Finite Group Databasebeta

← C13×#9042 #15695381

Subgroups — C13×#9042 #15695381

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#450C211yesmaximal, characteristic
2C13×#2329C211yesmaximal, characteristic, complemented
3C13×#1786C211yesmaximal, characteristic
4C2×C13×#328C211yesmaximal, characteristic, complemented
5C13×#1438C211yesmaximal, characteristic
6C13×#1294C211yesmaximal, characteristic, complemented
7C13×#1280C211yesmaximal, characteristic, complemented
8C23×D4×C13C2211yescharacteristic
9C22×C13×SD16—21no—
10C2×C13×C22⋊Q8C2211yescharacteristic
11C22×C13×C22⋊C4—21no—
12C22×C13×C22⋊C4—21no—
13C13×#450—22no—
14C13×#450C414yescomplemented
15C2×C13×#102—21no—
16C2×C13×#102—21no—
17C2×C13×#102—21no—
18C2×C13×C22⋊C8C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C13×#391—21no—
21C13×#389—21no—
22C13×#387—21no—
23C13×#387—21no—
24C13×#385—21no—
25C13×#380C2211yescharacteristic
26C4×C13×C22⋊C4—21no—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C13×#328—22no—
30C25×C13—21no—
31C22×Q8×C13D411yescharacteristic
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×C412yes—
40C23×C4×C13—21no—
41C23×C4×C13D411yescharacteristic
42C23×C4×C13D411yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C2×C13×SD16—24no—
45C2×C13×SD16—42no—
46C2×C13×SD16—42no—
47C22×C8×C13—21no—
48C22×C8×C13—21no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8C2×C412yes—
52C13×C22⋊Q8D412yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—42no—
62C2×C13×C22⋊C4—42no—
63C2×C13×C22⋊C4—42no—
64C2×C13×C22⋊C4—42no—
65C2×C13×C22⋊C4—42no—
66C2×C13×C22⋊C4—42no—
67C2×C42×C13—21no—
68C2×C42×C13—21no—
69C13×#102—24no—
70C13×#102—42no—
71C13×#102—42no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8C2×C412yes—
76C13×#95—21no—
77C13×#95—21no—
78C13×#95—21no—
79C13×#95—21no—
80C13×#95—21no—
81C13×#95—21no—
82C13×#95—21no—
83C13×#95—21no—
84C13×#95—21no—
85#9042C1311yesmaximal, characteristic, direct product factor, Sylow
86C24×C13—22no—
87C24×C13—22no—
88C24×C13—22no—
89C24×C13—41no—
90C24×C13—41no—
91C24×C13—41no—
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×C13C2×D411yescharacteristic
102C2×Q8×C13—21no—
103C2×Q8×C13—41no—
104C2×Q8×C13—41no—
105C2×Q8×C13C22⋊C412yescomplemented
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—41no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C2×D4×C13—44no—
117C2×D4×C13—44no—
118C2×D4×C13—44no—
119C2×D4×C13—44no—
120C2×D4×C13—41no—
121C2×D4×C13—41no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13—41no—
136C22×C4×C13—41no—
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13—41no—
144C22×C4×C13SD1612yescomplemented
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13#4111yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C13×SD16—48no—
152C2×C8×C13—22no—
153C2×C8×C13—41no—
154C2×C8×C13—41no—
155C2×C8×C13—41no—
156C2×C8×C13—41no—
157C2×C8×C13—41no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—41no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4—81no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4C22⋊C412yescomplemented
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—48no—
169C13×C22⋊C4—48no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C42×C13—81no—
173C42×C13—81no—
174C2×#450C2×C1311yescharacteristic
175#2329C2×C1311yescharacteristic, complemented
176#1786C2×C1311yescharacteristic
177C2×#328C2×C1311yescharacteristic, complemented
178#1438C2×C1311yescharacteristic
