Finite Group Databasebeta

← C13×#33855 #15720194

Subgroups — C13×#33855 #15720194

Order 3328.

640 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3417C211yesmaximal, characteristic, complemented
2C13×#3416C211yesmaximal, characteristic, complemented
3C13×#3293C211yesmaximal, characteristic, complemented
4C13×#3290C211yesmaximal, characteristic, complemented
5C13×#2251C211yesmaximal, characteristic, complemented
6C13×#2223C211yesmaximal, characteristic, complemented
7C13×#2222C211yesmaximal, characteristic, complemented
8C13×#2214C211yesmaximal, characteristic, complemented
9C13×#2212C211yesmaximal, characteristic, complemented
10C13×#2195C211yesmaximal, characteristic, complemented
11C13×#2195C211yesmaximal, characteristic, complemented
12C13×#2194C211yesmaximal, characteristic, complemented
13C13×#2193C211yesmaximal, characteristic, complemented
14C13×#2179C211yesmaximal, characteristic, complemented
15C13×#2171C211yesmaximal, characteristic, complemented
16C13×#578—21no—
17C13×#578C2211yescharacteristic
18C13×#578C2211yescharacteristic
19C13×#578C2211yescharacteristic, complemented
20C13×#577—21no—
21C13×#576C2211yescharacteristic
22C13×#510—21no—
23C13×#510—21no—
24C13×#510—21no—
25C13×#510C2211yescharacteristic
26C13×#510C2211yescharacteristic
27C13×#510C2211yescharacteristic, complemented
28C13×#509—21no—
29C13×#509C2211yescharacteristic
30C13×#508—21no—
31C13×#508—21no—
32C13×#508C2211yescharacteristic
33C2×C13×Q32—21no—
34C2×C13×Q32C2211yescharacteristic, complemented
35C2×C13×Q32C2211yescharacteristic, complemented
36C2×C13×SD32—21no—
37C2×C13×SD32C2211yescharacteristic
38C2×C13×SD32C2211yescharacteristic
39C13×#504C2211yescharacteristic
40C13×#504C2211yescharacteristic, complemented
41C13×#495C2211yescharacteristic
42C13×#494C2211yescharacteristic, complemented
43C13×#473—21no—
44C13×#473C2211yescharacteristic
45C13×#473C2211yescharacteristic
46C13×#473C2211yescharacteristic, complemented
47C13×#472C2211yescharacteristic
48C13×#471—21no—
49C13×#456—21no—
50C13×#456—21no—
51C13×#455—21no—
52C13×#454—21no—
53C13×#443C2211yescharacteristic
54C13×#443C2211yescharacteristic
55C13×#443C2211yescharacteristic, complemented
56C13×#368C2211yescharacteristic, complemented
57C13×#364C2211yescharacteristic, complemented
58C13×#362C2211yescharacteristic, complemented
59C13×#362C2211yescharacteristic, complemented
60C13×#362C2211yescharacteristic, complemented
61C13×#361C2211yescharacteristic
62C13×#359C2211yescharacteristic
63C13×#359C2211yescharacteristic, complemented
64C13×#350C2211yescharacteristic
65C13×#350C2211yescharacteristic, complemented
66C13×#346C2211yescharacteristic, complemented
67C13×2−1+4—21no—
68C13×2−1+4—21no—
69C13×2−1+4—21no—
70C13×H(5,𝔽2)—21no—
71C13×#137—21no—
72C13×#137—21no—
73C13×#137—21no—
74C13×#137—21no—
75C13×#137—21no—
76C13×#137—21no—
77C13×#137—41no—
78C13×#137—41no—
79C13×#137—41no—
80C13×#137—41no—
81C13×#137—41no—
82C13×#137—41no—
83C13×AGL(1,ℤ/8)—21no—
84C13×AGL(1,ℤ/8)—21no—
85C13×AGL(1,ℤ/8)—41no—
86C13×AGL(1,ℤ/8)—41no—
87C13×#135—21no—
88C13×#135—21no—
89C13×#135—21no—
90C13×#135—21no—
91C13×#135—41no—
92C13×#135—41no—
93C13×#135D411yescharacteristic
94C13×#135C2311yescharacteristic
95C13×#135C2311yescharacteristic
96C2×C13×Q16—21no—
97C2×C13×Q16—21no—
98C2×C13×Q16—21no—
99C2×C13×Q16—21no—
100C2×C13×Q16—41no—
