Finite Group Databasebeta

← C13×#13086 #15699425

Subgroups — C13×#13086 #15699425

Order 3328.

1118 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#99C211yesmaximal, characteristic, complemented
2C13×#2403C211yesmaximal, characteristic
3C2×C13×AΣL(1,𝔽16)C212yesmaximal, complemented
4C13×#1783C211yesmaximal, characteristic, complemented
5C13×#1390C212yesmaximal, complemented
6C23×D4×C13C411yescharacteristic, complemented
7C23×D4×C13C2211yescharacteristic
8C2×C13×#120—21no—
9C2×C13×#120C411yescharacteristic, complemented
10C2×C13×#120C2211yescharacteristic
11C22×C13×C22⋊C4—21no—
12C2×C13×#100—21no—
13C2×C13×#100C2212yes—
14C2×C13×#99—21no—
15C2×C13×#99—24no—
16C2×C13×#99C2212yes—
17C13×#407—21no—
18C13×#392—21no—
19C13×#392—21no—
20C13×#386—21no—
21C13×#386C411yescharacteristic, complemented
22C13×#386C2211yescharacteristic
23C13×#379C411yescharacteristic, complemented
24C13×AΣL(1,𝔽16)—24no—
25C25×C13C2×C411yescharacteristic
26C25×C13C2×C411yescharacteristic, complemented
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—41no—
35C22×D4×C13—41no—
36C22×D4×C13—42no—
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×C13—41no—
45C23×C4×C13C2×C411yescharacteristic, complemented
46C23×C4×C13D411yescharacteristic
47C2×C13×M16—22no—
48C13×#120—22no—
49C13×#120—22no—
50C13×#120—44no—
51C13×#120—42no—
52C2×C13×C22⋊C4—24no—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—21no—
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—41no—
61C2×C13×C22⋊C4—42no—
62C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
63C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
64C13×#100—22no—
65C13×#100—22no—
66C13×#100—42no—
67C13×#99—24no—
68C13×#99—22no—
69C13×#99D414yescomplemented
70C13×C22⋊C8—41no—
71C13×C22⋊C8—41no—
72C13×#95—21no—
73C13×#95—21no—
74#13086C1311yesmaximal, 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—21no—
83C24×C13—22no—
84C24×C13—22no—
85C24×C13—41no—
86C24×C13—42no—
87C24×C13—41no—
88C24×C13—42no—
89C24×C13—42no—
90C24×C13—41no—
91C24×C13—81no—
92C24×C13—81no—
93C24×C13—81no—
94C24×C13C22⋊C411yescharacteristic
95C24×C13C22⋊C411yescharacteristic
96C24×C13C22⋊C411yescharacteristic
97C24×C13C22×C411yescharacteristic
98C24×C13C2×D411yescharacteristic
99C2×D4×C13—24no—
100C2×D4×C13—22no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13—21no—
104C2×D4×C13—21no—
105C2×D4×C13—22no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—41no—
110C2×D4×C13—41no—
111C2×D4×C13—41no—
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—44no—
121C2×D4×C13—44no—
122C2×D4×C13—44no—
123C2×D4×C13—41no—
124C2×D4×C13—41no—
125C2×D4×C13—44no—
126C2×D4×C13—42no—
127C2×D4×C13—42no—
128C2×D4×C13—42no—
129C2×D4×C13—41no—
130C2×D4×C13—41no—
131C2×D4×C13—81no—
132C2×D4×C13—81no—
133C2×D4×C13C2×D412yes—
134C2×D4×C13#4112yes—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—41no—
142C22×C4×C13—42no—
143C22×C4×C13—41no—
144C22×C4×C13—44no—
145C22×C4×C13—42no—
146C22×C4×C13—82no—
147C22×C4×C13—82no—
148C22×C4×C13C22⋊C411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C13×M16—42no—
151C13×M16—42no—
152C2×C8×C13—42no—
153C13×C22⋊C4—22no—
154C13×C22⋊C4—24no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4—42no—
157C13×C22⋊C4—42no—
158C13×C22⋊C4—44no—
159C13×C22⋊C4—42no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—42no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—81no—
164C22×#99C2×C1311yescharacteristic, complemented
165#2403C2×C1311yescharacteristic
166C2×AΣL(1,𝔽16)C2×C1312yescomplemented
167#1783C2×C1311yescharacteristic, complemented
168#1390C2×C1312yescomplemented
169C23×C13—22no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—22no—
