Finite Group Databasebeta

← C13×#18421 #15704760

Subgroups — C13×#18421 #15704760

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3536C211yesmaximal, characteristic
2C13×#3195C211yesmaximal, characteristic, complemented
3C13×#3190C211yesmaximal, characteristic, complemented
4C13×#2639C211yesmaximal, characteristic, complemented
5C13×#1612C212yesmaximal, complemented
6C13×#1608C212yesmaximal, complemented
7C13×#1606C212yesmaximal, complemented
8C13×#1602C212yesmaximal, complemented
9C13×#1504C211yesmaximal, characteristic, complemented
10C2×C13×#328C211yesmaximal, characteristic, complemented
11C13×#1471C211yesmaximal, characteristic, complemented
12C13×#562—22no—
13C13×#554—21no—
14C13×#548—21no—
15C13×#547—21no—
16C13×#546—22no—
17C13×#546—21no—
18C13×#543C2212yes—
19C13×#542—21no—
20C13×#539—21no—
21C13×#538C2212yes—
22C13×#537—21no—
23C13×#537—21no—
24C13×#525C2211yescharacteristic
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C13×#121C2211yescharacteristic
28C13×#485—21no—
29C13×#483—21no—
30C13×#483C2211yescharacteristic
31C13×#483C2212yes—
32C13×#480C2211yescharacteristic
33C13×#470—22no—
34C13×#467—21no—
35C13×#465—21no—
36C13×#452—21no—
37C13×#451—21no—
38C13×#451C2211yescharacteristic
39C13×#451C2212yes—
40C13×#448C2211yescharacteristic
41C13×#407C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C13×#400—21no—
44C13×#397C2212yes—
45C13×#394—21no—
46C13×#393C2212yes—
47C13×#386—22no—
48C2×C13×#95C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#323C2212yes—
54C13×#323C2212yes—
55C2×C13×#41—22no—
56C2×C13×#41—21no—
57C2×C13×#41D411yescharacteristic
58C22×Q8×C13D411yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13D412yes—
61C22×D4×C13D411yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C2×C13×Q16—22no—
65C2×C13×Q16—21no—
66C2×C13×SD16—21no—
67C2×C13×M16—21no—
68C22×C8×C13—21no—
69C13×C4⋊Q8—21no—
70C13×#126—22no—
71C13×#125—22no—
72C13×#124—21no—
73C13×#124—22no—
74C13×#124—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—21no—
79C13×#123—22no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8D411yescharacteristic
94C13×C22⋊Q8D412yes—
95C13×C22⋊Q8C2312yes—
96C13×C22⋊Q8C2311yescharacteristic
97C13×#121—21no—
98C13×#121—22no—
99C13×#121—22no—
100C13×#121—22no—
101C13×#121—22no—
102C13×#121—22no—
103C13×#121—21no—
104C13×#121—21no—
105C13×#121—21no—
106C13×#121—21no—
107C13×#121D411yescharacteristic
108C13×#121C2311yescharacteristic
109C13×#120—21no—
110C13×#120—22no—
111C4×Q8×C13—21no—
112C4×D4×C13—22no—
113C4×D4×C13—21no—
114C4×D4×C13—21no—
115C4×D4×C13—21no—
116C4×D4×C13—22no—
117C13×#117D411yescharacteristic
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4D411yescharacteristic
123C2×C13×C4⋊C4C2311yescharacteristic
124C2×C13×C22⋊C4—21no—
125C2×C13×C22⋊C4—22no—
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4C2312yes—
130C13×#107—21no—
131C13×#106—21no—
132C13×#106—22no—
133C13×#103—22no—
134C13×#103—21no—
135C13×#103—21no—
136C13×#103—21no—
137C13×#103—22no—
138C13×#102—21no—
139C13×C22⋊C8—21no—
140C13×C22⋊C8—21no—
141C13×C22⋊C8C2312yes—
142C13×C22⋊C8C2311yescharacteristic
143C13×C22⋊C8C2311yescharacteristic
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—21no—
147C13×#95C2312yes—
148#18421C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13C2×D411yescharacteristic
150C24×C13C2×D412yes—
