Finite Group Databasebeta

← C13×#18349 #15704688

Subgroups — C13×#18349 #15704688

Order 3328.

954 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3492C211yesmaximal, characteristic
2C13×#3196C212yesmaximal, complemented
3C13×#2627C211yesmaximal, characteristic, complemented
4C13×#1617C211yesmaximal, characteristic, complemented
5C13×#1616C211yesmaximal, characteristic, complemented
6C13×#1615C212yesmaximal, complemented
7C13×#1605C211yesmaximal, characteristic, complemented
8C13×#1604C211yesmaximal, characteristic, complemented
9C13×#1603C212yesmaximal, complemented
10C13×#1513C212yesmaximal, complemented
11C13×#1463C211yesmaximal, characteristic, complemented
12C13×#554—22no—
13C13×#553—22no—
14C13×#552—22no—
15C13×#547—22no—
16C13×#544C2211yescharacteristic
17C13×#539—21no—
18C13×#539C2212yes—
19C13×#537C2211yescharacteristic
20C13×#525—21no—
21C13×#525—21no—
22C13×#525C2212yes—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C13×#520—21no—
25C22×C13×C4⋊C4C2211yescharacteristic
26C13×#485—22no—
27C13×#484C2212yes—
28C13×#481C2212yes—
29C13×#470—22no—
30C13×#468—22no—
31C13×#452—22no—
32C13×#451C2212yes—
33C13×#448C2212yes—
34C13×#407C2212yes—
35C13×#400C2211yescharacteristic
36C13×#400C2211yescharacteristic
37C13×#398—21no—
38C13×#398—21no—
39C13×#395C2211yescharacteristic
40C13×#395C2211yescharacteristic
41C13×#385—21no—
42C13×#381—21no—
43C13×#380C2211yescharacteristic
44C13×#328C2212yes—
45C13×#328C2212yes—
46C13×#327C2212yes—
47C13×#327C2212yes—
48C13×#324C2212yes—
49C13×#324C2211yescharacteristic
50C13×#324C2211yescharacteristic
51C2×C13×#41—21no—
52C2×C13×#41—21no—
53C2×C13×#41D412yes—
54C22×Q8×C13C2311yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13D411yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C2×C13×Q16—22no—
59C2×C13×SD16—22no—
60C2×C13×M16—22no—
61C13×C4⋊Q8—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#125—22no—
65C13×#125—22no—
66C13×#125—22no—
67C13×#123—22no—
68C13×#123—22no—
69C13×#123—22no—
70C13×#123—22no—
71C13×#123—22no—
72C13×C22⋊Q8—21no—
73C13×C22⋊Q8—21no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8—21no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8D412yes—
82C13×C22⋊Q8C2312yes—
83C13×#121—21no—
84C13×#121—21no—
85C13×#121—21no—
86C13×#121—22no—
87C13×#121—21no—
88C13×#121D412yes—
89C13×#121C2312yes—
90C13×#120—22no—
91C4×Q8×C13—22no—
92C4×D4×C13—22no—
93C4×D4×C13—22no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C13×#117—22no—
100C13×#117—21no—
101C13×#117—21no—
102C13×#117D412yes—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C4⋊C4C2311yescharacteristic
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C13×#107—22no—
118C13×#106—22no—
119C13×#103—22no—
120C13×#103—22no—
121C13×#103—22no—
122C13×#102—22no—
123C13×C22⋊C8—22no—
124C13×C22⋊C8C2312yes—
125C13×C22⋊C8C2312yes—
126C13×#95—21no—
127C13×#95—21no—
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95C2311yescharacteristic
133C13×#95C2311yescharacteristic
134#18349C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13C2×D411yescharacteristic
136C13×#41—42no—
137C13×#41—42no—
138C13×#41—82no—
139C13×#41—82no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—22no—
143C2×Q8×C13—81no—
144C2×Q8×C13C2×D412yes—
145C2×D4×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—21no—
150C2×D4×C13C2×D412yes—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—41no—
164C22×C4×C13—81no—
165C22×C4×C13—81no—
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2411yescharacteristic
174C13×Q16—82no—
175C13×SD16—82no—