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—22no—
183C23×C13—21no—
184C23×C13—21no—
185C23×C13—21no—
186C23×C13—41no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—42no—
198C23×C13—41no—
199C23×C13—41no—
200C23×C13—41no—
201C23×C13—41no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—42no—
209C23×C13—81no—
210C23×C13—81no—
211C23×C13—81no—
212C23×C13—81no—
213C23×C13—82no—
214C23×C13—84no—
215C23×C13—82no—
216C23×C13—82no—
217C23×C13—84no—
218C23×C13—84no—
219C23×C13—84no—
220C23×C13—84no—
221C23×C13—82no—
222C23×C13#9911yescharacteristic
223C23×C13#9911yescharacteristic
224C23×C13#9912yes—
225C23×C13C2×C22⋊C411yescharacteristic
226C23×C13C4×D412yes—
227C23×C13#12011yescharacteristic
228C23×C13#12311yescharacteristic
229D4×C13—42no—
230D4×C13—42no—
231D4×C13—44no—
232D4×C13—44no—
233D4×C13—44no—
234D4×C13—42no—
235D4×C13—42no—
236D4×C13—48no—
237D4×C13—44no—
238D4×C13—84no—
239D4×C13—82no—
240D4×C13—82no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—44no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—88no—
261C2×C4×C13—82no—
262C2×C4×C13—82no—
263C2×C4×C13#12112yes—
264C8×C13—82no—
265C23×D4C4×C1311yescharacteristic, complemented
266C23×D4C22×C1311yescharacteristic
267C2×#120—21no—
268C2×#120C4×C1311yescharacteristic, complemented
269C2×#120C22×C1311yescharacteristic
270C22×C22⋊C4—21no—
271C2×#100—21no—
272C2×#100C22×C1312yes—
273C2×#99—21no—
274C2×#99—24no—
275C2×#99C22×C1312yes—
276#407—21no—
277#392—21no—
278#392—21no—
279#386—21no—
280#386C4×C1311yescharacteristic, complemented
281#386C22×C1311yescharacteristic
282#379C4×C1311yescharacteristic, complemented
283AΣL(1,𝔽16)—24no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—22no—
293C22×C13—21no—
294C22×C13—22no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—42no—
301C22×C13—44no—
302C22×C13—44no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—41no—
307C22×C13—41no—
308C22×C13—41no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—42no—
313C22×C13—41no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13—84no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13—81no—
322C22×C13—81no—
323C22×C13—82no—
324C22×C13—82no—
325C22×C13—84no—
326C22×C13—84no—
327C22×C13—84no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13AΣL(1,𝔽16)12yescomplemented
331C22×C13#38611yescharacteristic
332C22×C13C2×#9911yescharacteristic
333C22×C13C2×#9911yescharacteristic
334C4×C13—22no—
335C4×C13—42no—
336C4×C13—41no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13—84no—
340C25C2×C4×C1311yescharacteristic
341C25C2×C4×C1311yescharacteristic, complemented
342C25D4×C1311yescharacteristic
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4—42no—
352C22×D4—44no—
353C22×D4—41no—
354C22×D4—41no—
355C22×D4C2×C4×C1311yescharacteristic
356C22×D4D4×C1311yescharacteristic
357C22×D4D4×C1311yescharacteristic
358C22×D4C23×C1311yescharacteristic
359C23×C4—41no—
360C23×C4C2×C4×C1311yescharacteristic, complemented
361C23×C4D4×C1311yescharacteristic
362C2×M16—22no—
363#120—22no—
364#120—22no—
365#120—44no—
366#120—42no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4C2×C4×C1311yescharacteristic, complemented
378C2×C22⋊C4C2×C4×C1311yescharacteristic, complemented
379#100—22no—
380#100—22no—
381#100—42no—
382#99—24no—
383#99—22no—
384#99D4×C1314yescomplemented
385C22⋊C8—41no—
386C22⋊C8—41no—
387#95—21no—
388#95—21no—
389C2×C13—21no—
390C2×C13—21no—
391C2×C13—22no—
392C2×C13—41no—
393C2×C13—41no—
394C2×C13—42no—
395C2×C13—41no—
396C2×C13—42no—
397C2×C13—82no—
398C2×C13—81no—
399C2×C13#189811yescharacteristic
400C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
