Finite Group Databasebeta

← C13×#9041 #15695380

Subgroups — C13×#9041 #15695380

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#447C211yesmaximal, characteristic
2C13×#2325C211yesmaximal, characteristic, complemented
3C13×#1786C211yesmaximal, characteristic, complemented
4C2×C13×#327C211yesmaximal, characteristic, complemented
5C13×#1438C211yesmaximal, characteristic, complemented
6C13×#1294C211yesmaximal, characteristic, complemented
7C13×#1280C211yesmaximal, characteristic, complemented
8C23×D4×C13C2211yescharacteristic
9C22×C13×D8—21no—
10C2×C13×#121C2211yescharacteristic
11C2×C4×D4×C13—21no—
12C22×C13×C22⋊C4—21no—
13C22×C13×C22⋊C4—21no—
14C13×#447—22no—
15C13×#447C414yescomplemented
16C2×C13×#102—21no—
17C2×C13×#102—21no—
18C2×C13×#102—21no—
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C13×#388—21no—
22C13×#387—21no—
23C13×#386—21no—
24C13×#386—21no—
25C13×#385—21no—
26C13×#380C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C13×#327—22no—
30C25×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13—21no—
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—42no—
38C22×D4×C13—42no—
39C22×D4×C13C2×C412yescomplemented
40C22×D4×C13D411yescharacteristic
41C23×C4×C13—21no—
42C23×C4×C13—21no—
43C23×C4×C13D411yescharacteristic
44C23×C4×C13D411yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C2×C13×D8—24no—
47C2×C13×D8—42no—
48C2×C13×D8—42no—
49C22×C8×C13—21no—
50C22×C8×C13—21no—
51C13×#121—21no—
52C13×#121—21no—
53C13×#121C2×C412yes—
54C13×#121D412yes—
55C4×D4×C13—42no—
56C4×D4×C13—42no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—42no—
67C2×C13×C22⋊C4—42no—
68C2×C13×C22⋊C4—42no—
69C2×C13×C22⋊C4—42no—
70C2×C13×C22⋊C4—42no—
71C2×C13×C22⋊C4—42no—
72C2×C42×C13—21no—
73C13×#102—24no—
74C13×#102—42no—
75C13×#102—42no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×C22⋊C8C2×C412yescomplemented
80C13×#95—21no—
81C13×#95—21no—
82C13×#95—21no—
83C13×#95—21no—
84C13×#95—21no—
85C13×#95—21no—
86C13×#95—21no—
87#9041C1311yesmaximal, characteristic, direct product factor, Sylow
88C24×C13—22no—
89C24×C13—22no—
90C24×C13—22no—
91C24×C13—21no—
92C24×C13—41no—
93C24×C13—41no—
94C24×C13—41no—
95C24×C13—41no—
96C24×C13—41no—
97C24×C13—41no—
98C24×C13—41no—
99C24×C13—41no—
100C24×C13—41no—
101C24×C13—41no—
102C24×C13—41no—
103C24×C13—41no—
104C24×C13C2×D411yescharacteristic
105C2×D4×C13—22no—
106C2×D4×C13—22no—
107C2×D4×C13—22no—
108C2×D4×C13—22no—
109C2×D4×C13—22no—
110C2×D4×C13—22no—
111C2×D4×C13—22no—
112C2×D4×C13—22no—
113C2×D4×C13—21no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C2×D4×C13—41no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C2×D4×C13—44no—
121C2×D4×C13—44no—
122C2×D4×C13—44no—
123C2×D4×C13—44no—
124C2×D4×C13—41no—
125C2×D4×C13—41no—
126C2×D4×C13—41no—
127C2×D4×C13—41no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13C22⋊C412yescomplemented
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13—42no—
143C22×C4×C13—41no—
144C22×C4×C13—41no—
145C22×C4×C13—41no—
146C22×C4×C13—41no—
147C22×C4×C13—41no—
148C22×C4×C13—41no—
149C22×C4×C13—41no—
150C22×C4×C13—41no—
151C22×C4×C13—41no—
152C22×C4×C13—41no—
153C22×C4×C13—81no—
154C22×C4×C13—81no—
155C22×C4×C13D812yescomplemented
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C13×D8—48no—
163C2×C8×C13—22no—
164C2×C8×C13—41no—
165C2×C8×C13—41no—
166C2×C8×C13—41no—
167C2×C8×C13—41no—
168C2×C8×C13—41no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4—41no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4C22⋊C412yescomplemented
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—48no—
178C13×C22⋊C4—48no—
179C13×C22⋊C4—41no—
180C13×C22⋊C4—41no—
181C13×C22⋊C4—81no—
182C13×C22⋊C4—81no—
183C42×C13—42no—
184C2×#447C2×C1311yescharacteristic
185#2325C2×C1311yescharacteristic, complemented
186#1786C2×C1311yescharacteristic, complemented
187C2×#327C2×C1311yescharacteristic, complemented
188#1438C2×C1311yescharacteristic, complemented
189#1294C2×C1311yescharacteristic, complemented
