Finite Group Databasebeta

← C13×#10322 #15696661

Subgroups — C13×#10322 #15696661

Order 3328.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3187C211yesmaximal, characteristic, complemented
2C13×#2848C211yesmaximal, characteristic, complemented
3C13×#2847C211yesmaximal, characteristic
4C13×#1779C211yesmaximal, characteristic, complemented
5C13×#1520C211yesmaximal, characteristic, complemented
6C13×#1519C211yesmaximal, characteristic, complemented
7C13×#1289C211yesmaximal, characteristic, complemented
8C24×C4×C13C2211yescharacteristic
9C2×C13×C22⋊Q8—21no—
10C2×C13×C22⋊Q8C2211yescharacteristic
11C2×C13×#121—21no—
12C2×C13×#121C2211yescharacteristic
13C2×C13×#120—21no—
14C13×#483—21no—
15C13×#481—21no—
16C13×#465—22no—
17C13×#450—21no—
18C13×#448—21no—
19C2×C13×C22⋊C8—22no—
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C13×#386—21no—
23C13×#386—22no—
24C13×#385—21no—
25C13×#385—22no—
26C13×#380—21no—
27C13×#380—21no—
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C13×#379—21no—
31C13×#328—22no—
32C13×#327—22no—
33C25×C13D411yescharacteristic
34C22×Q8×C13D411yescharacteristic, complemented
35C22×D4×C13—22no—
36C22×D4×C13—21no—
37C22×D4×C13D411yescharacteristic
38C23×C4×C13—21no—
39C23×C4×C13—21no—
40C23×C4×C13—21no—
41C23×C4×C13—21no—
42C23×C4×C13—21no—
43C23×C4×C13—21no—
44C23×C4×C13—44no—
45C23×C4×C13D411yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C2×C13×SD16—22no—
48C22×C8×C13—21no—
49C22×C8×C13D412yescomplemented
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×C22⋊Q8—21no—
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—44no—
55C13×#121—21no—
56C13×#121—21no—
57C13×#121—21no—
58C13×#121—21no—
59C13×#121—44no—
60C13×#120—42no—
61C13×#120—42no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4D411yescharacteristic, complemented
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C13×#106—22no—
77C13×#103—22no—
78C13×#102—22no—
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—44no—
84C13×#95—22no—
85C13×#95—22no—
86C13×#95D412yes—
87C13×#95D412yescomplemented
88#10322C1311yesmaximal, characteristic, direct product factor, Sylow
89C24×C13—21no—
90C24×C13—21no—
91C24×C13—21no—
92C24×C13—21no—
93C24×C13—21no—
94C24×C13—21no—
95C24×C13—21no—
96C24×C13—42no—
97C24×C13—42no—
98C24×C13SD1612yescomplemented
99C24×C13C2×D411yescharacteristic
100C2×Q8×C13—21no—
101C2×Q8×C13—21no—
102C2×Q8×C13—42no—
103C2×D4×C13—21no—
104C2×D4×C13—21no—
105C2×D4×C13—42no—
106C2×D4×C13—44no—
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C2×D4×C13—41no—
110C2×D4×C13—41no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C22×C4×C13—24no—
116C22×C4×C13—24no—
117C22×C4×C13—24no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13#4111yescharacteristic
147C13×SD16—82no—
148C2×C8×C13—22no—
149C2×C8×C13—42no—
150C2×C8×C13—42no—
151C2×C8×C13—41no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4—44no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—41no—
161C13×C22⋊C4—44no—
162C13×C22⋊C4—44no—
163C13×C22⋊C4—44no—
164C13×C22⋊C4—44no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4—41no—
169C13×C22⋊C4—41no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173#3187C2×C1311yescharacteristic, complemented
174#2848C2×C1311yescharacteristic, complemented
175#2847C2×C1311yescharacteristic
176#1779C2×C1311yescharacteristic, complemented
177#1520C2×C1311yescharacteristic, complemented
178#1519C2×C1311yescharacteristic, complemented
179#1289C2×C1311yescharacteristic, complemented
180C23×C13—22no—
181C23×C13—22no—
182C23×C13—22no—
183C23×C13—22no—
184C23×C13—22no—
185C23×C13—22no—
186C23×C13—22no—
187C23×C13—22no—
188C23×C13—22no—
189C23×C13—41no—
190C23×C13—44no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—44no—
199C23×C13—44no—
200C23×C13—44no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13#12011yescharacteristic
211C23×C13#12011yescharacteristic
212C23×C13#12111yescharacteristic
213C23×C13C2×SD1611yescharacteristic
214C23×C13#13511yescharacteristic
215C23×C13AGL(1,ℤ/8)11yescharacteristic
216C23×C13#13711yescharacteristic
217Q8×C13—42no—
218Q8×C13—81no—
219D4×C13—42no—
220D4×C13—81no—
221D4×C13—88no—
222D4×C13—81no—
223D4×C13—81no—
224D4×C13—81no—
225D4×C13—81no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—44no—
236C2×C4×C13—44no—
237C2×C4×C13—44no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—44no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13#12011yescharacteristic
257C2×C4×C13#12111yescharacteristic
258C2×C4×C13#12111yescharacteristic
259C2×C4×C13#12711yescharacteristic
260C8×C13—42no—
261C8×C13—81no—
262C24×C4C22×C1311yescharacteristic
263C2×C22⋊Q8—21no—
264C2×C22⋊Q8C22×C1311yescharacteristic
265C2×#121—21no—
266C2×#121C22×C1311yescharacteristic