151C13×#41—81no—
152C13×#41—84no—
153C13×#41—82no—
154C2×Q8×C13—22no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—21no—
158C2×Q8×C13—81no—
159C2×Q8×C13—81no—
160C2×Q8×C13C2×D411yescharacteristic
161C2×Q8×C13C2×D412yes—
162C2×D4×C13—21no—
163C2×D4×C13—22no—
164C2×D4×C13—21no—
165C2×D4×C13—22no—
166C2×D4×C13—22no—
167C2×D4×C13—21no—
168C2×D4×C13—22no—
169C2×D4×C13—21no—
170C2×D4×C13—21no—
171C2×D4×C13—44no—
172C2×D4×C13—81no—
173C2×D4×C13C2×D411yescharacteristic
174C22×C4×C13—21no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—22no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—42no—
184C22×C4×C13—81no—
185C22×C4×C13—81no—
186C22×C4×C13—81no—
187C22×C4×C13C2×D412yes—
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2411yescharacteristic
194C13×Q16—81no—
195C13×Q16—82no—
196C13×SD16—81no—
197C13×M16—81no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—22no—
201C2×C8×C13—81no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—22no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—22no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4—22no—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—22no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—21no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—41no—
216C13×C4⋊C4—41no—
217C13×C4⋊C4C2×D412yes—
218C13×C4⋊C4C2×D411yescharacteristic
219C13×C4⋊C4C2×D411yescharacteristic
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—22no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—22no—
226C13×C22⋊C4—21no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—22no—
229C13×C22⋊C4—21no—
230C13×C22⋊C4—21no—
231C13×C22⋊C4—22no—
232C13×C22⋊C4—22no—
233C13×C22⋊C4—21no—
234C13×C22⋊C4—41no—
235C13×C22⋊C4—41no—
236C13×C22⋊C4—82no—
237C13×C22⋊C4—82no—
238C42×C13—22no—
239C42×C13—21no—
240#3536C2×C1311yescharacteristic
241#3195C2×C1311yescharacteristic, complemented
242#3190C2×C1311yescharacteristic, complemented
243#2639C2×C1311yescharacteristic, complemented
244#1612C2×C1312yescomplemented
245#1608C2×C1312yescomplemented
246#1606C2×C1312yescomplemented
247#1602C2×C1312yescomplemented
248#1504C2×C1311yescharacteristic, complemented
249C2×#328C2×C1311yescharacteristic, complemented
250#1471C2×C1311yescharacteristic, complemented
251C23×C13—21no—
252C23×C13—21no—
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—21no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—41no—
259C23×C13—42no—
260C23×C13—42no—
261C23×C13#12011yescharacteristic
262C23×C13#12011yescharacteristic
263C23×C13C22×D411yescharacteristic
264Q8×C13—42no—
265Q8×C13—42no—
266Q8×C13—41no—
267Q8×C13—41no—
268Q8×C13—41no—
269Q8×C13—42no—
270Q8×C13—82no—
271D4×C13—42no—
272D4×C13—41no—
273D4×C13—41no—
274D4×C13—41no—
275D4×C13—44no—
276D4×C13—42no—
277D4×C13—81no—
278D4×C13—82no—
279D4×C13—81no—
280D4×C13—82no—
281D4×C13—82no—
282C2×C4×C13—21no—
283C2×C4×C13—22no—
284C2×C4×C13—21no—
285C2×C4×C13—22no—
286C2×C4×C13—21no—
287C2×C4×C13—22no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—42no—
304C2×C4×C13—41no—
305C2×C4×C13—81no—
306C2×C4×C13—82no—
307C2×C4×C13—82no—
308C2×C4×C13—82no—
309C2×C4×C13—84no—
310C2×C4×C13#12011yescharacteristic
311C2×C4×C13#12011yescharacteristic
312C2×C4×C13C22×D411yescharacteristic
313C2×C4×C13C22×D411yescharacteristic
314C8×C13—41no—
315C8×C13—41no—
316C8×C13—42no—
317#562—22no—
