Finite Group Databasebeta

← C13×#13082 #15699421

Subgroups — C13×#13082 #15699421

Order 3328.

1088 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×#100C211yesmaximal, characteristic, complemented
2C13×#2403C211yesmaximal, characteristic
3C2×C13×AΣL(1,𝔽16)C212yesmaximal, complemented
4C13×#1781C211yesmaximal, characteristic, complemented
5C13×#1390C212yesmaximal, complemented
6C23×D4×C13C411yescharacteristic, complemented
7C23×D4×C13C2211yescharacteristic
8C22×C13×M16—21no—
9C2×C13×#120—21no—
10C2×C13×#120C411yescharacteristic, complemented
11C2×C13×#120C2211yescharacteristic
12C2×C13×#100—21no—
13C2×C13×#100—24no—
14C2×C13×#100C2212yes—
15C2×C13×#99—21no—
16C2×C13×#99C2212yes—
17C13×#392—21no—
18C13×#392—21no—
19C13×#386—21no—
20C13×#386C411yescharacteristic, complemented
21C13×#386C2211yescharacteristic
22C13×#379—21no—
23C13×#379C411yescharacteristic, complemented
24C13×AΣL(1,𝔽16)—24no—
25C25×C13C2×C411yescharacteristic
26C25×C13C2×C411yescharacteristic
27C25×C13D411yescharacteristic
28C22×D4×C13—21no—
29C22×D4×C13—22no—
30C22×D4×C13—22no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13—42no—
35C22×D4×C13—41no—
36C22×D4×C13—41no—
37C22×D4×C13—44no—
38C22×D4×C13—41no—
39C22×D4×C13—41no—
40C22×D4×C13C2×C411yescharacteristic
41C22×D4×C13D411yescharacteristic
42C22×D4×C13D411yescharacteristic
43C22×D4×C13C2311yescharacteristic
44C23×C4×C13C2×C411yescharacteristic
45C23×C4×C13D411yescharacteristic
46C2×C13×M16—24no—
47C2×C13×M16—22no—
48C2×C13×M16—41no—
49C2×C13×M16—42no—
50C22×C8×C13—41no—
51C13×#120—22no—
52C13×#120—22no—
53C13×#120—44no—
54C13×#120—42no—
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—21no—
62C2×C13×C22⋊C4—41no—
63C2×C13×C22⋊C4—41no—
64C2×C13×C22⋊C4C2×C411yescharacteristic
65C2×C13×C22⋊C4C2×C411yescharacteristic
66C13×#100—24no—
67C13×#100—22no—
68C13×#100D414yescomplemented
69C13×#99—22no—
70C13×#99—22no—
71C13×#99—42no—
72C13×#95—21no—
73C13×#95—21no—
74#13082C1311yesmaximal, characteristic, direct product factor, Sylow
75C24×C13—21no—
76C24×C13—21no—
77C24×C13—21no—
78C24×C13—21no—
79C24×C13—21no—
80C24×C13—22no—
81C24×C13—22no—
82C24×C13—22no—
83C24×C13—41no—
84C24×C13—41no—
85C24×C13—42no—
86C24×C13—41no—
87C24×C13—42no—
88C24×C13—42no—
89C24×C13—41no—
90C24×C13—81no—
91C24×C13—81no—
92C24×C13—81no—
93C24×C13C22⋊C411yescharacteristic
94C24×C13C22⋊C411yescharacteristic
95C24×C13C22⋊C411yescharacteristic
96C24×C13C22×C411yescharacteristic
97C24×C13C2×D411yescharacteristic
98C2×D4×C13—24no—
99C2×D4×C13—22no—
100C2×D4×C13—22no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13—21no—
104C2×D4×C13—21no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—41no—
110C2×D4×C13—41no—
111C2×D4×C13—44no—
112C2×D4×C13—44no—
113C2×D4×C13—44no—
114C2×D4×C13—44no—
115C2×D4×C13—42no—
116C2×D4×C13—42no—
117C2×D4×C13—42no—
118C2×D4×C13—42no—
119C2×D4×C13—44no—
120C2×D4×C13—44no—
121C2×D4×C13—44no—
122C2×D4×C13—41no—
123C2×D4×C13—41no—
124C2×D4×C13—44no—
125C2×D4×C13—42no—
126C2×D4×C13—42no—
127C2×D4×C13—42no—
128C2×D4×C13—42no—
129C2×D4×C13—81no—
130C2×D4×C13—81no—
131C2×D4×C13C2×D412yes—
132C2×D4×C13#4112yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—42no—
142C22×C4×C13—41no—
143C22×C4×C13—42no—
144C22×C4×C13C22⋊C411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C13×M16—24no—