101C2×C13×Q16C2311yescharacteristic
102C2×C13×Q16C2311yescharacteristic
103C2×C13×Q16C2311yescharacteristic
104C2×C13×SD16—21no—
105C2×C13×SD16—41no—
106C2×C13×D8—21no—
107C2×C13×D8C2311yescharacteristic
108C13×#131—21no—
109C13×#131—21no—
110C13×#131C2311yescharacteristic
111C13×#131C2311yescharacteristic
112C13×C4⋊Q8—21no—
113C13×#124—21no—
114C13×Q32—21no—
115C13×Q32—21no—
116C13×Q32—21no—
117C13×Q32—21no—
118C13×Q32—21no—
119C13×Q32—41no—
120C13×Q32D411yescharacteristic
121C13×SD32—21no—
122C13×SD32—21no—
123C13×SD32—21no—
124C13×SD32—21no—
125C13×SD32—21no—
126C13×SD32—21no—
127C13×SD32—41no—
128C13×SD32D411yescharacteristic
129C13×SD32D411yescharacteristic
130C13×D16—21no—
131C13×D16D411yescharacteristic
132C13×M32—21no—
133C13×M32—21no—
134C13×M32C2311yescharacteristic
135C13×M32C2311yescharacteristic
136C2×C13×C16—21no—
137C2×C13×C16—21no—
138C2×C13×C16C2311yescharacteristic
139C2×C13×C16C2311yescharacteristic
140C13×#108D411yescharacteristic
141C13×#108C2311yescharacteristic
142C13×#108C2311yescharacteristic
143C13×#104—21no—
144C13×#104—21no—
145C13×#104D411yescharacteristic
146C13×#104D411yescharacteristic
147C13×#101—21no—
148C13×#101—21no—
149C13×#101—21no—
150C13×#100—21no—
151C4×C8×C13C2311yescharacteristic
152#33855C1311yesmaximal, characteristic, direct product factor, Sylow
153C13×#41—21no—
154C13×#41—21no—
155C13×#41—41no—
156C13×#41—41no—
157C13×#41—41no—
158C13×#41—41no—
159C13×#41—41no—
160C13×#41—41no—
161C13×#41—41no—
162C13×#41—41no—
163C13×#41—81no—
164C13×#41—81no—
165C13×#41—81no—
166C13×#41C2×D411yescharacteristic
167C13×#41C2×D411yescharacteristic
168C2×Q8×C13—21no—
169C2×Q8×C13—21no—
170C2×Q8×C13—21no—
171C2×Q8×C13—41no—
172C2×Q8×C13—41no—
173C2×Q8×C13—41no—
174C2×Q8×C13—41no—
175C2×Q8×C13—41no—
176C2×Q8×C13—41no—
177C2×D4×C13—21no—
178C2×D4×C13—41no—
179C2×D4×C13—41no—
180C2×D4×C13—81no—
181C13×Q16—21no—
182C13×Q16—21no—
183C13×Q16—21no—
184C13×Q16—21no—
185C13×Q16—21no—
186C13×Q16—21no—
187C13×Q16—41no—
188C13×Q16—41no—
189C13×Q16—41no—
190C13×Q16—41no—
191C13×Q16—41no—
192C13×Q16—41no—
193C13×Q16—41no—
194C13×Q16—41no—
195C13×Q16D811yescharacteristic
196C13×Q16C2×D411yescharacteristic
197C13×Q16C2×D411yescharacteristic
198C13×SD16—21no—
199C13×SD16—21no—
200C13×SD16—41no—
201C13×SD16—41no—
202C13×SD16—41no—
203C13×SD16—41no—
204C13×SD16—41no—
205C13×SD16—41no—
206C13×SD16—41no—
207C13×SD16—41no—
208C13×SD16—41no—
209C13×SD16—41no—
210C13×SD16D811yescharacteristic
211C13×SD16D811yescharacteristic
212C13×D8—21no—
213C13×D8—21no—
214C13×D8—41no—
215C13×D8—41no—
216C13×D8D811yescharacteristic
217C13×D8C2×D411yescharacteristic
218C13×D8C2×D411yescharacteristic
219C13×M16—21no—
220C13×M16—21no—
221C13×M16—21no—
222C13×M16—21no—
223C13×M16—41no—
224C13×M16—41no—
225C13×M16C2×D411yescharacteristic
226C13×M16C2×D411yescharacteristic
227C2×C8×C13—21no—
228C2×C8×C13—21no—
229C2×C8×C13—41no—
230C2×C8×C13—41no—
231C2×C8×C13C2×D411yescharacteristic
232C2×C8×C13C2411yescharacteristic
233C13×C4⋊C4—81no—
234C13×C22⋊C4—81no—
235C42×C13C2×D411yescharacteristic
236C13×C16—21no—
237C13×C16—21no—
238C13×C16—21no—
239C13×C16C2×D411yescharacteristic
240C13×C16C2×D411yescharacteristic
241#3417C2×C1311yescharacteristic, complemented
242#3416C2×C1311yescharacteristic, complemented
243#3293C2×C1311yescharacteristic, complemented
244#3290C2×C1311yescharacteristic, complemented
