Finite Group Databasebeta

← C13×#18453 #15704792

Subgroups — C13×#18453 #15704792

Order 3328.

970 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3536C211yesmaximal, characteristic
2C13×#3196C211yesmaximal, characteristic, complemented
3C13×#3189C211yesmaximal, characteristic, complemented
4C13×#2816C211yesmaximal, characteristic, complemented
5C13×#1618C212yesmaximal, complemented
6C13×#1614C212yesmaximal, complemented
7C13×#1606C212yesmaximal, complemented
8C13×#1602C212yesmaximal, complemented
9C13×#1516C211yesmaximal, characteristic, complemented
10C13×#1511C211yesmaximal, 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×#484—21no—
30C13×#484C2211yescharacteristic
31C13×#484C2212yes—
32C13×#481C2211yescharacteristic
33C13×#470—21no—
34C13×#468—21no—
35C13×#467—22no—
36C13×#452—21no—
37C13×#451—21no—
38C13×#451C2211yescharacteristic
39C13×#451C2212yes—
40C13×#448C2211yescharacteristic
41C13×#407C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C13×#399C2212yes—
44C13×#398—21no—
45C13×#394—21no—
46C13×#394—22no—
47C13×#393C2212yes—
48C13×#381C2211yescharacteristic
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×C13C2311yescharacteristic
63C2×C13×Q16—22no—
64C2×C13×Q16—21no—
65C2×C13×SD16—21no—
66C2×C13×M16—21no—
67C22×C8×C13—21no—
68C13×C4⋊Q8—21no—
69C13×#126—22no—
70C13×#125—22no—
71C13×#124—21no—
72C13×#124—22no—
73C13×#124—22no—
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—21no—
78C13×#123—22no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8D412yes—
93C13×C22⋊Q8D411yescharacteristic
94C13×C22⋊Q8C2312yes—
95C13×C22⋊Q8C2311yescharacteristic
96C13×#121—21no—
97C13×#121—22no—
98C13×#121—22no—
99C13×#121—22no—
100C13×#121—22no—
101C13×#121—22no—
102C13×#121—21no—
103C13×#121—21no—
104C13×#121—21no—
105C13×#121—21no—
106C13×#121D411yescharacteristic
107C13×#121C2311yescharacteristic
108C13×#120—21no—
109C13×#120—22no—
110C4×Q8×C13—21no—
111C4×D4×C13—22no—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—21no—
115C4×D4×C13—22no—
116C13×#117D411yescharacteristic
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—22no—
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—21no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4C2312yes—
131C13×#107—22no—
132C13×#107—21no—
133C13×#106—21no—
134C13×#103—22no—
135C13×#103—21no—
136C13×#103—21no—
137C13×#103—22no—
138C13×#103—21no—
139C13×#102—21no—
140C13×C22⋊C8—21no—
141C13×C22⋊C8—21no—
142C13×C22⋊C8C2312yes—
143C13×C22⋊C8C2311yescharacteristic
144C13×C22⋊C8C2311yescharacteristic
145C13×#95—21no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18453C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13C2×D412yes—
150C24×C13C2×D411yescharacteristic
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—81no—
172C2×D4×C13—82no—
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—81no—
184C22×C4×C13C2×D412yes—
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2411yescharacteristic
191C13×Q16—82no—
192C13×Q16—81no—
193C13×SD16—81no—
194C13×M16—81no—
195C2×C8×C13—21no—
196C2×C8×C13—22no—
197C2×C8×C13—21no—
198C2×C8×C13—81no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
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—21no—
212C13×C4⋊C4—41no—
213C13×C4⋊C4—41no—
214C13×C4⋊C4—82no—
215C13×C4⋊C4C2×D411yescharacteristic
216C13×C4⋊C4C2×D412yes—
217C13×C4⋊C4C2×D411yescharacteristic
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—22no—
224C13×C22⋊C4—21no—
225C13×C22⋊C4—21no—
226C13×C22⋊C4—22no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—21no—
229C13×C22⋊C4—22no—
230C13×C22⋊C4—22no—
231C13×C22⋊C4—21no—
232C13×C22⋊C4—41no—
233C13×C22⋊C4—41no—
234C13×C22⋊C4—81no—
235C13×C22⋊C4—82no—
236C13×C22⋊C4—82no—
237C42×C13—22no—
238C42×C13—21no—
239#3536C2×C1311yescharacteristic
240#3196C2×C1311yescharacteristic, complemented