147C13×M16—44no—
148C13×M16—42no—
149C2×C8×C13—44no—
150C2×C8×C13—42no—
151C13×C22⋊C4—22no—
152C13×C22⋊C4—42no—
153C13×C22⋊C4—42no—
154C13×C22⋊C4—42no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—42no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—81no—
162C13×C22⋊C4—82no—
163C13×C22⋊C4—82no—
164C22×#100C2×C1311yescharacteristic, complemented
165#2403C2×C1311yescharacteristic
166C2×AΣL(1,𝔽16)C2×C1312yescomplemented
167#1781C2×C1311yescharacteristic, complemented
168#1390C2×C1312yescomplemented
169C23×C13—22no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13—21no—
173C23×C13—21no—
174C23×C13—21no—
175C23×C13—21no—
176C23×C13—22no—
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—42no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—42no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13—41no—
200C23×C13—41no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—42no—
208C23×C13—81no—
209C23×C13—81no—
210C23×C13—81no—
211C23×C13—81no—
212C23×C13—82no—
213C23×C13—84no—
214C23×C13—84no—
215C23×C13—84no—
216C23×C13—84no—
217C23×C13—84no—
218C23×C13—84no—
219C23×C13—82no—
220C23×C13#9911yescharacteristic
221C23×C13#9911yescharacteristic
222C23×C13C2×C22⋊C411yescharacteristic
223C23×C13C4×D412yes—
224C23×C13#12112yes—
225D4×C13—42no—
226D4×C13—42no—
227D4×C13—44no—
228D4×C13—44no—
229D4×C13—42no—
230D4×C13—42no—
231D4×C13—44no—
232D4×C13—48no—
233D4×C13—44no—
234D4×C13—84no—
235D4×C13—84no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—41no—
246C2×C4×C13—42no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—82no—
256C2×C4×C13—82no—
257C2×C4×C13—82no—
258C2×C4×C13#9912yes—
259C2×C4×C13#12011yescharacteristic
260C2×C4×C13#12311yescharacteristic
261C8×C13—44no—
262C23×D4C4×C1311yescharacteristic, complemented
263C23×D4C22×C1311yescharacteristic
264C22×M16—21no—
265C2×#120—21no—
266C2×#120C4×C1311yescharacteristic, complemented
267C2×#120C22×C1311yescharacteristic
268C2×#100—21no—
269C2×#100—24no—
270C2×#100C22×C1312yes—
271C2×#99—21no—
272C2×#99C22×C1312yes—
273#392—21no—
274#392—21no—
275#386—21no—
276#386C4×C1311yescharacteristic, complemented
277#386C22×C1311yescharacteristic
278#379—21no—
279#379C4×C1311yescharacteristic, complemented
280AΣL(1,𝔽16)—24no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—22no—
289C22×C13—22no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—42no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—41no—
306C22×C13—41no—
307C22×C13—41no—
308C22×C13—41no—
309C22×C13—81no—
310C22×C13—84no—
311C22×C13—84no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—84no—
318C22×C13—84no—
319C22×C13—84no—
320C22×C13—84no—
321C22×C13—81no—
322C22×C13—81no—
323C22×C13AΣL(1,𝔽16)12yescomplemented
324C22×C13#38611yescharacteristic
325C22×C13C2×#9911yescharacteristic
326C22×C13C2×#9911yescharacteristic
327C4×C13—21no—
328C4×C13—22no—
329C4×C13—21no—
330C4×C13—42no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13—162no—
334C25C2×C4×C1311yescharacteristic
335C25C2×C4×C1311yescharacteristic
336C25D4×C1311yescharacteristic
337C22×D4—21no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—42no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—44no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4C2×C4×C1311yescharacteristic
350C22×D4D4×C1311yescharacteristic