190#1280C2×C1311yescharacteristic, complemented
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13—24no—
196C23×C13—22no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—81no—
222C23×C13—81no—
223C23×C13—81no—
224C23×C13—81no—
225C23×C13—81no—
226C23×C13—81no—
227C23×C13—81no—
228C23×C13—81no—
229C23×C13—81no—
230C23×C13—81no—
231C23×C13—81no—
232C23×C13—81no—
233C23×C13—81no—
234C23×C13—81no—
235C23×C13—81no—
236C23×C13—81no—
237C23×C13C4×D411yescharacteristic
238C23×C13#12011yescharacteristic
239C23×C13#12111yescharacteristic
240C23×C13C2×D811yescharacteristic
241C23×C13#13511yescharacteristic
242C23×C13AGL(1,ℤ/8)11yescharacteristic
243C23×C13AGL(1,ℤ/8)11yescharacteristic
244D4×C13—24no—
245D4×C13—24no—
246D4×C13—42no—
247D4×C13—42no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—42no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—42no—
254D4×C13—42no—
255D4×C13—42no—
256D4×C13—42no—
257D4×C13—81no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
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—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—81no—
287C2×C4×C13—84no—
288C2×C4×C13—81no—
289C2×C4×C13—81no—
290C2×C4×C13—81no—
291C2×C4×C13—81no—
292C2×C4×C13—81no—
293C2×C4×C13C2×C22⋊C411yescharacteristic
294C2×C4×C13C4×D411yescharacteristic
295C2×C4×C13#12111yescharacteristic
296C2×C4×C13#12311yescharacteristic
297C8×C13—42no—
298C8×C13—81no—
299C23×D4C22×C1311yescharacteristic
300C22×D8—21no—
301C2×#121C22×C1311yescharacteristic
302C2×C4×D4—21no—
303C22×C22⋊C4—21no—
304C22×C22⋊C4—21no—
305#447—22no—
306#447C4×C1314yescomplemented
307C2×#102—21no—
308C2×#102—21no—
309C2×#102—21no—
310C2×C22⋊C8C22×C1311yescharacteristic
311C2×C22⋊C8C22×C1311yescharacteristic
312#388—21no—
313#387—21no—
314#386—21no—
315#386—21no—
316#385—21no—
317#380C22×C1311yescharacteristic
318C2×#95C22×C1311yescharacteristic
319C2×#95C22×C1311yescharacteristic
320#327—22no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—44no—
334C22×C13—44no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13—44no—
338C22×C13—42no—
339C22×C13—82no—
340C22×C13—82no—
341C22×C13—82no—
342C22×C13—82no—
343C22×C13—82no—
344C22×C13—82no—
345C22×C13—81no—
346C22×C13—82no—
347C22×C13—81no—
348C22×C13—82no—
349C22×C13—81no—
350C22×C13—82no—
351C22×C13—81no—
352C22×C13—82no—
353C22×C13—82no—
354C22×C13—82no—
355C22×C13#38611yescharacteristic
356C22×C13C4×D811yescharacteristic
357C22×C13#44211yescharacteristic
358C22×C13#44711yescharacteristic
359C22×C13#44911yescharacteristic
360C22×C13#45311yescharacteristic
361C22×C13#45411yescharacteristic
362C22×C13B(4,𝔽2)11yescharacteristic
363C22×C13B(4,𝔽2)11yescharacteristic
364C22×C13#45911yescharacteristic
365C22×C13#46311yescharacteristic
366C4×C13—21no—
367C4×C13—21no—
368C4×C13—21no—
369C4×C13—21no—
370C4×C13—42no—
371C4×C13—42no—
372C4×C13—82no—
373C4×C13—81no—
374C4×C13—81no—
375C4×C13—81no—
376C25—21no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4C2×C4×C1312yescomplemented
386C22×D4D4×C1311yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4D4×C1311yescharacteristic
390C23×C4D4×C1311yescharacteristic
391C23×C4C23×C1311yescharacteristic
392C2×D8—24no—
393C2×D8—42no—
394C2×D8—42no—
395C22×C8—21no—
396C22×C8—21no—
397#121—21no—
398#121—21no—
399#121C2×C4×C1312yes—
400#121D4×C1312yes—
401C4×D4—42no—
402C4×D4—42no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4D4×C1311yescharacteristic
405C2×C4⋊C4D4×C1311yescharacteristic
406C2×C4⋊C4D4×C1311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C42—21no—
419#102—24no—
420#102—42no—
421#102—42no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8C2×C4×C1312yescomplemented
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433C2×C13—21no—
434C2×C13—21no—
435C2×C13—21no—
436C2×C13—21no—
437C2×C13—82no—
438C2×C13—84no—
439C2×C13#159511yescharacteristic
440C2×C13#159711yescharacteristic
441C2×C13#159811yescharacteristic
442C2×C13#160011yescharacteristic
443C2×C13#187911yescharacteristic