267C2×#120—21no—
268#483—21no—
269#481—21no—
270#465—22no—
271#450—21no—
272#448—21no—
273C2×C22⋊C8—22no—
274C2×C22⋊C8C22×C1311yescharacteristic
275C2×C22⋊C8C22×C1311yescharacteristic
276#386—21no—
277#386—22no—
278#385—21no—
279#385—22no—
280#380—21no—
281#380—21no—
282#380C22×C1311yescharacteristic
283#380C22×C1311yescharacteristic
284#379—21no—
285#328—22no—
286#327—22no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—24no—
294C22×C13—24no—
295C22×C13—24no—
296C22×C13—41no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—82no—
313C22×C13—82no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13#39211yescharacteristic
318C22×C13#44811yescharacteristic
319C22×C13#44911yescharacteristic
320C22×C13#45011yescharacteristic
321C22×C13#45211yescharacteristic
322C22×C13#46511yescharacteristic
323C22×C13#46811yescharacteristic
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—21no—
327C4×C13—42no—
328C4×C13—82no—
329C4×C13—82no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13B(4,𝔽2)12yes—
334C25D4×C1311yescharacteristic
335C22×Q8D4×C1311yescharacteristic, complemented
336C22×D4—22no—
337C22×D4—21no—
338C22×D4D4×C1311yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—44no—
346C23×C4D4×C1311yescharacteristic
347C23×C4C23×C1311yescharacteristic
348C2×SD16—22no—
349C22×C8—21no—
350C22×C8D4×C1312yescomplemented
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—44no—
356#121—21no—
357#121—21no—
358#121—21no—
359#121—21no—
360#121—44no—
361#120—42no—
362#120—42no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C1311yescharacteristic
368C2×C4⋊C4D4×C1311yescharacteristic, complemented
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377#106—22no—
378#103—22no—
379#102—22no—
380C22⋊C8—21no—
381C22⋊C8—21no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384C22⋊C8—44no—
385#95—22no—
386#95—22no—
387#95D4×C1312yes—
388#95D4×C1312yescomplemented
389C2×C13—21no—
390C2×C13—21no—
391C2×C13—21no—
392C2×C13—21no—
393C2×C13—21no—
394C2×C13—21no—
395C2×C13—44no—
396C2×C13—161no—
397C2×C13#200011yescharacteristic
398C2×C13#201011yescharacteristic
399C2×C13#202111yescharacteristic
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—42no—
408C24—42no—
409C24C13×SD1612yescomplemented
410C24C2×D4×C1311yescharacteristic
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—42no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C2×D4×C1311yescharacteristic
453C22×C4C2×D4×C1311yescharacteristic
454C22×C4C2×D4×C1311yescharacteristic
455C22×C4C2×D4×C1311yescharacteristic
456C22×C4C2×D4×C1311yescharacteristic
457C22×C4C13×#4111yescharacteristic
458SD16—82no—
459C2×C8—22no—
460C2×C8—42no—
461C2×C8—42no—
462C2×C8—41no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—44no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C22⋊C4—44no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C13#1032211yescharacteristic, direct product factor, Sylow
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C13×#12011yescharacteristic
516C23C13×#12011yescharacteristic
517C23C13×#12111yescharacteristic
518C23C2×C13×SD1611yescharacteristic
519C23C13×#13511yescharacteristic
520C23C13×AGL(1,ℤ/8)11yescharacteristic
521C23C13×#13711yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4C13×#12011yescharacteristic
562C2×C4C13×#12111yescharacteristic
563C2×C4C13×#12111yescharacteristic
564C2×C4C13×#12711yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C13×#39211yescharacteristic
598C22C13×#44811yescharacteristic
599C22C13×#44911yescharacteristic
600C22C13×#45011yescharacteristic
601C22C13×#45211yescharacteristic
602C22C13×#46511yescharacteristic
603C22C13×#46811yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C13×B(4,𝔽2)12yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2C13×#200011yescharacteristic
623C2C13×#201011yescharacteristic
624C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2847C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3187C2semidirect
2. C13×#2848C2semidirect
4. C13×#1779C2semidirect
5. C13×#1520C2semidirect
6. C13×#1519C2semidirect
7. C13×#1289C2semidirect
34. C22×Q8×C13D4semidirect
49. C22×C8×C13D4semidirect
67. C2×C13×C4⋊C4D4semidirect
87. C13×#95D4semidirect
88. #10322C13direct (N × H)
98. C24×C13SD16semidirect
173. #3187C2×C13semidirect
174. #2848C2×C13semidirect
176. #1779C2×C13semidirect
177. #1520C2×C13semidirect
178. #1519C2×C13semidirect
179. #1289C2×C13semidirect
335. C22×Q8D4×C13semidirect
350. C22×C8D4×C13semidirect
368. C2×C4⋊C4D4×C13semidirect
388. #95D4×C13semidirect
409. C24C13×SD16semidirect
484. C13#10322direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31872
C13×#28482
C13×#28472
C13×#17792
C13×#15202
C13×#15192
C13×#12892
#1032213