Finite Group Databasebeta

← C13×#13088 #15699427

Subgroups — C13×#13088 #15699427

Order 3328.

1040 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#99C211yesmaximal, characteristic, complemented
2C13×#2433C211yesmaximal, characteristic
3C2×C13×#353C212yesmaximal, complemented
4C13×#1781C211yesmaximal, characteristic, complemented
5C13×#1393C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#127C411yescharacteristic, complemented
8C2×C13×#127C2211yescharacteristic
9C2×C13×#121C411yescharacteristic, complemented
10C2×C13×#120—21no—
11C2×C13×#120—21no—
12C22×C13×C22⋊C4—21no—
13C2×C13×#99—21no—
14C2×C13×#99—24no—
15C2×C13×#99—21no—
16C2×C13×#99C2212yes—
17C2×C13×#99C2212yes—
18C13×#392—21no—
19C13×#392—21no—
20C13×#390C411yescharacteristic, complemented
21C13×#390C2211yescharacteristic
22C13×#379—21no—
23C4×C13×C22⋊C4C411yescharacteristic, complemented
24C13×#353—24no—
25C25×C13D411yescharacteristic
26C25×C13D411yescharacteristic
27C22×D4×C13—22no—
28C22×D4×C13—22no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13—41no—
35C22×D4×C13—41no—
36C22×D4×C13—42no—
37C22×D4×C13C2×C411yescharacteristic
38C22×D4×C13C2×C411yescharacteristic, complemented
39C22×D4×C13D411yescharacteristic
40C22×D4×C13D411yescharacteristic
41C22×D4×C13C2311yescharacteristic
42C23×C4×C13—41no—
43C23×C4×C13C2×C411yescharacteristic
44C13×#127—22no—
45C13×#127—22no—
46C13×#127—42no—
47C13×#121—41no—
48C13×#121—41no—
49C13×#120—44no—
50C13×#120—44no—
51C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—24no—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—41no—
62C2×C13×C22⋊C4—42no—
63C2×C13×C22⋊C4—41no—
64C2×C13×C22⋊C4—41no—
65C2×C42×C13C2×C411yescharacteristic, complemented
66C2×C42×C13C2×C411yescharacteristic, complemented
67C13×#99—24no—
68C13×#99—22no—
69C13×#99—22no—
70C13×#99—22no—
71C13×#99—42no—
72C13×#99D414yescomplemented
73C13×#95—21no—
74#13088C1311yesmaximal, characteristic, direct product factor, Sylow
75C24×C13—21no—
76C24×C13—22no—
77C24×C13—21no—
78C24×C13—21no—
79C24×C13—21no—
80C24×C13—21no—
81C24×C13—21no—
82C24×C13—22no—
83C24×C13—21no—
84C24×C13—41no—
85C24×C13—42no—
86C24×C13—42no—
87C24×C13—81no—
88C24×C13—81no—
89C24×C13C22⋊C411yescharacteristic
90C24×C13C22⋊C411yescharacteristic
91C24×C13C22⋊C411yescharacteristic
92C24×C13C2×D411yescharacteristic
93C24×C13C2×D411yescharacteristic
94C2×D4×C13—22no—
95C2×D4×C13—22no—
96C2×D4×C13—21no—
97C2×D4×C13—22no—
98C2×D4×C13—21no—
99C2×D4×C13—22no—
100C2×D4×C13—22no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—41no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—42no—
110C2×D4×C13—42no—
111C2×D4×C13—42no—
112C2×D4×C13—42no—
113C2×D4×C13—44no—
114C2×D4×C13—44no—
115C2×D4×C13—44no—
116C2×D4×C13—44no—
117C2×D4×C13—42no—
118C2×D4×C13—42no—
119C2×D4×C13—42no—
120C2×D4×C13—41no—
121C2×D4×C13—41no—
122C2×D4×C13—42no—
123C2×D4×C13—41no—
124C2×D4×C13—42no—
125C2×D4×C13—41no—
126C2×D4×C13—81no—
127C2×D4×C13—81no—
128C2×D4×C13—81no—
129C2×D4×C13—81no—
130C2×D4×C13C2×D412yes—
131C2×D4×C13#4112yes—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—41no—
139C22×C4×C13—44no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—82no—
143C22×C4×C13—82no—
144C22×C4×C13C22⋊C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C13×C4⋊C4—41no—
147C13×C22⋊C4—24no—
148C13×C22⋊C4—24no—
149C13×C22⋊C4—42no—
150C13×C22⋊C4—42no—
151C13×C22⋊C4—42no—
152C13×C22⋊C4—42no—
153C13×C22⋊C4—42no—
154C13×C22⋊C4—44no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4—42no—
157C13×C22⋊C4—42no—
158C13×C22⋊C4—82no—
159C13×C22⋊C4—82no—
160C42×C13—22no—
161C42×C13—41no—
162C22×#99C2×C1311yescharacteristic, complemented
163#2433C2×C1311yescharacteristic
164C2×#353C2×C1312yescomplemented
165#1781C2×C1311yescharacteristic, complemented