318#554—21no—
319#548—21no—
320#547—21no—
321#546—22no—
322#546—21no—
323#543C22×C1312yes—
324#542—21no—
325#539—21no—
326#538C22×C1312yes—
327#537—21no—
328#537—21no—
329#525C22×C1311yescharacteristic
330C2×C22⋊Q8C22×C1311yescharacteristic
331C2×C22⋊Q8C22×C1311yescharacteristic
332C2×#121C22×C1311yescharacteristic
333#485—21no—
334#483—21no—
335#483C22×C1311yescharacteristic
336#483C22×C1312yes—
337#480C22×C1311yescharacteristic
338#470—22no—
339#467—21no—
340#465—21no—
341#452—21no—
342#451—21no—
343#451C22×C1311yescharacteristic
344#451C22×C1312yes—
345#448C22×C1311yescharacteristic
346#407C22×C1311yescharacteristic
347C2×C22⋊C8C22×C1311yescharacteristic
348#400—21no—
349#397C22×C1312yes—
350#394—21no—
351#393C22×C1312yes—
352#386—22no—
353C2×#95C22×C1311yescharacteristic
354#328C22×C1312yes—
355#328C22×C1312yes—
356#328C22×C1312yes—
357#327C22×C1312yes—
358#323C22×C1312yes—
359#323C22×C1312yes—
360C22×C13—21no—
361C22×C13—21no—
362C22×C13—21no—
363C22×C13—21no—
364C22×C13—21no—
365C22×C13—21no—
366C22×C13—21no—
367C22×C13—42no—
368C22×C13—42no—
369C22×C13—41no—
370C22×C13—42no—
371C22×C13—41no—
372C22×C13—42no—
373C22×C13—41no—
374C22×C13—42no—
375C22×C13—82no—
376C22×C13—82no—
377C22×C13#45512yes—
378C22×C13C2×#12011yescharacteristic
379C22×C13#57711yescharacteristic
380C22×C13#57811yescharacteristic
381C4×C13—21no—
382C4×C13—21no—
383C4×C13—21no—
384C4×C13—21no—
385C4×C13—41no—
386C4×C13—42no—
387C4×C13—42no—
388C4×C13—41no—
389C4×C13—41no—
390C4×C13—42no—
391C4×C13—82no—
392C4×C13—81no—
393C4×C13—81no—
394C2×#41—22no—
395C2×#41—21no—
396C2×#41D4×C1311yescharacteristic
397C22×Q8D4×C1311yescharacteristic
398C22×Q8C23×C1311yescharacteristic
399C22×D4D4×C1312yes—
400C22×D4D4×C1311yescharacteristic
401C23×C4—21no—
402C23×C4C23×C1311yescharacteristic
403C2×Q16—22no—
404C2×Q16—21no—
405C2×SD16—21no—
406C2×M16—21no—
407C22×C8—21no—
408C4⋊Q8—21no—
409#126—22no—
410#125—22no—
411#124—21no—
412#124—22no—
413#124—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—21no—
418#123—22no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8D4×C1312yes—
433C22⋊Q8D4×C1311yescharacteristic
434C22⋊Q8C23×C1312yes—
435C22⋊Q8C23×C1311yescharacteristic
436#121—21no—
437#121—22no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—22no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121D4×C1311yescharacteristic
447#121C23×C1311yescharacteristic
448#120—21no—
449#120—22no—
450C4×Q8—21no—
451C4×D4—22no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—22no—
456#117D4×C1311yescharacteristic
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4D4×C1311yescharacteristic
461C2×C4⋊C4D4×C1311yescharacteristic
462C2×C4⋊C4C23×C1311yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4C23×C1312yes—
469#107—21no—
470#106—21no—
471#106—22no—
472#103—22no—
473#103—21no—
474#103—21no—
475#103—21no—
476#103—22no—
477#102—21no—
478C22⋊C8—21no—
479C22⋊C8—21no—
480C22⋊C8C23×C1312yes—
481C22⋊C8C23×C1311yescharacteristic
482C22⋊C8C23×C1311yescharacteristic
483#95—21no—
484#95—22no—
485#95—22no—
486#95C23×C1312yes—
487C2×C13—21no—
488C2×C13—21no—
489C2×C13—22no—
490C2×C13—41no—
491C2×C13—81no—
492C2×C13—82no—
493C2×C13#301311yescharacteristic
494C2×C13C2×#45511yescharacteristic
495C2×C13#302611yescharacteristic
496C24C2×D4×C1311yescharacteristic
497C24C2×D4×C1312yes—
498#41—81no—
499#41—84no—