179#1294C2×C1311yescharacteristic, complemented
180#1280C2×C1311yescharacteristic, complemented
181C23×C13—21no—
182C23×C13—21no—
183C23×C13—21no—
184C23×C13—21no—
185C23×C13—24no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—42no—
195C23×C13—42no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—81no—
205C23×C13—81no—
206C23×C13—81no—
207C23×C13—81no—
208C23×C13—81no—
209C23×C13—81no—
210C23×C13—81no—
211C23×C13—81no—
212C23×C13—81no—
213C23×C13—81no—
214C23×C13—81no—
215C23×C13—81no—
216C23×C13—81no—
217C23×C13—81no—
218C23×C13—81no—
219C23×C13—81no—
220C23×C13C4×D411yescharacteristic
221C23×C13#12011yescharacteristic
222C23×C13#12111yescharacteristic
223C23×C13C2×SD1611yescharacteristic
224C23×C13#13511yescharacteristic
225C23×C13AGL(1,ℤ/8)11yescharacteristic
226C23×C13#13711yescharacteristic
227Q8×C13—42no—
228Q8×C13—81no—
229D4×C13—24no—
230D4×C13—24no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—42no—
234D4×C13—42no—
235D4×C13—42no—
236D4×C13—42no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—81no—
269C2×C4×C13—81no—
270C2×C4×C13—81no—
271C2×C4×C13—81no—
272C2×C4×C13—81no—
273C2×C4×C13—81no—
274C2×C4×C13C2×C22⋊C411yescharacteristic
275C2×C4×C13C4×D411yescharacteristic
276C2×C4×C13#12111yescharacteristic
277C2×C4×C13#12311yescharacteristic
278C8×C13—42no—
279C8×C13—81no—
280C23×D4C22×C1311yescharacteristic
281C22×SD16—21no—
282C2×C22⋊Q8C22×C1311yescharacteristic
283C22×C22⋊C4—21no—
284C22×C22⋊C4—21no—
285#450—22no—
286#450C4×C1314yescomplemented
287C2×#102—21no—
288C2×#102—21no—
289C2×#102—21no—
290C2×C22⋊C8C22×C1311yescharacteristic
291C2×C22⋊C8C22×C1311yescharacteristic
292#391—21no—
293#389—21no—
294#387—21no—
295#387—21no—
296#385—21no—
297#380C22×C1311yescharacteristic
298C4×C22⋊C4—21no—
299C2×#95C22×C1311yescharacteristic
300C2×#95C22×C1311yescharacteristic
301#328—22no—
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—21no—
311C22×C13—21no—
312C22×C13—21no—
313C22×C13—21no—
314C22×C13—44no—
315C22×C13—44no—
316C22×C13—44no—
317C22×C13—82no—
318C22×C13—82no—
319C22×C13—82no—
320C22×C13—82no—
321C22×C13—82no—
322C22×C13—82no—
323C22×C13—82no—
324C22×C13—82no—
325C22×C13—82no—
326C22×C13—82no—
327C22×C13—82no—
328C22×C13—82no—
329C22×C13#38611yescharacteristic
330C22×C13C4×SD1611yescharacteristic
331C22×C13#44011yescharacteristic
332C22×C13#44811yescharacteristic
333C22×C13#44911yescharacteristic
334C22×C13#45311yescharacteristic
335C22×C13#45411yescharacteristic
336C22×C13B(4,𝔽2)11yescharacteristic
337C22×C13B(4,𝔽2)11yescharacteristic
338C22×C13#46011yescharacteristic
339C22×C13#46411yescharacteristic
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—42no—
347C4×C13—82no—
348C4×C13—81no—
349C4×C13—81no—
350C4×C13—81no—
351C25—21no—
352C22×Q8D4×C1311yescharacteristic
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4C2×C4×C1312yes—
361C23×C4—21no—
362C23×C4D4×C1311yescharacteristic
363C23×C4D4×C1311yescharacteristic
364C23×C4C23×C1311yescharacteristic
365C2×SD16—24no—
366C2×SD16—42no—
367C2×SD16—42no—
368C22×C8—21no—
369C22×C8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8C2×C4×C1312yes—
373C22⋊Q8D4×C1312yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4D4×C1311yescharacteristic
378C2×C4⋊C4D4×C1311yescharacteristic
379C2×C4⋊C4D4×C1311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C42—21no—
389C2×C42—21no—
390#102—24no—
391#102—42no—
