Finite Group Databasebeta

← C13×#18306 #15704645

Subgroups — C13×#18306 #15704645

Order 3328.

1040 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3459C211yesmaximal, characteristic, complemented
2C13×#3211C212yesmaximal, complemented
3C13×#2631C211yesmaximal, characteristic, complemented
4C13×#1606C212yesmaximal, complemented
5C13×#1602C211yesmaximal, characteristic, complemented
6C13×#1601C211yesmaximal, characteristic, complemented
7C13×#1600C212yesmaximal, complemented
8C13×#1596C211yesmaximal, characteristic, complemented
9C13×#1595C211yesmaximal, characteristic, complemented
10C13×#1521C212yesmaximal, complemented
11C13×#1460C211yesmaximal, characteristic, complemented
12C13×#543C2211yescharacteristic
13C13×#539—22no—
14C13×#539—21no—
15C13×#538—22no—
16C13×#538C2212yes—
17C13×#534—21no—
18C13×#534C2211yescharacteristic
19C13×#529—22no—
20C13×#529C2212yes—
21C2×C13×#124C2211yescharacteristic, complemented
22C13×#525—21no—
23C13×#525—22no—
24C2×C4×D4×C13—21no—
25C2×C4×D4×C13C2211yescharacteristic
26C13×#495—22no—
27C13×#488—22no—
28C13×#464—22no—
29C13×#463—22no—
30C13×#451C2212yescomplemented
31C13×#450C2212yescomplemented
32C13×#448C2212yes—
33C13×#447C2212yes—
34C13×#431C2212yescomplemented
35C13×#397—21no—
36C13×#393C2211yescharacteristic
37C13×#393C2211yescharacteristic, complemented
38C13×#392—21no—
39C13×#392C2211yescharacteristic
40C13×#392C2211yescharacteristic, complemented
41C13×#386—21no—
42C13×#386—21no—
43C13×#383C2211yescharacteristic, complemented
44C13×#328C2212yescomplemented
45C13×#328C2212yescomplemented
46C13×#327C2212yes—
47C13×#327C2212yes—
48C13×#323C2211yescharacteristic
49C13×#323C2211yescharacteristic
50C13×#323C2212yescomplemented
51C2×C13×#41—21no—
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13—21no—
54C22×D4×C13—21no—
55C22×D4×C13—21no—
56C22×D4×C13D411yescharacteristic
57C22×D4×C13C2311yescharacteristic
58C23×C4×C13—21no—
59C23×C4×C13D411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C2×C13×Q16—22no—
62C2×C13×SD16—22no—
63C2×C13×SD16—22no—
64C2×C13×D8—22no—
65C13×#126—22no—
66C13×#126—22no—
67C13×#126—22no—
68C13×#125—22no—
69C13×#125D412yescomplemented
70C13×#124—22no—
71C13×#124—22no—
72C13×#124—22no—
73C13×#124D412yescomplemented
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—22no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8C2312yes—
86C13×#121—22no—
87C13×#121—21no—
88C13×#121—22no—
89C13×#121—22no—
90C13×#121—21no—
91C13×#121C2312yes—
92C13×#120—22no—
93C13×#120—22no—
94C13×#120—22no—
95C4×Q8×C13D412yescomplemented
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C4×D4×C13—22no—
100C4×D4×C13—22no—
101C4×D4×C13—22no—
102C4×D4×C13—22no—
103C4×D4×C13D412yescomplemented
104C13×#117—21no—
105C13×#117—22no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
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⋊C4C2311yescharacteristic
117C2×C13×C22⋊C4C2311yescharacteristic
118C2×C42×C13—21no—
119C2×C42×C13C2311yescharacteristic
120C13×C4⋊C8—22no—
121C13×#103—22no—
122C13×#103—22no—
123C13×#102—22no—
124C13×#102—22no—
125C13×C22⋊C8C2312yes—
126C13×C22⋊C8C2312yes—
127C4×C8×C13—22no—
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95C2311yescharacteristic
133C13×#95C2311yescharacteristic