245#2251C2×C1311yescharacteristic, complemented
246#2223C2×C1311yescharacteristic, complemented
247#2222C2×C1311yescharacteristic, complemented
248#2214C2×C1311yescharacteristic, complemented
249#2212C2×C1311yescharacteristic, complemented
250#2195C2×C1311yescharacteristic, complemented
251#2195C2×C1311yescharacteristic, complemented
252#2194C2×C1311yescharacteristic, complemented
253#2193C2×C1311yescharacteristic, complemented
254#2179C2×C1311yescharacteristic, complemented
255#2171C2×C1311yescharacteristic, complemented
256C23×C13—41no—
257C23×C13—81no—
258Q8×C13—21no—
259Q8×C13—21no—
260Q8×C13—41no—
261Q8×C13—41no—
262Q8×C13—41no—
263Q8×C13—41no—
264Q8×C13—41no—
265Q8×C13—41no—
266Q8×C13—81no—
267Q8×C13—81no—
268Q8×C13—81no—
269Q8×C13C2×D811yescharacteristic
270Q8×C13C2×D811yescharacteristic
271D4×C13—21no—
272D4×C13—21no—
273D4×C13—21no—
274D4×C13—21no—
275D4×C13—41no—
276D4×C13—41no—
277D4×C13—41no—
278D4×C13—41no—
279D4×C13—81no—
280D4×C13—81no—
281D4×C13—81no—
282D4×C13—81no—
283D4×C13—81no—
284D4×C13C2×D811yescharacteristic
285D4×C13C2×D811yescharacteristic
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—81no—
295C2×C4×C13—81no—
296C2×C4×C13—81no—
297C2×C4×C13—81no—
298C2×C4×C13—81no—
299C2×C4×C13—81no—
300C2×C4×C13—81no—
301C2×C4×C13C22×D411yescharacteristic
302C8×C13—21no—
303C8×C13—21no—
304C8×C13—41no—
305C8×C13—41no—
306C8×C13C2×D811yescharacteristic
307C8×C13C2×D811yescharacteristic
308C8×C13C22×D411yescharacteristic
309C8×C13H(5,𝔽2)11yescharacteristic
310#578—21no—
311#578C22×C1311yescharacteristic
312#578C22×C1311yescharacteristic
313#578C22×C1311yescharacteristic, complemented
314#577—21no—
315#576C22×C1311yescharacteristic
316#510—21no—
317#510—21no—
318#510—21no—
319#510C22×C1311yescharacteristic
320#510C22×C1311yescharacteristic
321#510C22×C1311yescharacteristic, complemented
322#509—21no—
323#509C22×C1311yescharacteristic
324#508—21no—
325#508—21no—
326#508C22×C1311yescharacteristic
327C2×Q32—21no—
328C2×Q32C22×C1311yescharacteristic, complemented
329C2×Q32C22×C1311yescharacteristic, complemented
330C2×SD32—21no—
331C2×SD32C22×C1311yescharacteristic
332C2×SD32C22×C1311yescharacteristic
333#504C22×C1311yescharacteristic
334#504C22×C1311yescharacteristic, complemented
335#495C22×C1311yescharacteristic
336#494C22×C1311yescharacteristic, complemented
337#473—21no—
338#473C22×C1311yescharacteristic
339#473C22×C1311yescharacteristic
340#473C22×C1311yescharacteristic, complemented
341#472C22×C1311yescharacteristic
342#471—21no—
343#456—21no—
344#456—21no—
345#455—21no—
346#454—21no—
347#443C22×C1311yescharacteristic
348#443C22×C1311yescharacteristic
349#443C22×C1311yescharacteristic, complemented
350#368C22×C1311yescharacteristic, complemented
351#364C22×C1311yescharacteristic, complemented
352#362C22×C1311yescharacteristic, complemented
353#362C22×C1311yescharacteristic, complemented
354#362C22×C1311yescharacteristic, complemented
355#361C22×C1311yescharacteristic
356#359C22×C1311yescharacteristic
357#359C22×C1311yescharacteristic, complemented
358#350C22×C1311yescharacteristic
359#350C22×C1311yescharacteristic, complemented
360#346C22×C1311yescharacteristic, complemented
361C22×C13—21no—
362C22×C13—21no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—81no—
366C22×C13—161no—
367C22×C13—321no—
368C22×C13#57611yescharacteristic