392#102—42no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8C2×C4×C1312yes—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406C2×C13—21no—
407C2×C13—21no—
408C2×C13—21no—
409C2×C13—21no—
410C2×C13—84no—
411C2×C13#159611yescharacteristic
412C2×C13#159711yescharacteristic
413C2×C13#159911yescharacteristic
414C2×C13#160011yescharacteristic
415C2×C13#188011yescharacteristic
416C2×C13#188311yescharacteristic
417C2×C13#188911yescharacteristic
418C24—22no—
419C24—22no—
420C24—22no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24C2×D4×C1311yescharacteristic
434C2×Q8—21no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8C13×C22⋊C412yescomplemented
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—41no—
453C2×D4—41no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4C13×SD1612yescomplemented
477C22×C4C22×C4×C1311yescharacteristic
478C22×C4C2×D4×C1311yescharacteristic
479C22×C4C2×D4×C1311yescharacteristic
480C22×C4C2×D4×C1311yescharacteristic
481C22×C4C13×#4111yescharacteristic
482C22×C4C13×#4111yescharacteristic
483SD16—48no—
484C2×C8—22no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4C13×C22⋊C412yescomplemented
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—48no—
501C22⋊C4—48no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—81no—
505C42—81no—
506C13#904211yescharacteristic, direct product factor, Sylow
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×D4×C1311yescharacteristic
547C23C13×#12011yescharacteristic
548C23C13×#12111yescharacteristic
549C23C2×C13×SD1611yescharacteristic
550C23C13×#13511yescharacteristic
551C23C13×AGL(1,ℤ/8)11yescharacteristic
552C23C13×#13711yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
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—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4C2×C13×C22⋊C411yescharacteristic
601C2×C4C4×D4×C1311yescharacteristic
602C2×C4C13×#12111yescharacteristic
603C2×C4C13×#12311yescharacteristic
604C8—42no—
605C8—81no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22C13×#38611yescharacteristic
634C22C4×C13×SD1611yescharacteristic
635C22C13×#44011yescharacteristic
636C22C13×#44811yescharacteristic
637C22C13×#44911yescharacteristic
638C22C13×#45311yescharacteristic
639C22C13×#45411yescharacteristic
640C22C13×B(4,𝔽2)11yescharacteristic
641C22C13×B(4,𝔽2)11yescharacteristic
642C22C13×#46011yescharacteristic
643C22C13×#46411yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—82no—
652C4—81no—
653C4—81no—
654C4—81no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2C13×#159611yescharacteristic
661C2C13×#159711yescharacteristic
662C2C13×#159911yescharacteristic
663C2C13×#160011yescharacteristic
664C2C13×#188011yescharacteristic
665C2C13×#188311yescharacteristic
666C2C13×#188911yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC23×D4×C13C22
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×#2329C2semidirect
4. C2×C13×#328C2semidirect
6. C13×#1294C2semidirect
7. C13×#1280C2semidirect
14. C13×#450C4semidirect
85. #9042C13direct (N × H)
105. C2×Q8×C13C22⋊C4semidirect
144. C22×C4×C13SD16semidirect
165. C13×C4⋊C4C22⋊C4semidirect
175. #2329C2×C13semidirect
177. C2×#328C2×C13semidirect
179. #1294C2×C13semidirect
180. #1280C2×C13semidirect
286. #450C4×C13semidirect
437. C2×Q8C13×C22⋊C4semidirect
476. C22×C4C13×SD16semidirect
497. C4⋊C4C13×C22⋊C4semidirect
506. C13#9042direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4502
C13×#23292
C13×#17862
C2×C13×#3282
C13×#14382
C13×#12942
C13×#12802
#904213