166#1393C2×C1312yescomplemented
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—22no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—21no—
173C23×C13—21no—
174C23×C13—21no—
175C23×C13—21no—
176C23×C13—21no—
177C23×C13—21no—
178C23×C13—21no—
179C23×C13—21no—
180C23×C13—21no—
181C23×C13—21no—
182C23×C13—21no—
183C23×C13—41no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—41no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—42no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13—41no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—81no—
206C23×C13—81no—
207C23×C13—81no—
208C23×C13—81no—
209C23×C13—84no—
210C23×C13—82no—
211C23×C13—82no—
212C23×C13—84no—
213C23×C13—84no—
214C23×C13#9911yescharacteristic
215C23×C13#9911yescharacteristic
216C23×C13#9912yes—
217C23×C13C2×C22⋊C411yescharacteristic
218C23×C13#12011yescharacteristic
219C23×C13#12112yes—
220C23×C13#12311yescharacteristic
221D4×C13—42no—
222D4×C13—42no—
223D4×C13—44no—
224D4×C13—44no—
225D4×C13—42no—
226D4×C13—42no—
227D4×C13—82no—
228D4×C13—84no—
229D4×C13—82no—
230D4×C13—84no—
231D4×C13—82no—
232D4×C13—84no—
233D4×C13—82no—
234D4×C13—82no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—44no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—88no—
253C2×C4×C13—82no—
254C2×C4×C13—82no—
255C2×C4×C13—82no—
256C2×C4×C13—82no—
257C2×C4×C13—82no—
258C2×C4×C13C4×D412yes—
259C23×D4C22×C1311yescharacteristic
260C2×#127C4×C1311yescharacteristic, complemented
261C2×#127C22×C1311yescharacteristic
262C2×#121C4×C1311yescharacteristic, complemented
263C2×#120—21no—
264C2×#120—21no—
265C22×C22⋊C4—21no—
266C2×#99—21no—
267C2×#99—24no—
268C2×#99—21no—
269C2×#99C22×C1312yes—
270C2×#99C22×C1312yes—
271#392—21no—
272#392—21no—
273#390C4×C1311yescharacteristic, complemented
274#390C22×C1311yescharacteristic
275#379—21no—
276C4×C22⋊C4C4×C1311yescharacteristic, complemented
277#353—24no—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—21no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—22no—
287C22×C13—22no—
288C22×C13—21no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—41no—
293C22×C13—42no—
294C22×C13—41no—
295C22×C13—44no—
296C22×C13—44no—
297C22×C13—42no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—41no—
306C22×C13—41no—
307C22×C13—81no—
308C22×C13—81no—
309C22×C13—81no—
310C22×C13—84no—
311C22×C13—81no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13—82no—
317C22×C13—82no—
318C22×C13—84no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13—81no—
322C22×C13#35312yescomplemented
323C22×C13#38611yescharacteristic
324C22×C13C2×#9911yescharacteristic
325C22×C13C2×#9911yescharacteristic
326C4×C13—22no—
327C4×C13—42no—
328C4×C13—42no—
329C4×C13—41no—
330C4×C13—84no—
331C4×C13—81no—
332C4×C13—162no—
333C25D4×C1311yescharacteristic
334C25D4×C1311yescharacteristic
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—42no—
345C22×D4C2×C4×C1311yescharacteristic
346C22×D4C2×C4×C1311yescharacteristic, complemented
347C22×D4D4×C1311yescharacteristic
348C22×D4D4×C1311yescharacteristic
349C22×D4C23×C1311yescharacteristic
350C23×C4—41no—
351C23×C4C2×C4×C1311yescharacteristic
352#127—22no—
353#127—22no—
354#127—42no—
355#121—41no—
356#121—41no—
357#120—44no—
358#120—44no—
359C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
360C2×C22⋊C4—21no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C42C2×C4×C1311yescharacteristic, complemented
374C2×C42C2×C4×C1311yescharacteristic, complemented
375#99—24no—
376#99—22no—
377#99—22no—
378#99—22no—
379#99—42no—
380#99D4×C1314yescomplemented
381#95—21no—
382C2×C13—21no—
383C2×C13—21no—
384C2×C13—22no—
385C2×C13—41no—
386C2×C13—42no—
387C2×C13—41no—
388C2×C13—42no—
389C2×C13—41no—
