
220. #3558C2×C13semidirect
221. #3217C2×C13semidirect
222. #3205C2×C13semidirect
223. #2657C2×C13semidirect
224. #1600C2×C13semidirect
225. #1595C2×C13semidirect
226. #1505C2×C13semidirect
227. #1500C2×C13semidirect
228. #1469C2×C13semidirect
307. C2×#127C22×C13semidirect
318. #450C22×C13semidirect
320. #447C22×C13semidirect
321. #432C22×C13semidirect
322. #431C22×C13semidirect
324. #392C22×C13semidirect
325. #376C22×C13semidirect
326. #328C22×C13semidirect
328. #327C22×C13semidirect
329. #323C22×C13semidirect
375. C4⋊Q8D4×C13semidirect
382. #127D4×C13semidirect
385. #125D4×C13semidirect
396. #124D4×C13semidirect
421. C4×Q8D4×C13semidirect
427. C4×D4D4×C13semidirect
428. C4×D4D4×C13semidirect
542. C13#18426direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35582
C13×#32172
C13×#32052
C13×#26572
C13×#16002
C13×#15952
C13×#15052
C13×#15002
C13×#14692
#1842613