241#3189C2×C1311yescharacteristic, complemented
242#2816C2×C1311yescharacteristic, complemented
243#1618C2×C1312yescomplemented
244#1614C2×C1312yescomplemented
245#1606C2×C1312yescomplemented
246#1602C2×C1312yescomplemented
247#1516C2×C1311yescharacteristic, complemented
248#1511C2×C1311yescharacteristic, complemented
249#1471C2×C1311yescharacteristic, complemented
250C23×C13—22no—
251C23×C13—22no—
252C23×C13—21no—
253C23×C13—24no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—42no—
257C23×C13—42no—
258C23×C13#12011yescharacteristic
259C23×C13#12011yescharacteristic
260C23×C13C22×D411yescharacteristic
261Q8×C13—42no—
262Q8×C13—42no—
263Q8×C13—41no—
264Q8×C13—41no—
265Q8×C13—41no—
266Q8×C13—42no—
267Q8×C13—82no—
268D4×C13—42no—
269D4×C13—41no—
270D4×C13—44no—
271D4×C13—42no—
272D4×C13—42no—
273D4×C13—81no—
274D4×C13—82no—
275D4×C13—81no—
276D4×C13—82no—
277D4×C13—82no—
278C2×C4×C13—21no—
279C2×C4×C13—22no—
280C2×C4×C13—21no—
281C2×C4×C13—22no—
282C2×C4×C13—21no—
283C2×C4×C13—22no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—41no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—42no—
301C2×C4×C13—81no—
302C2×C4×C13—82no—
303C2×C4×C13—82no—
304C2×C4×C13—82no—
305C2×C4×C13#12011yescharacteristic
306C2×C4×C13#12011yescharacteristic
307C2×C4×C13C22×D411yescharacteristic
308C2×C4×C13C22×D411yescharacteristic
309C8×C13—42no—
310C8×C13—41no—
311C8×C13—41no—
312#562—22no—
313#554—21no—
314#548—21no—
315#547—21no—
316#546—22no—
317#546—21no—
318#543C22×C1312yes—
319#542—21no—
320#539—21no—
321#538C22×C1312yes—
322#537—21no—
323#537—21no—
324#525C22×C1311yescharacteristic
325C2×C22⋊Q8C22×C1311yescharacteristic
326C2×C22⋊Q8C22×C1311yescharacteristic
327C2×#121C22×C1311yescharacteristic
328#485—21no—
329#484—21no—
330#484C22×C1311yescharacteristic
331#484C22×C1312yes—
332#481C22×C1311yescharacteristic
333#470—21no—
334#468—21no—
335#467—22no—
336#452—21no—
337#451—21no—
338#451C22×C1311yescharacteristic
339#451C22×C1312yes—
340#448C22×C1311yescharacteristic
341#407C22×C1311yescharacteristic
342C2×C22⋊C8C22×C1311yescharacteristic
343#399C22×C1312yes—
344#398—21no—
345#394—21no—
346#394—22no—
347#393C22×C1312yes—
348#381C22×C1311yescharacteristic
349#328C22×C1312yes—
350#328C22×C1312yes—
351#328C22×C1312yes—
352#327C22×C1312yes—
353#323C22×C1312yes—
354#323C22×C1312yes—
355C22×C13—21no—
356C22×C13—21no—
357C22×C13—21no—
358C22×C13—21no—
359C22×C13—21no—
360C22×C13—21no—
361C22×C13—21no—
362C22×C13—21no—
363C22×C13—41no—
364C22×C13—42no—
365C22×C13—41no—
366C22×C13—42no—
367C22×C13—41no—
368C22×C13—42no—
369C22×C13—82no—
370C22×C13—84no—
371C22×C13C2×#12011yescharacteristic
372C22×C13#57812yes—
373C4×C13—21no—
374C4×C13—21no—
375C4×C13—21no—
376C4×C13—21no—
377C4×C13—41no—
378C4×C13—42no—
379C4×C13—42no—
380C4×C13—41no—
381C4×C13—41no—
382C4×C13—42no—
383C4×C13—82no—
384C4×C13—81no—
385C4×C13—81no—
386C2×#41—22no—
387C2×#41—21no—
388C2×#41D4×C1311yescharacteristic
389C22×Q8D4×C1311yescharacteristic
390C22×Q8C23×C1311yescharacteristic
391C22×D4D4×C1312yes—
392C22×D4D4×C1311yescharacteristic
393C23×C4C23×C1311yescharacteristic
394C2×Q16—22no—
395C2×Q16—21no—
396C2×SD16—21no—
397C2×M16—21no—
398C22×C8—21no—
399C4⋊Q8—21no—
400#126—22no—
401#125—22no—
402#124—21no—
403#124—22no—
404#124—22no—
405#123—22no—
406#123—22no—
407#123—22no—
408#123—21no—
409#123—22no—
410C22⋊Q8—21no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8D4×C1312yes—
424C22⋊Q8D4×C1311yescharacteristic
425C22⋊Q8C23×C1312yes—
426C22⋊Q8C23×C1311yescharacteristic
427#121—21no—
428#121—22no—
429#121—22no—
430#121—22no—
431#121—22no—
432#121—22no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121—21no—
437#121D4×C1311yescharacteristic
438#121C23×C1311yescharacteristic
439#120—21no—
440#120—22no—
441C4×Q8—21no—
442C4×D4—22no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—22no—