401C2×C13#212111yescharacteristic
402C24—21no—
403C24—22no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—41no—
413C24—42no—
414C24—41no—
415C24—42no—
416C24—42no—
417C24—41no—
418C24—81no—
419C24—81no—
420C24—81no—
421C24C13×C22⋊C411yescharacteristic
422C24C13×C22⋊C411yescharacteristic
423C24C13×C22⋊C411yescharacteristic
424C24C22×C4×C1311yescharacteristic
425C24C2×D4×C1311yescharacteristic
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—22no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—44no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—81no—
459C2×D4—81no—
460C2×D4C2×D4×C1312yes—
461C2×D4C13×#4112yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—42no—
470C22×C4—41no—
471C22×C4—44no—
472C22×C4—42no—
473C22×C4—82no—
474C22×C4—82no—
475C22×C4C13×C22⋊C411yescharacteristic
476C22×C4C2×D4×C1311yescharacteristic
477M16—42no—
478M16—42no—
479C2×C8—42no—
480C22⋊C4—22no—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—44no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—41no—
490C22⋊C4—81no—
491C13#1308611yescharacteristic, direct product factor, Sylow
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—22no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—82no—
537C23—84no—
538C23—82no—
539C23—82no—
540C23—84no—
541C23—84no—
542C23—84no—
543C23—84no—
544C23—82no—
545C23C13×#9911yescharacteristic
546C23C13×#9911yescharacteristic
547C23C13×#9912yes—
548C23C2×C13×C22⋊C411yescharacteristic
549C23C4×D4×C1312yes—
550C23C13×#12011yescharacteristic
551C23C13×#12311yescharacteristic
552D4—42no—
553D4—42no—
554D4—44no—
555D4—44no—
556D4—44no—
557D4—42no—
558D4—42no—
559D4—48no—
560D4—44no—
561D4—84no—
562D4—82no—
563D4—82no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—88no—
584C2×C4—82no—
585C2×C4—82no—
586C2×C4C13×#12112yes—
587C8—82no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—22no—
597C22—21no—
598C22—22no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—44no—
606C22—44no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—81no—
621C22—81no—
622C22—84no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—82no—
628C22—82no—
629C22—84no—
630C22—84no—
631C22—84no—
632C22—81no—
633C22—81no—
634C22C13×AΣL(1,𝔽16)12yescomplemented
635C22C13×#38611yescharacteristic
636C22C2×C13×#9911yescharacteristic
637C22C2×C13×#9911yescharacteristic
638C4—22no—
639C4—42no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—84no—
644C2—21no—
645C2—21no—
646C2—22no—
647C2—41no—
648C2—41no—
649C2—42no—
650C2—41no—
651C2—42no—
652C2—82no—
653C2—81no—
654C2C13×#189811yescharacteristic
655C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
656C2C13×#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×#99C2semidirect
3. C2×C13×AΣL(1,𝔽16)C2semidirect
4. C13×#1783C2semidirect
5. C13×#1390C2semidirect
6. C23×D4×C13C4semidirect
9. C2×C13×#120C4semidirect
21. C13×#386C4semidirect
23. C13×#379C4semidirect
26. C25×C13C2×C4semidirect
45. C23×C4×C13C2×C4semidirect
62. C2×C13×C22⋊C4C2×C4semidirect
63. C2×C13×C22⋊C4C2×C4semidirect
69. C13×#99D4semidirect
74. #13086C13direct (N × H)
164. C22×#99C2×C13semidirect
166. C2×AΣL(1,𝔽16)C2×C13semidirect
167. #1783C2×C13semidirect
168. #1390C2×C13semidirect
265. C23×D4C4×C13semidirect
268. C2×#120C4×C13semidirect
280. #386C4×C13semidirect
282. #379C4×C13semidirect
330. C22×C13AΣL(1,𝔽16)semidirect
341. C25C2×C4×C13semidirect
360. C23×C4C2×C4×C13semidirect
377. C2×C22⋊C4C2×C4×C13semidirect
378. C2×C22⋊C4C2×C4×C13semidirect
384. #99D4×C13semidirect
491. C13#13086direct (N × H)
634. 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×#992
C13×#24032
C2×C13×AΣL(1,𝔽16)2
C13×#17832
C13×#13902
#1308613