134#18306C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13—21no—
136C24×C13—21no—
137C24×C13C2×D411yescharacteristic
138C24×C13C2×D411yescharacteristic
139C13×#41—82no—
140C2×Q8×C13—21no—
141C2×Q8×C13—22no—
142C2×Q8×C13—81no—
143C2×Q8×C13C2×D412yes—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—22no—
152C2×D4×C13—41no—
153C2×D4×C13—42no—
154C2×D4×C13—42no—
155C2×D4×C13—42no—
156C2×D4×C13—42no—
157C2×D4×C13—81no—
158C2×D4×C13—81no—
159C2×D4×C13—81no—
160C2×D4×C13—81no—
161C2×D4×C13—81no—
162C2×D4×C13C2×D412yes—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—22no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—81no—
176C22×C4×C13—81no—
177C22×C4×C13—82no—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2411yescharacteristic
183C13×Q16—82no—
184C13×SD16—82no—
185C13×SD16—82no—
186C13×D8—82no—
187C2×C8×C13—22no—
188C2×C8×C13—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4C2×D412yes—
199C13×C4⋊C4C2×D412yes—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—41no—
213C13×C22⋊C4—42no—
214C13×C22⋊C4—41no—
215C13×C22⋊C4—81no—
216C13×C22⋊C4—81no—
217C13×C22⋊C4—81no—
218C13×C22⋊C4—81no—
219C42×C13—22no—
220C42×C13—22no—
221C42×C13C2×D412yes—
222C42×C13C2×D412yes—
223#3459C2×C1311yescharacteristic, complemented
224#3211C2×C1312yescomplemented
225#2631C2×C1311yescharacteristic, complemented
226#1606C2×C1312yescomplemented
227#1602C2×C1311yescharacteristic, complemented
228#1601C2×C1311yescharacteristic, complemented
229#1600C2×C1312yescomplemented
230#1596C2×C1311yescharacteristic, complemented
231#1595C2×C1311yescharacteristic, complemented
232#1521C2×C1312yescomplemented
233#1460C2×C1311yescharacteristic, complemented
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—22no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—42no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—81no—
253C23×C13—81no—
254C23×C13#13512yes—
255C23×C13C22×D411yescharacteristic
256Q8×C13—42no—
257Q8×C13—42no—
258Q8×C13—42no—
259Q8×C13—81no—
260D4×C13—44no—
261D4×C13—42no—
262D4×C13—42no—
263D4×C13—42no—
264D4×C13—44no—
265D4×C13—42no—
266D4×C13—42no—
267D4×C13—82no—
268D4×C13—81no—
269D4×C13—82no—
270D4×C13—84no—
271D4×C13—84no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—22no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—44no—
284C2×C4×C13—42no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—81no—
297C2×C4×C13—81no—
298C2×C4×C13—81no—
299C2×C4×C13—82no—
300C2×C4×C13—81no—
301C2×C4×C13#12011yescharacteristic
302C2×C4×C13#12012yes—
303C2×C4×C13#12011yescharacteristic
304C2×C4×C13C22×D412yes—
305C8×C13—42no—
306C8×C13—42no—
307#543C22×C1311yescharacteristic
308#539—22no—
309#539—21no—
310#538—22no—
311#538C22×C1312yes—
312#534—21no—
313#534C22×C1311yescharacteristic
314#529—22no—
315#529C22×C1312yes—
316C2×#124C22×C1311yescharacteristic, complemented
317#525—21no—
318#525—22no—
319C2×C4×D4—21no—
320C2×C4×D4C22×C1311yescharacteristic
321#495—22no—
322#488—22no—
323#464—22no—
324#463—22no—
325#451C22×C1312yescomplemented
326#450C22×C1312yescomplemented
327#448C22×C1312yes—
328#447C22×C1312yes—
329#431C22×C1312yescomplemented
330#397—21no—
331#393C22×C1311yescharacteristic
332#393C22×C1311yescharacteristic, complemented
333#392—21no—