176C13×M16—82no—
177C2×C8×C13—22no—
178C2×C8×C13—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—42no—
195C13×C4⋊C4—81no—
196C13×C4⋊C4—81no—
197C13×C4⋊C4—81no—
198C13×C4⋊C4C2×D412yes—
199C13×C4⋊C4C2×D412yes—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—42no—
210C13×C22⋊C4—41no—
211C13×C22⋊C4—41no—
212C42×C13—22no—
213C42×C13—22no—
214C42×C13—22no—
215#3492C2×C1311yescharacteristic
216#3196C2×C1312yescomplemented
217#2627C2×C1311yescharacteristic, complemented
218#1617C2×C1311yescharacteristic, complemented
219#1616C2×C1311yescharacteristic, complemented
220#1615C2×C1312yescomplemented
221#1605C2×C1311yescharacteristic, complemented
222#1604C2×C1311yescharacteristic, complemented
223#1603C2×C1312yescomplemented
224#1513C2×C1312yescomplemented
225#1463C2×C1311yescharacteristic, complemented
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—22no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13#12011yescharacteristic
232C23×C13#12011yescharacteristic
233C23×C13C22×D411yescharacteristic
234Q8×C13—42no—
235Q8×C13—42no—
236Q8×C13—42no—
237Q8×C13—42no—
238Q8×C13—81no—
239D4×C13—42no—
240D4×C13—42no—
241D4×C13—44no—
242D4×C13—44no—
243D4×C13—42no—
244D4×C13—42no—
245D4×C13—81no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—41no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—41no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—44no—
263C2×C4×C13—42no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—42no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—82no—
278C2×C4×C13—81no—
279C2×C4×C13—82no—
280C2×C4×C13#12012yes—
281C2×C4×C13#13712yes—
282C2×C4×C13C22×D412yes—
283C8×C13—42no—
284C8×C13—42no—
285#554—22no—
286#553—22no—
287#552—22no—
288#547—22no—
289#544C22×C1311yescharacteristic
290#539—21no—
291#539C22×C1312yes—
292#537C22×C1311yescharacteristic
293#525—21no—
294#525—21no—
295#525C22×C1312yes—
296C2×C22⋊Q8C22×C1311yescharacteristic
297#520—21no—
298C22×C4⋊C4C22×C1311yescharacteristic
299#485—22no—
300#484C22×C1312yes—
301#481C22×C1312yes—
302#470—22no—
303#468—22no—
304#452—22no—
305#451C22×C1312yes—
306#448C22×C1312yes—
307#407C22×C1312yes—
308#400C22×C1311yescharacteristic
309#400C22×C1311yescharacteristic
310#398—21no—
311#398—21no—
312#395C22×C1311yescharacteristic
313#395C22×C1311yescharacteristic
314#385—21no—
315#381—21no—
316#380C22×C1311yescharacteristic
317#328C22×C1312yes—
318#328C22×C1312yes—
319#327C22×C1312yes—
320#327C22×C1312yes—
321#324C22×C1312yes—
322#324C22×C1311yescharacteristic
323#324C22×C1311yescharacteristic
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13C2×#12011yescharacteristic
338C22×C13C2×#13711yescharacteristic
339C22×C13#57511yescharacteristic
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—22no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—42no—
349C4×C13—81no—
350C4×C13—81no—
351C4×C13—81no—
352C4×C13—81no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41D4×C1312yes—
356C22×Q8C23×C1311yescharacteristic
357C23×C4D4×C1311yescharacteristic
358C23×C4D4×C1311yescharacteristic
359C23×C4C23×C1311yescharacteristic
360C2×Q16—22no—
361C2×SD16—22no—
362C2×M16—22no—
363C4⋊Q8—22no—
364#126—22no—
365#126—22no—
366#125—22no—
367#125—22no—
368#125—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372#123—22no—
373#123—22no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8D4×C1312yes—
384C22⋊Q8C23×C1312yes—
385#121—21no—
386#121—21no—
387#121—21no—
388#121—22no—
389#121—21no—
390#121D4×C1312yes—
391#121C23×C1312yes—
392#120—22no—
