Finite Group Databasebeta

← C13×#18276 #15704615

Subgroups — C13×#18276 #15704615

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic, complemented
2C13×#3109C211yesmaximal, characteristic, complemented
3C13×#3105C211yesmaximal, characteristic, complemented
4C13×#2562C211yesmaximal, characteristic, complemented
5C13×#1616C212yesmaximal, complemented
6C13×#1615C212yesmaximal, complemented
7C13×#1598C212yesmaximal, complemented
8C13×#1597C212yesmaximal, complemented
9C13×#1509C211yesmaximal, characteristic, complemented
10C13×#1502C211yesmaximal, 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×C4×D4×C13C2211yescharacteristic
28C13×#484C2211yescharacteristic
29C13×#481C2211yescharacteristic
30C13×#481C2212yes—
31C13×#478—21no—
32C13×#476—21no—
33C13×#463—21no—
34C13×#459—21no—
35C13×#450C2211yescharacteristic
36C13×#447C2211yescharacteristic
37C13×#447C2212yes—
38C13×#442—22no—
39C4×C13×SD16—21no—
40C4×C13×D8—21no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#400C2212yes—
44C13×#394C2212yes—
45C13×#388—22no—
46C13×#380—21no—
47C13×#380—21no—
48C4×C13×C4⋊C4C2211yescharacteristic
49C13×#328C2212yes—
50C13×#327C2212yes—
51C13×#327C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C2×C13×#41—21no—
56C2×C13×#41—22no—
57C22×D4×C13C2311yescharacteristic
58C23×C4×C13—21no—
59C2×C13×SD16—21no—
60C2×C13×D8—21no—
61C2×C13×D8—22no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—22no—
64C13×C4⋊Q8D411yescharacteristic
65C13×#127D411yescharacteristic
66C13×#126—22no—
67C13×#126—22no—
68C13×#126—21no—
69C13×#125—21no—
70C13×#125—22no—
71C13×#125—21no—
72C13×#125—21no—
73C13×#125—21no—
74C13×#125—21no—
75C13×#125D411yescharacteristic
76C13×#124—21no—
77C13×#124D411yescharacteristic
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—22no—
83C13×#123—21no—
84C13×#123—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8C2311yescharacteristic
92C13×#121—21no—
93C13×#121—22no—
94C13×#121—21no—
95C13×#121—22no—
96C13×#121—22no—
97C13×#121—21no—
98C13×#121—22no—
99C13×#121C2311yescharacteristic
100C13×#121C2312yes—
101C4×Q8×C13D411yescharacteristic
102C4×D4×C13—22no—
103C4×D4×C13—21no—
104C4×D4×C13—21no—
105C4×D4×C13—21no—
106C4×D4×C13—22no—
107C4×D4×C13—21no—
108C4×D4×C13—21no—
109C4×D4×C13—21no—
110C4×D4×C13—21no—
111C4×D4×C13—21no—
112C4×D4×C13D411yescharacteristic
113C4×D4×C13D412yes—
114C13×#117—21no—
115C13×#117—21no—
116C2×C13×C4⋊C4—22no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4D411yescharacteristic
120C2×C13×C4⋊C4D411yescharacteristic
121C2×C13×C4⋊C4D412yes—
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C4⋊C4C2312yes—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—22no—
127C2×C42×C13—21no—
128C2×C42×C13C2311yescharacteristic
129C13×#107—21no—
130C13×#106—21no—
131C13×#106—22no—
132C13×C4⋊C8—21no—
133C13×C4⋊C8—21no—
134C13×#103—21no—
135C13×#102—21no—
136C13×#102—22no—
137C13×#102—21no—
138C13×#102—21no—
139C13×#102—22no—
140C13×C22⋊C8C2311yescharacteristic
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2312yes—
143C13×#97—21no—
144C4×C8×C13—21no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18276C1311yesmaximal, 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×C13C2×D411yescharacteristic
157C2×D4×C13—21no—
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13—22no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—42no—
166C2×D4×C13C2×D411yescharacteristic
167C2×D4×C13C2×D412yes—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—21no—
172C22×C4×C13—22no—
173C22×C4×C13—21no—
174C22×C4×C13—22no—
175C22×C4×C13—42no—
176C22×C4×C13—42no—
177C22×C4×C13—41no—
178C22×C4×C13—41no—
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D412yes—
183C22×C4×C13C2411yescharacteristic
184C13×SD16—42no—
185C13×D8—44no—
186C13×D8—42no—
187C2×C8×C13—21no—
188C2×C8×C13—21no—
189C2×C8×C13—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—22no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—42no—