334#392C22×C1311yescharacteristic
335#392C22×C1311yescharacteristic, complemented
336#386—21no—
337#386—21no—
338#383C22×C1311yescharacteristic, complemented
339#328C22×C1312yescomplemented
340#328C22×C1312yescomplemented
341#327C22×C1312yes—
342#327C22×C1312yes—
343#323C22×C1311yescharacteristic
344#323C22×C1311yescharacteristic
345#323C22×C1312yescomplemented
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—22no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—42no—
355C22×C13—41no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—41no—
359C22×C13—81no—
360C22×C13—81no—
361C22×C13—81no—
362C22×C13—81no—
363C22×C13—81no—
364C22×C13—81no—
365C22×C13—84no—
366C22×C13—81no—
367C22×C13—81no—
368C22×C13—81no—
369C22×C13C2×#12011yescharacteristic
370C22×C13C2×#13511yescharacteristic
371C22×C13#57511yescharacteristic
372C4×C13—22no—
373C4×C13—21no—
374C4×C13—21no—
375C4×C13—22no—
376C4×C13—42no—
377C4×C13—41no—
378C4×C13—41no—
379C4×C13—42no—
380C4×C13—42no—
381C4×C13—81no—
382C4×C13—81no—
383C4×C13—81no—
384C2×#41—21no—
385C22×Q8C23×C1311yescharacteristic
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4D4×C1311yescharacteristic
390C22×D4C23×C1311yescharacteristic
391C23×C4—21no—
392C23×C4D4×C1311yescharacteristic
393C23×C4D4×C1311yescharacteristic
394C2×Q16—22no—
395C2×SD16—22no—
396C2×SD16—22no—
397C2×D8—22no—
398#126—22no—
399#126—22no—
400#126—22no—
401#125—22no—
402#125D4×C1312yescomplemented
403#124—22no—
404#124—22no—
405#124—22no—
406#124D4×C1312yescomplemented
407#123—22no—
408#123—22no—
409#123—22no—
410#123—22no—
411#123—22no—
412#123—22no—
413C22⋊Q8—21no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8—22no—
418C22⋊Q8C23×C1312yes—
419#121—22no—
420#121—21no—
421#121—22no—
422#121—22no—
423#121—21no—
424#121C23×C1312yes—
425#120—22no—
426#120—22no—
427#120—22no—
428C4×Q8D4×C1312yescomplemented
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4D4×C1312yescomplemented
437#117—21no—
438#117—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4D4×C1311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4C23×C1311yescharacteristic
450C2×C22⋊C4C23×C1311yescharacteristic
451C2×C42—21no—
452C2×C42C23×C1311yescharacteristic
453C4⋊C8—22no—
454#103—22no—
455#103—22no—
456#102—22no—
457#102—22no—
458C22⋊C8C23×C1312yes—
459C22⋊C8C23×C1312yes—
460C4×C8—22no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95C23×C1311yescharacteristic
466#95C23×C1311yescharacteristic
467C2×C13—21no—
468C2×C13—21no—
469C2×C13—42no—
470C2×C13—81no—
471C2×C13—82no—
472C2×C13—161no—
473C2×C13#300211yescharacteristic
474C2×C13#301911yescharacteristic
475C2×C13#302711yescharacteristic
476C24—21no—
477C24—21no—
478C24C2×D4×C1311yescharacteristic
479C24C2×D4×C1311yescharacteristic
480#41—82no—
481C2×Q8—21no—
482C2×Q8—22no—
483C2×Q8—81no—
484C2×Q8C2×D4×C1312yes—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—41no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4C2×D4×C1312yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—82no—
519C22×C4C2×D4×C1311yescharacteristic
520C22×C4C2×D4×C1311yescharacteristic
521C22×C4C2×D4×C1311yescharacteristic
522C22×C4C2×D4×C1311yescharacteristic
523C22×C4C24×C1311yescharacteristic
524Q16—82no—
525SD16—82no—
526SD16—82no—
527D8—82no—
528C2×C8—22no—