447#117D4×C1311yescharacteristic
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4D4×C1311yescharacteristic
453C2×C4⋊C4D4×C1311yescharacteristic
454C2×C4⋊C4C23×C1311yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4C23×C1312yes—
462#107—22no—
463#107—21no—
464#106—21no—
465#103—22no—
466#103—21no—
467#103—21no—
468#103—22no—
469#103—21no—
470#102—21no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8C23×C1312yes—
474C22⋊C8C23×C1311yescharacteristic
475C22⋊C8C23×C1311yescharacteristic
476#95—21no—
477#95—22no—
478#95C23×C1312yes—
479C2×C13—22no—
480C2×C13—41no—
481C2×C13—41no—
482C2×C13—81no—
483C2×C13—82no—
484C2×C13#301111yescharacteristic
485C2×C13#301911yescharacteristic
486C2×C13#302611yescharacteristic
487C24C2×D4×C1312yes—
488C24C2×D4×C1311yescharacteristic
489#41—81no—
490#41—84no—
491#41—82no—
492C2×Q8—22no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—81no—
497C2×Q8—81no—
498C2×Q8C2×D4×C1311yescharacteristic
499C2×Q8C2×D4×C1312yes—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—81no—
510C2×D4—82no—
511C2×D4C2×D4×C1311yescharacteristic
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—81no—
522C22×C4C2×D4×C1312yes—
523C22×C4C2×D4×C1311yescharacteristic
524C22×C4C2×D4×C1311yescharacteristic
525C22×C4C2×D4×C1311yescharacteristic
526C22×C4C2×D4×C1311yescharacteristic
527C22×C4C2×D4×C1311yescharacteristic
528C22×C4C24×C1311yescharacteristic
529Q16—82no—
530Q16—81no—
531SD16—81no—
532M16—81no—
533C2×C8—21no—
534C2×C8—22no—
535C2×C8—21no—
536C2×C8—81no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—82no—
553C4⋊C4C2×D4×C1311yescharacteristic
554C4⋊C4C2×D4×C1312yes—
555C4⋊C4C2×D4×C1311yescharacteristic
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—81no—
573C22⋊C4—82no—
574C22⋊C4—82no—
575C42—22no—
576C42—21no—
577C13#1845311yescharacteristic, direct product factor, Sylow
578C23—22no—
579C23—22no—
580C23—21no—
581C23—24no—
582C23—41no—
583C23—41no—
584C23—42no—
585C23—42no—
586C23C13×#12011yescharacteristic
587C23C13×#12011yescharacteristic
588C23C22×D4×C1311yescharacteristic
589Q8—42no—
590Q8—41no—
591Q8—42no—
592Q8—41no—
593Q8—41no—
594Q8—42no—
595Q8—82no—
596D4—41no—
597D4—42no—
598D4—44no—
599D4—42no—
600D4—42no—
601D4—81no—
602D4—82no—
603D4—81no—
604D4—82no—
605D4—82no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4C13×#12011yescharacteristic
634C2×C4C13×#12011yescharacteristic
635C2×C4C22×D4×C1311yescharacteristic
636C2×C4C22×D4×C1311yescharacteristic
637C8—42no—
638C8—41no—
639C8—41no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—41no—
649C22—42no—
650C22—41no—
651C22—42no—
652C22—41no—
653C22—42no—
654C22—82no—
655C22—84no—
656C22C2×C13×#12011yescharacteristic
657C22C13×#57812yes—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—41no—
663C4—42no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—42no—
668C4—82no—
669C4—81no—
670C4—81no—
671C2—22no—
672C2—41no—
673C2—41no—
674C2—82no—
675C2—81no—
676C2C13×#301111yescharacteristic
677C2C13×#301911yescharacteristic
678C2C13×#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×#3196C2semidirect
3. C13×#3189C2semidirect
4. C13×#2816C2semidirect
5. C13×#1618C2semidirect
6. C13×#1614C2semidirect
7. C13×#1606C2semidirect
8. C13×#1602C2semidirect
9. C13×#1516C2semidirect
10. C13×#1511C2semidirect
11. C13×#1471C2semidirect
148. #18453C13direct (N × H)
240. #3196C2×C13semidirect
241. #3189C2×C13semidirect
242. #2816C2×C13semidirect
243. #1618C2×C13semidirect
244. #1614C2×C13semidirect
245. #1606C2×C13semidirect
246. #1602C2×C13semidirect
247. #1516C2×C13semidirect
248. #1511C2×C13semidirect
249. #1471C2×C13semidirect
577. C13#18453direct (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×#31962
C13×#31892
C13×#28162
C13×#16182
C13×#16142
C13×#16062
C13×#16022
C13×#15162
C13×#15112
C13×#14712
#1845313