500#41—82no—
501C2×Q8—22no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—81no—
506C2×Q8—81no—
507C2×Q8C2×D4×C1311yescharacteristic
508C2×Q8C2×D4×C1312yes—
509C2×D4—21no—
510C2×D4—22no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—22no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—44no—
519C2×D4—81no—
520C2×D4C2×D4×C1311yescharacteristic
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C1312yes—
535C22×C4C2×D4×C1311yescharacteristic
536C22×C4C2×D4×C1311yescharacteristic
537C22×C4C2×D4×C1311yescharacteristic
538C22×C4C2×D4×C1311yescharacteristic
539C22×C4C2×D4×C1311yescharacteristic
540C22×C4C24×C1311yescharacteristic
541Q16—81no—
542Q16—82no—
543SD16—81no—
544M16—81no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—22no—
548C2×C8—81no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4C2×D4×C1312yes—
565C4⋊C4C2×D4×C1311yescharacteristic
566C4⋊C4C2×D4×C1311yescharacteristic
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—21no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—82no—
584C22⋊C4—82no—
585C42—22no—
586C42—21no—
587C13#1842111yescharacteristic, direct product factor, Sylow
588C23—22no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—21no—
593C23—22no—
594C23—22no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23C13×#12011yescharacteristic
599C23C13×#12011yescharacteristic
600C23C22×D4×C1311yescharacteristic
601Q8—42no—
602Q8—41no—
603Q8—42no—
604Q8—41no—
605Q8—41no—
606Q8—42no—
607Q8—82no—
608D4—41no—
609D4—42no—
610D4—44no—
611D4—42no—
612D4—41no—
613D4—41no—
614D4—81no—
615D4—82no—
616D4—81no—
617D4—82no—
618D4—82no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—81no—
643C2×C4—82no—
644C2×C4—82no—
645C2×C4—82no—
646C2×C4—84no—
647C2×C4C13×#12011yescharacteristic
648C2×C4C13×#12011yescharacteristic
649C2×C4C22×D4×C1311yescharacteristic
650C2×C4C22×D4×C1311yescharacteristic
651C8—41no—
652C8—41no—
653C8—42no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—42no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—42no—
669C22—82no—
670C22—82no—
671C22C13×#45512yes—
672C22C2×C13×#12011yescharacteristic
673C22C13×#57711yescharacteristic
674C22C13×#57811yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—41no—
680C4—42no—
681C4—42no—
682C4—41no—
683C4—41no—
684C4—42no—
685C4—82no—
686C4—81no—
687C4—81no—
688C2—21no—
689C2—21no—
690C2—22no—
691C2—41no—
692C2—82no—
693C2—81no—
694C2C13×#301311yescharacteristic
695C2C2×C13×#45511yescharacteristic
696C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3536C2
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×#3195C2semidirect
3. C13×#3190C2semidirect
4. C13×#2639C2semidirect
5. C13×#1612C2semidirect
6. C13×#1608C2semidirect
7. C13×#1606C2semidirect
8. C13×#1602C2semidirect
9. C13×#1504C2semidirect
10. C2×C13×#328C2semidirect
11. C13×#1471C2semidirect
148. #18421C13direct (N × H)
241. #3195C2×C13semidirect
242. #3190C2×C13semidirect
243. #2639C2×C13semidirect
244. #1612C2×C13semidirect
245. #1608C2×C13semidirect
246. #1606C2×C13semidirect
247. #1602C2×C13semidirect
248. #1504C2×C13semidirect
249. C2×#328C2×C13semidirect
250. #1471C2×C13semidirect
587. C13#18421direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35362
C13×#31952
C13×#31902
C13×#26392
C13×#16122
C13×#16082
C13×#16062
C13×#16022
C13×#15042
C2×C13×#3282
C13×#14712
#1842113