529C2×C8—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4C2×D4×C1312yes—
540C4⋊C4C2×D4×C1312yes—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—41no—
554C22⋊C4—42no—
555C22⋊C4—41no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C42—22no—
561C42—22no—
562C42C2×D4×C1312yes—
563C42C2×D4×C1312yes—
564C13#1830611yescharacteristic, direct product factor, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—22no—
569C23—21no—
570C23—21no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—81no—
584C23—81no—
585C23C13×#13512yes—
586C23C22×D4×C1311yescharacteristic
587Q8—42no—
588Q8—42no—
589Q8—42no—
590Q8—81no—
591D4—44no—
592D4—42no—
593D4—42no—
594D4—42no—
595D4—44no—
596D4—42no—
597D4—42no—
598D4—82no—
599D4—81no—
600D4—82no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—82no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4C13×#12011yescharacteristic
633C2×C4C13×#12012yes—
634C2×C4C13×#12011yescharacteristic
635C2×C4C22×D4×C1312yes—
636C8—42no—
637C8—42no—
638C22—21no—
639C22—21no—
640C22—22no—
641C22—42no—
642C22—42no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—41no—
649C22—41no—
650C22—42no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—84no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C13×#12011yescharacteristic
662C22C2×C13×#13511yescharacteristic
663C22C13×#57511yescharacteristic
664C4—21no—
665C4—21no—
666C4—22no—
667C4—22no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—81no—
674C4—81no—
675C4—81no—
676C2—21no—
677C2—21no—
678C2—42no—
679C2—81no—
680C2—82no—
681C2—161no—
682C2C13×#300211yescharacteristic
683C2C13×#301911yescharacteristic
684C2C13×#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×#3459C2semidirect
2. C13×#3211C2semidirect
3. C13×#2631C2semidirect
4. C13×#1606C2semidirect
5. C13×#1602C2semidirect
6. C13×#1601C2semidirect
7. C13×#1600C2semidirect
8. C13×#1596C2semidirect
9. C13×#1595C2semidirect
10. C13×#1521C2semidirect
11. C13×#1460C2semidirect
21. C2×C13×#124C22semidirect
30. C13×#451C22semidirect
31. C13×#450C22semidirect
34. C13×#431C22semidirect
37. C13×#393C22semidirect
40. C13×#392C22semidirect
43. C13×#383C22semidirect
44. C13×#328C22semidirect
45. C13×#328C22semidirect
50. C13×#323C22semidirect
69. C13×#125D4semidirect
73. C13×#124D4semidirect
95. C4×Q8×C13D4semidirect
103. C4×D4×C13D4semidirect
134. #18306C13direct (N × H)
223. #3459C2×C13semidirect
224. #3211C2×C13semidirect
225. #2631C2×C13semidirect
226. #1606C2×C13semidirect
227. #1602C2×C13semidirect
228. #1601C2×C13semidirect
229. #1600C2×C13semidirect
230. #1596C2×C13semidirect
231. #1595C2×C13semidirect
232. #1521C2×C13semidirect
233. #1460C2×C13semidirect
316. C2×#124C22×C13semidirect
325. #451C22×C13semidirect
326. #450C22×C13semidirect
329. #431C22×C13semidirect
332. #393C22×C13semidirect
335. #392C22×C13semidirect
338. #383C22×C13semidirect
339. #328C22×C13semidirect
340. #328C22×C13semidirect
345. #323C22×C13semidirect
402. #125D4×C13semidirect
406. #124D4×C13semidirect
428. C4×Q8D4×C13semidirect
436. C4×D4D4×C13semidirect
564. C13#18306direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34592
C13×#32112
C13×#26312
C13×#16062
C13×#16022
C13×#16012
C13×#16002
C13×#15962
C13×#15952
C13×#15212
C13×#14602
#1830613