444C2×C13#188311yescharacteristic
445C2×C13#188911yescharacteristic
446C24—22no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24C2×D4×C1311yescharacteristic
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4C13×C22⋊C412yescomplemented
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4C13×D812yescomplemented
514C22×C4C22×C4×C1311yescharacteristic
515C22×C4C2×D4×C1311yescharacteristic
516C22×C4C2×D4×C1311yescharacteristic
517C22×C4C2×D4×C1311yescharacteristic
518C22×C4C13×#4111yescharacteristic
519C22×C4C13×#4111yescharacteristic
520D8—48no—
521C2×C8—22no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—42no—
531C4⋊C4C13×C22⋊C412yescomplemented
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—42no—
535C22⋊C4—48no—
536C22⋊C4—48no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—81no—
540C22⋊C4—81no—
541C42—42no—
542C13#904111yescharacteristic, direct product factor, Sylow
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—24no—
548C23—22no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—42no—
572C23—42no—
573C23—81no—
574C23—81no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23C4×D4×C1311yescharacteristic
590C23C13×#12011yescharacteristic
591C23C13×#12111yescharacteristic
592C23C2×C13×D811yescharacteristic
593C23C13×#13511yescharacteristic
594C23C13×AGL(1,ℤ/8)11yescharacteristic
595C23C13×AGL(1,ℤ/8)11yescharacteristic
596D4—24no—
597D4—24no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—42no—
608D4—42no—
609D4—81no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
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—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—81no—
639C2×C4—84no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4C2×C13×C22⋊C411yescharacteristic
646C2×C4C4×D4×C1311yescharacteristic
647C2×C4C13×#12111yescharacteristic
648C2×C4C13×#12311yescharacteristic
649C8—42no—
650C8—81no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—44no—
665C22—42no—
666C22—42no—
667C22—44no—
668C22—42no—
669C22—82no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—81no—
676C22—82no—
677C22—81no—
678C22—82no—
679C22—81no—
680C22—82no—
681C22—81no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22C13×#38611yescharacteristic
686C22C4×C13×D811yescharacteristic
687C22C13×#44211yescharacteristic
688C22C13×#44711yescharacteristic
689C22C13×#44911yescharacteristic
690C22C13×#45311yescharacteristic
691C22C13×#45411yescharacteristic
692C22C13×B(4,𝔽2)11yescharacteristic
693C22C13×B(4,𝔽2)11yescharacteristic
694C22C13×#45911yescharacteristic
695C22C13×#46311yescharacteristic
696C4—21no—
697C4—21no—
698C4—21no—
699C4—21no—
700C4—42no—
701C4—42no—
702C4—82no—
703C4—81no—
704C4—81no—
705C4—81no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—21no—
710C2—84no—
711C2—82no—
712C2C13×#159511yescharacteristic
713C2C13×#159711yescharacteristic
714C2C13×#159811yescharacteristic
715C2C13×#160011yescharacteristic
716C2C13×#187911yescharacteristic
717C2C13×#188311yescharacteristic
718C2C13×#188911yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#447C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C13×#2325C2semidirect
3. C13×#1786C2semidirect
4. C2×C13×#327C2semidirect
5. C13×#1438C2semidirect
6. C13×#1294C2semidirect
7. C13×#1280C2semidirect
15. C13×#447C4semidirect
39. C22×D4×C13C2×C4semidirect
79. C13×C22⋊C8C2×C4semidirect
87. #9041C13direct (N × H)
130. C2×D4×C13C22⋊C4semidirect
155. C22×C4×C13D8semidirect
173. C13×C4⋊C4C22⋊C4semidirect
185. #2325C2×C13semidirect
186. #1786C2×C13semidirect
187. C2×#327C2×C13semidirect
188. #1438C2×C13semidirect
189. #1294C2×C13semidirect
190. #1280C2×C13semidirect
306. #447C4×C13semidirect
385. C22×D4C2×C4×C13semidirect
425. C22⋊C8C2×C4×C13semidirect
488. C2×D4C13×C22⋊C4semidirect
513. C22×C4C13×D8semidirect
531. C4⋊C4C13×C22⋊C4semidirect
542. C13#9041direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4472
C13×#23252
C13×#17862
C2×C13×#3272
C13×#14382
C13×#12942
C13×#12802
#904113