369C4×C13—21no—
370C4×C13—21no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13—41no—
374C4×C13—81no—
375C4×C13—81no—
376C4×C13—81no—
377C4×C13D4211yescharacteristic
378C4×C13C22×D811yescharacteristic
3792−1+4—21no—
3802−1+4—21no—
3812−1+4—21no—
382H(5,𝔽2)—21no—
383#137—21no—
384#137—21no—
385#137—21no—
386#137—21no—
387#137—21no—
388#137—21no—
389#137—41no—
390#137—41no—
391#137—41no—
392#137—41no—
393#137—41no—
394#137—41no—
395AGL(1,ℤ/8)—21no—
396AGL(1,ℤ/8)—21no—
397AGL(1,ℤ/8)—41no—
398AGL(1,ℤ/8)—41no—
399#135—21no—
400#135—21no—
401#135—21no—
402#135—21no—
403#135—41no—
404#135—41no—
405#135D4×C1311yescharacteristic
406#135C23×C1311yescharacteristic
407#135C23×C1311yescharacteristic
408C2×Q16—21no—
409C2×Q16—21no—
410C2×Q16—21no—
411C2×Q16—21no—
412C2×Q16—41no—
413C2×Q16C23×C1311yescharacteristic
414C2×Q16C23×C1311yescharacteristic
415C2×Q16C23×C1311yescharacteristic
416C2×SD16—21no—
417C2×SD16—41no—
418C2×D8—21no—
419C2×D8C23×C1311yescharacteristic
420#131—21no—
421#131—21no—
422#131C23×C1311yescharacteristic
423#131C23×C1311yescharacteristic
424C4⋊Q8—21no—
425#124—21no—
426Q32—21no—
427Q32—21no—
428Q32—21no—
429Q32—21no—
430Q32—21no—
431Q32—41no—
432Q32D4×C1311yescharacteristic
433SD32—21no—
434SD32—21no—
435SD32—21no—
436SD32—21no—
437SD32—21no—
438SD32—21no—
439SD32—41no—
440SD32D4×C1311yescharacteristic
441SD32D4×C1311yescharacteristic
442D16—21no—
443D16D4×C1311yescharacteristic
444M32—21no—
445M32—21no—
446M32C23×C1311yescharacteristic
447M32C23×C1311yescharacteristic
448C2×C16—21no—
449C2×C16—21no—
450C2×C16C23×C1311yescharacteristic
451C2×C16C23×C1311yescharacteristic
452#108D4×C1311yescharacteristic
453#108C23×C1311yescharacteristic
454#108C23×C1311yescharacteristic
455#104—21no—
456#104—21no—
457#104D4×C1311yescharacteristic
458#104D4×C1311yescharacteristic
459#101—21no—
460#101—21no—
461#101—21no—
462#100—21no—
463C4×C8C23×C1311yescharacteristic
464C2×C13—21no—
465C2×C13—41no—
466C2×C13—41no—
467C2×C13—81no—
468C2×C13—81no—
469C2×C13—161no—
470C2×C13D4×D811yescharacteristic
471#41—21no—
472#41—21no—
473#41—41no—
474#41—41no—
475#41—41no—
476#41—41no—
477#41—41no—
478#41—41no—
479#41—41no—
480#41—41no—
481#41—81no—
482#41—81no—
483#41—81no—
484#41C2×D4×C1311yescharacteristic
485#41C2×D4×C1311yescharacteristic
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×D4—21no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—81no—
499Q16—21no—
500Q16—21no—
501Q16—21no—
502Q16—21no—
503Q16—21no—
504Q16—21no—
505Q16—41no—
506Q16—41no—
507Q16—41no—
508Q16—41no—
509Q16—41no—
510Q16—41no—
511Q16—41no—
512Q16—41no—
513Q16C13×D811yescharacteristic
514Q16C2×D4×C1311yescharacteristic
515Q16C2×D4×C1311yescharacteristic
516SD16—21no—
517SD16—21no—
518SD16—41no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523SD16—41no—
524SD16—41no—
525SD16—41no—
526SD16—41no—
527SD16—41no—
528SD16C13×D811yescharacteristic
529SD16C13×D811yescharacteristic
530D8—21no—
531D8—21no—
532D8—41no—
533D8—41no—
534D8C13×D811yescharacteristic
535D8C2×D4×C1311yescharacteristic
536D8C2×D4×C1311yescharacteristic
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—41no—
542M16—41no—
543M16C2×D4×C1311yescharacteristic
544M16C2×D4×C1311yescharacteristic
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8C2×D4×C1311yescharacteristic
550C2×C8C24×C1311yescharacteristic
551C4⋊C4—81no—