210C13×C4⋊C4C2×D412yes—
211C13×C4⋊C4C2×D411yescharacteristic
212C13×C4⋊C4C2×D411yescharacteristic
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—22no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—21no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—44no—
226C13×C22⋊C4—41no—
227C13×C22⋊C4—41no—
228C13×C22⋊C4—82no—
229C42×C13—22no—
230C42×C13—21no—
231C42×C13—81no—
232C42×C13C2×D411yescharacteristic
233C42×C13C2×D411yescharacteristic
234C42×C13C2×D411yescharacteristic
235C42×C13C2×D411yescharacteristic
236#3559C2×C1311yescharacteristic, complemented
237#3109C2×C1311yescharacteristic, complemented
238#3105C2×C1311yescharacteristic, complemented
239#2562C2×C1311yescharacteristic, complemented
240#1616C2×C1312yescomplemented
241#1615C2×C1312yescomplemented
242#1598C2×C1312yescomplemented
243#1597C2×C1312yescomplemented
244#1509C2×C1311yescharacteristic, complemented
245#1502C2×C1311yescharacteristic, complemented
246#1470C2×C1311yescharacteristic, complemented
247C23×C13—22no—
248C23×C13—21no—
249C23×C13—22no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13C22×D411yescharacteristic
257Q8×C13—41no—
258Q8×C13—81no—
259Q8×C13—82no—
260D4×C13—22no—
261D4×C13—22no—
262D4×C13—41no—
263D4×C13—41no—
264D4×C13—42no—
265D4×C13—41no—
266D4×C13—42no—
267D4×C13—41no—
268D4×C13—42no—
269D4×C13—41no—
270D4×C13—42no—
271D4×C13—81no—
272D4×C13—82no—
273D4×C13—82no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—22no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—21no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—41no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—42no—
294C2×C4×C13—82no—
295C2×C4×C13—82no—
296C2×C4×C13—82no—
297C2×C4×C13—82no—
298C2×C4×C13—82no—
299C2×C4×C13—82no—
300C2×C4×C13#12011yescharacteristic
301C2×C4×C13#12011yescharacteristic
302C2×C4×C13#12011yescharacteristic
303C2×C4×C13#12011yescharacteristic
304C2×C4×C13C22×D411yescharacteristic
305C2×C4×C13C22×D411yescharacteristic
306C8×C13—42no—
307C8×C13—41no—
308C8×C13—41no—
309#563—21no—
310#562—21no—
311#554—21no—
312#553—21no—
313#553—21no—
314#547—22no—
315#547—21no—
316#544—21no—
317#540—21no—
318#539—22no—
319#539C22×C1312yes—
320#537C22×C1312yes—
321#532C22×C1311yescharacteristic
322#529C22×C1311yescharacteristic
323C2×#125C22×C1311yescharacteristic
324C2×C4×D4C22×C1311yescharacteristic
325#484C22×C1311yescharacteristic
326#481C22×C1311yescharacteristic
327#481C22×C1312yes—
328#478—21no—
329#476—21no—
330#463—21no—
331#459—21no—
332#450C22×C1311yescharacteristic
333#447C22×C1311yescharacteristic
334#447C22×C1312yes—
335#442—22no—
336C4×SD16—21no—
337C4×D8—21no—
338#432C22×C1311yescharacteristic
339#431C22×C1311yescharacteristic
340#400C22×C1312yes—
341#394C22×C1312yes—
342#388—22no—
343#380—21no—
344#380—21no—
345C4×C4⋊C4C22×C1311yescharacteristic
346#328C22×C1312yes—
347#327C22×C1312yes—
348#327C22×C1312yes—
349#327C22×C1312yes—
350#324C22×C1312yes—
351#324C22×C1312yes—
352C22×C13—21no—
353C22×C13—21no—
354C22×C13—42no—
355C22×C13—42no—
356C22×C13—42no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13—42no—
362C22×C13—41no—
363C22×C13—81no—
364C22×C13—81no—
365C22×C13—81no—
366C22×C13—81no—
367C22×C13C2×#12011yescharacteristic
368C22×C13#57611yescharacteristic
369C22×C13#57711yescharacteristic
370C4×C13—21no—
371C4×C13—21no—
372C4×C13—21no—
373C4×C13—21no—
374C4×C13—21no—
375C4×C13—42no—
376C4×C13—42no—
377C4×C13—41no—
378C4×C13—41no—
379C4×C13—42no—
380C4×C13—41no—
381C4×C13—82no—
382C4×C13—81no—
383C4×C13#45412yes—
384C2×#41—21no—
385C2×#41—22no—
386C22×D4C23×C1311yescharacteristic
387C23×C4—21no—
388C2×SD16—21no—
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#124D4×C1311yescharacteristic
407#123—22no—
408#123—22no—
409#123—22no—
410#123—22no—
411#123—22no—
412#123—21no—
413#123—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8C23×C1311yescharacteristic
421#121—21no—