390C2×C13—81no—
391C2×C13—161no—
392C2×C13#189811yescharacteristic
393C2×C13C2×#35311yescharacteristic
394C2×C13#212711yescharacteristic
395C24—21no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—41no—
405C24—42no—
406C24—42no—
407C24—81no—
408C24—81no—
409C24C13×C22⋊C411yescharacteristic
410C24C13×C22⋊C411yescharacteristic
411C24C13×C22⋊C411yescharacteristic
412C24C2×D4×C1311yescharacteristic
413C24C2×D4×C1311yescharacteristic
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—42no—
445C2×D4—41no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—81no—
450C2×D4C2×D4×C1312yes—
451C2×D4C13×#4112yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—44no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—82no—
463C22×C4—82no—
464C22×C4C13×C22⋊C411yescharacteristic
465C22×C4C22×C4×C1311yescharacteristic
466C4⋊C4—41no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—44no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—82no—
479C22⋊C4—82no—
480C42—22no—
481C42—41no—
482C13#1308811yescharacteristic, direct product factor, Sylow
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—81no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—84no—
526C23—82no—
527C23—82no—
528C23—84no—
529C23—84no—
530C23C13×#9911yescharacteristic
531C23C13×#9911yescharacteristic
532C23C13×#9912yes—
533C23C2×C13×C22⋊C411yescharacteristic
534C23C13×#12011yescharacteristic
535C23C13×#12112yes—
536C23C13×#12311yescharacteristic
537D4—42no—
538D4—42no—
539D4—44no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—82no—
544D4—84no—
545D4—82no—
546D4—84no—
547D4—82no—
548D4—84no—
549D4—82no—
550D4—82no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—44no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—88no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C4×D4×C1312yes—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—22no—
584C22—22no—
585C22—21no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—44no—
593C22—44no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—84no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—82no—
614C22—82no—
615C22—84no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C13×#35312yescomplemented
620C22C13×#38611yescharacteristic
621C22C2×C13×#9911yescharacteristic
622C22C2×C13×#9911yescharacteristic
623C4—22no—
624C4—42no—
625C4—42no—
626C4—41no—
627C4—84no—
628C4—81no—
629C4—162no—
630C2—21no—
631C2—21no—
632C2—22no—
633C2—41no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—41no—
638C2—81no—
639C2—161no—
640C2C13×#189811yescharacteristic
641C2C2×C13×#35311yescharacteristic
642C2C13×#212711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC13×#2433C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C23×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×#99C2semidirect
3. C2×C13×#353C2semidirect
4. C13×#1781C2semidirect
5. C13×#1393C2semidirect
7. C2×C13×#127C4semidirect
9. C2×C13×#121C4semidirect
20. C13×#390C4semidirect
23. C4×C13×C22⋊C4C4semidirect
38. C22×D4×C13C2×C4semidirect
51. C2×C13×C4⋊C4C2×C4semidirect
65. C2×C42×C13C2×C4semidirect
66. C2×C42×C13C2×C4semidirect
72. C13×#99D4semidirect
74. #13088C13direct (N × H)
162. C22×#99C2×C13semidirect
164. C2×#353C2×C13semidirect
165. #1781C2×C13semidirect
166. #1393C2×C13semidirect
260. C2×#127C4×C13semidirect
262. C2×#121C4×C13semidirect
273. #390C4×C13semidirect
276. C4×C22⋊C4C4×C13semidirect
322. C22×C13#353semidirect
346. C22×D4C2×C4×C13semidirect
359. C2×C4⋊C4C2×C4×C13semidirect
373. C2×C42C2×C4×C13semidirect
374. C2×C42C2×C4×C13semidirect
380. #99D4×C13semidirect
482. C13#13088direct (N × H)
619. C22C13×#353semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#992
C13×#24332
C2×C13×#3532
C13×#17812
C13×#13932
#1308813