552C22⋊C4—81no—
553C42C2×D4×C1311yescharacteristic
554C16—21no—
555C16—21no—
556C16—21no—
557C16C2×D4×C1311yescharacteristic
558C16C2×D4×C1311yescharacteristic
559C13#3385511yescharacteristic, direct product factor, Sylow
560C23—41no—
561C23—81no—
562Q8—21no—
563Q8—21no—
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570Q8—81no—
571Q8—81no—
572Q8—81no—
573Q8C2×C13×D811yescharacteristic
574Q8C2×C13×D811yescharacteristic
575D4—21no—
576D4—21no—
577D4—21no—
578D4—21no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—81no—
584D4—81no—
585D4—81no—
586D4—81no—
587D4—81no—
588D4C2×C13×D811yescharacteristic
589D4C2×C13×D811yescharacteristic
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4C22×D4×C1311yescharacteristic
606C8—21no—
607C8—21no—
608C8—41no—
609C8—41no—
610C8C2×C13×D811yescharacteristic
611C8C2×C13×D811yescharacteristic
612C8C22×D4×C1311yescharacteristic
613C8C13×H(5,𝔽2)11yescharacteristic
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—81no—
619C22—161no—
620C22—321no—
621C22C13×#57611yescharacteristic
622C4—21no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4D42×C1311yescharacteristic
631C4C22×C13×D811yescharacteristic
632C2—21no—
633C2—41no—
634C2—41no—
635C2—81no—
636C2—81no—
637C2—161no—
638C2D4×C13×D811yescharacteristic
subgroupG/H
center, socleC2×C13D4×D8
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×#443 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3417C2semidirect
2. C13×#3416C2semidirect
3. C13×#3293C2semidirect
4. C13×#3290C2semidirect
5. C13×#2251C2semidirect
6. C13×#2223C2semidirect
7. C13×#2222C2semidirect
8. C13×#2214C2semidirect
9. C13×#2212C2semidirect
10. C13×#2195C2semidirect
11. C13×#2195C2semidirect
12. C13×#2194C2semidirect
13. C13×#2193C2semidirect
14. C13×#2179C2semidirect
15. C13×#2171C2semidirect
19. C13×#578C22semidirect
27. C13×#510C22semidirect
34. C2×C13×Q32C22semidirect
35. C2×C13×Q32C22semidirect
40. C13×#504C22semidirect
42. C13×#494C22semidirect
46. C13×#473C22semidirect
55. C13×#443C22semidirect
56. C13×#368C22semidirect
57. C13×#364C22semidirect
58. C13×#362C22semidirect
59. C13×#362C22semidirect
60. C13×#362C22semidirect
63. C13×#359C22semidirect
65. C13×#350C22semidirect
66. C13×#346C22semidirect
152. #33855C13direct (N × H)
241. #3417C2×C13semidirect
242. #3416C2×C13semidirect
243. #3293C2×C13semidirect
244. #3290C2×C13semidirect
245. #2251C2×C13semidirect
246. #2223C2×C13semidirect
247. #2222C2×C13semidirect
248. #2214C2×C13semidirect
249. #2212C2×C13semidirect
250. #2195C2×C13semidirect
251. #2195C2×C13semidirect
252. #2194C2×C13semidirect
253. #2193C2×C13semidirect
254. #2179C2×C13semidirect
255. #2171C2×C13semidirect
313. #578C22×C13semidirect
321. #510C22×C13semidirect
328. C2×Q32C22×C13semidirect
329. C2×Q32C22×C13semidirect
334. #504C22×C13semidirect
336. #494C22×C13semidirect
340. #473C22×C13semidirect
349. #443C22×C13semidirect
350. #368C22×C13semidirect
351. #364C22×C13semidirect
352. #362C22×C13semidirect
353. #362C22×C13semidirect
354. #362C22×C13semidirect
357. #359C22×C13semidirect
359. #350C22×C13semidirect
360. #346C22×C13semidirect
559. C13#33855direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34172
C13×#34162
C13×#32932
C13×#32902
C13×#22512
C13×#22232
C13×#22222
C13×#22142
C13×#22122
C13×#21952
C13×#21942
C13×#21932
C13×#21792
C13×#21712
#3385513