422#121—22no—
423#121—21no—
424#121—22no—
425#121—22no—
426#121—21no—
427#121—22no—
428#121C23×C1311yescharacteristic
429#121C23×C1312yes—
430C4×Q8D4×C1311yescharacteristic
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
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⋊C4D4×C1311yescharacteristic
449C2×C4⋊C4D4×C1312yes—
450C2×C4⋊C4D4×C1311yescharacteristic
451C2×C4⋊C4C23×C1311yescharacteristic
452C2×C4⋊C4C23×C1312yes—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C42—21no—
457C2×C42C23×C1311yescharacteristic
458#107—21no—
459#106—21no—
460#106—22no—
461C4⋊C8—21no—
462C4⋊C8—21no—
463#103—21no—
464#102—21no—
465#102—22no—
466#102—21no—
467#102—21no—
468#102—22no—
469C22⋊C8C23×C1311yescharacteristic
470C22⋊C8C23×C1311yescharacteristic
471C22⋊C8C23×C1312yes—
472#97—21no—
473C4×C8—21no—
474#95—22no—
475#95—22no—
476#95C23×C1312yes—
477C2×C13—21no—
478C2×C13—21no—
479C2×C13—81no—
480C2×C13—82no—
481C2×C13—82no—
482C2×C13#301211yescharacteristic
483C2×C13C2×#45411yescharacteristic
484C2×C13#302511yescharacteristic
485C24—21no—
486#41—81no—
487#41—81no—
488#41—82no—
489#41—82no—
490C2×Q8—22no—
491C2×Q8—21no—
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—42no—
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—21no—
510C22×C4—22no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4C2×D4×C1312yes—
516C22×C4C2×D4×C1311yescharacteristic
517C22×C4C2×D4×C1311yescharacteristic
518C22×C4C2×D4×C1312yes—
519C22×C4C24×C1311yescharacteristic
520SD16—42no—
521D8—44no—
522D8—42no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4C2×D4×C1312yes—
547C4⋊C4C2×D4×C1311yescharacteristic
548C4⋊C4C2×D4×C1311yescharacteristic
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—44no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—82no—
565C42—22no—
566C42—21no—
567C42—81no—
568C42C2×D4×C1311yescharacteristic
569C42C2×D4×C1311yescharacteristic
570C42C2×D4×C1311yescharacteristic
571C42C2×D4×C1311yescharacteristic
572C13#1827611yescharacteristic, direct product factor, Sylow
573C23—22no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C22×D4×C1311yescharacteristic
583Q8—41no—
584Q8—81no—
585Q8—82no—
586D4—22no—
587D4—22no—
588D4—42no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—42no—
593D4—41no—
594D4—42no—
595D4—41no—
596D4—42no—
597D4—81no—
598D4—82no—
599D4—82no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4C13×#12011yescharacteristic
627C2×C4C13×#12011yescharacteristic
628C2×C4C13×#12011yescharacteristic
629C2×C4C13×#12011yescharacteristic
630C2×C4C22×D4×C1311yescharacteristic
631C2×C4C22×D4×C1311yescharacteristic
632C8—42no—
633C8—41no—
634C8—41no—
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—41no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22C2×C13×#12011yescharacteristic
651C22C13×#57611yescharacteristic
652C22C13×#57711yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—82no—
665C4—81no—
666C4C13×#45412yes—
667C2—21no—
668C2—21no—
669C2—82no—
670C2—81no—
671C2—82no—
672C2C13×#301211yescharacteristic
673C2C2×C13×#45411yescharacteristic
674C2C13×#302511yescharacteristic
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×#3109C2semidirect
3. C13×#3105C2semidirect
4. C13×#2562C2semidirect
5. C13×#1616C2semidirect
6. C13×#1615C2semidirect
7. C13×#1598C2semidirect
8. C13×#1597C2semidirect
9. C13×#1509C2semidirect
10. C13×#1502C2semidirect
11. C13×#1470C2semidirect
148. #18276C13direct (N × H)
236. #3559C2×C13semidirect
237. #3109C2×C13semidirect
238. #3105C2×C13semidirect
239. #2562C2×C13semidirect
240. #1616C2×C13semidirect
241. #1615C2×C13semidirect
242. #1598C2×C13semidirect
243. #1597C2×C13semidirect
244. #1509C2×C13semidirect
245. #1502C2×C13semidirect
246. #1470C2×C13semidirect
572. C13#18276direct (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×#31092
C13×#31052
C13×#25622
C13×#16162
C13×#16152
C13×#15982
C13×#15972
C13×#15092
C13×#15022
C13×#14702
#1827613