351C22×D4D4×C1311yescharacteristic
352C22×D4C23×C1311yescharacteristic
353C23×C4C2×C4×C1311yescharacteristic
354C23×C4D4×C1311yescharacteristic
355C2×M16—24no—
356C2×M16—22no—
357C2×M16—41no—
358C2×M16—42no—
359C22×C8—41no—
360#120—22no—
361#120—22no—
362#120—44no—
363#120—42no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4C2×C4×C1311yescharacteristic
374C2×C22⋊C4C2×C4×C1311yescharacteristic
375#100—24no—
376#100—22no—
377#100D4×C1314yescomplemented
378#99—22no—
379#99—22no—
380#99—42no—
381#95—21no—
382#95—21no—
383C2×C13—21no—
384C2×C13—21no—
385C2×C13—22no—
386C2×C13—42no—
387C2×C13—41no—
388C2×C13—42no—
389C2×C13—81no—
390C2×C13—82no—
391C2×C13—81no—
392C2×C13#189811yescharacteristic
393C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
394C2×C13#212111yescharacteristic
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—41no—
410C24—81no—
411C24—81no—
412C24—81no—
413C24C13×C22⋊C411yescharacteristic
414C24C13×C22⋊C411yescharacteristic
415C24C13×C22⋊C411yescharacteristic
416C24C22×C4×C1311yescharacteristic
417C24C2×D4×C1311yescharacteristic
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—81no—
450C2×D4—81no—
451C2×D4C2×D4×C1312yes—
452C2×D4C13×#4112yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4C13×C22⋊C411yescharacteristic
465C22×C4C2×D4×C1311yescharacteristic
466M16—24no—
467M16—44no—
468M16—42no—
469C2×C8—44no—
470C2×C8—42no—
471C22⋊C4—22no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—81no—
482C22⋊C4—82no—
483C22⋊C4—82no—
484C13#1308211yescharacteristic, direct product factor, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
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—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—42no—
523C23—42no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23C13×#9911yescharacteristic
537C23C13×#9911yescharacteristic
538C23C2×C13×C22⋊C411yescharacteristic
539C23C4×D4×C1312yes—
540C23C13×#12112yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C13×#9912yes—
575C2×C4C13×#12011yescharacteristic
576C2×C4C13×#12311yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22C13×AΣL(1,𝔽16)12yescomplemented
621C22C13×#38611yescharacteristic
622C22C2×C13×#9911yescharacteristic
623C22C2×C13×#9911yescharacteristic
624C4—21no—
625C4—22no—
626C4—21no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2C13×#189811yescharacteristic
641C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
642C2C13×#212111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC13×#2403C2
LCSG ▷ C24 ▷ 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×#100C2semidirect
3. C2×C13×AΣL(1,𝔽16)C2semidirect
4. C13×#1781C2semidirect
5. C13×#1390C2semidirect
6. C23×D4×C13C4semidirect
10. C2×C13×#120C4semidirect
20. C13×#386C4semidirect
23. C13×#379C4semidirect
68. C13×#100D4semidirect
74. #13082C13direct (N × H)
164. C22×#100C2×C13semidirect
166. C2×AΣL(1,𝔽16)C2×C13semidirect
167. #1781C2×C13semidirect
168. #1390C2×C13semidirect
262. C23×D4C4×C13semidirect
266. C2×#120C4×C13semidirect
276. #386C4×C13semidirect
279. #379C4×C13semidirect
323. C22×C13AΣL(1,𝔽16)semidirect
377. #100D4×C13semidirect
484. C13#13082direct (N × H)
620. C22C13×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1002
C13×#24032
C2×C13×AΣL(1,𝔽16)2
C13×#17812
C13×#13902
#1308213