393C4×Q8—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401#117—22no—
402#117—21no—
403#117—21no—
404#117D4×C1312yes—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4D4×C1311yescharacteristic
413C2×C4⋊C4D4×C1311yescharacteristic
414C2×C4⋊C4C23×C1311yescharacteristic
415C2×C4⋊C4C23×C1311yescharacteristic
416C2×C4⋊C4C23×C1311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419#107—22no—
420#106—22no—
421#103—22no—
422#103—22no—
423#103—22no—
424#102—22no—
425C22⋊C8—22no—
426C22⋊C8C23×C1312yes—
427C22⋊C8C23×C1312yes—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95C23×C1311yescharacteristic
435#95C23×C1311yescharacteristic
436C2×C13—21no—
437C2×C13—21no—
438C2×C13—41no—
439C2×C13—41no—
440C2×C13—82no—
441C2×C13#300711yescharacteristic
442C2×C13#302011yescharacteristic
443C2×C13#302611yescharacteristic
444C24C2×D4×C1311yescharacteristic
445#41—42no—
446#41—42no—
447#41—82no—
448#41—82no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—81no—
453C2×Q8C2×D4×C1312yes—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4C2×D4×C1312yes—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4C2×D4×C1311yescharacteristic
476C22×C4C2×D4×C1311yescharacteristic
477C22×C4C2×D4×C1311yescharacteristic
478C22×C4C2×D4×C1311yescharacteristic
479C22×C4C2×D4×C1311yescharacteristic
480C22×C4C2×D4×C1312yes—
481C22×C4C2×D4×C1312yes—
482C22×C4C24×C1311yescharacteristic
483Q16—82no—
484SD16—82no—
485M16—82no—
486C2×C8—22no—
487C2×C8—22no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—42no—
504C4⋊C4—81no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4C2×D4×C1312yes—
508C4⋊C4C2×D4×C1312yes—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—42no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—22no—
522C42—22no—
523C42—22no—
524C13#1834911yescharacteristic, direct product factor, Sylow
525C23—21no—
526C23—21no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23C13×#12011yescharacteristic
531C23C13×#12011yescharacteristic
532C23C22×D4×C1311yescharacteristic
533Q8—42no—
534Q8—42no—
535Q8—42no—
536Q8—42no—
537Q8—81no—
538D4—42no—
539D4—42no—
540D4—44no—
541D4—44no—
542D4—42no—
543D4—42no—
544D4—81no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—81no—
578C2×C4—82no—
579C2×C4C13×#12012yes—
580C2×C4C13×#13712yes—
581C2×C4C22×D4×C1312yes—
582C8—42no—
583C8—42no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22C2×C13×#12011yescharacteristic
598C22C2×C13×#13711yescharacteristic
599C22C13×#57511yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—41no—
604C4—42no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C2—21no—
614C2—21no—
615C2—41no—
616C2—41no—
617C2—82no—
618C2C13×#300711yescharacteristic
619C2C13×#302011yescharacteristic
620C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3492C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3196C2semidirect
3. C13×#2627C2semidirect
4. C13×#1617C2semidirect
5. C13×#1616C2semidirect
6. C13×#1615C2semidirect
7. C13×#1605C2semidirect
8. C13×#1604C2semidirect
9. C13×#1603C2semidirect
10. C13×#1513C2semidirect
11. C13×#1463C2semidirect
134. #18349C13direct (N × H)
216. #3196C2×C13semidirect
217. #2627C2×C13semidirect
218. #1617C2×C13semidirect
219. #1616C2×C13semidirect
220. #1615C2×C13semidirect
221. #1605C2×C13semidirect
222. #1604C2×C13semidirect
223. #1603C2×C13semidirect
224. #1513C2×C13semidirect
225. #1463C2×C13semidirect
524. C13#18349direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34922
C13×#31962
C13×#26272
C13×#16172
C13×#16162
C13×#16152
C13×#16052
C13×#16042
C13×#16032
C13×#15132
C13×#14632
#1834913