Finite Group Databasebeta

← C13×#61903 #15748242

Subgroups — C13×#61903 #15748242

Order 3328.

1974 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3497C211yesmaximal, characteristic, complemented
2C13×#3480C211yesmaximal, characteristic, complemented
3C13×#3399C213yesmaximal, complemented
4C13×#3397C213yesmaximal, complemented
5C13×#3392C211yesmaximal, characteristic, complemented
6C13×#3391C211yesmaximal, characteristic, complemented
7C13×#3373C213yesmaximal, complemented
8C13×#3367C213yesmaximal, complemented
9C13×#3359C211yesmaximal, characteristic, complemented
10C13×#3358C211yesmaximal, characteristic, complemented
11C13×#3214C213yesmaximal, complemented
12C13×#3207C213yesmaximal, complemented
13C13×#3115C213yesmaximal, complemented
14C13×#3106C213yesmaximal, complemented
15C13×#2984C211yesmaximal, characteristic, complemented
16C2×C13×2−1+4—21no—
17C13×#559C2213yes—
18C13×#557C2211yescharacteristic
19C13×#556C2213yes—
20C13×#553—23no—
21C13×#550C2211yescharacteristic
22C13×#550C2211yescharacteristic
23C13×#550C2213yes—
24D4×Q8×C13C2211yescharacteristic
25D4×Q8×C13C2213yes—
26C13×#548—21no—
27C13×#548—21no—
28C13×#548—23no—
29C13×#537—23no—
30C13×#532C2213yes—
31C13×#532C2213yes—
32C13×#532C2213yes—
33C13×#529—23no—
34C4×C13×#41—21no—
35C4×C13×#41C2213yes—
36C2×C4×Q8×C13C2211yescharacteristic
37C13×#496C2216yes—
38C13×#493C2213yes—
39C13×#492C2213yes—
40C13×#489C2216yes—
41C13×#487C2213yes—
42C13×#486C2213yes—
43C13×#482C2211yescharacteristic
44C13×#482C2213yes—
45C13×#477C2213yes—
46C13×#476C2213yes—
47C13×#475C2213yes—
48C13×#474C2213yes—
49C13×#463C2216yes—
50C13×#463C2216yes—
51C13×#461C2213yes—
52C13×#461C2213yes—
53C13×#460C2213yes—
54C13×#460C2213yes—
55C13×#459C2213yes—
56C13×#459C2213yes—
57C13×#459C2213yes—
58C13×#459C2213yes—
59C13×#449C2213yes—
60C13×#449C2213yes—
61C13×#449C2216yes—
62C13×#446C2213yes—
63C13×#446C2213yes—
64C8×Q8×C13C2211yescharacteristic
65C8×Q8×C13C2211yescharacteristic
66C13×#442C2216yes—
67C13×#440C2216yes—
68C4×C13×SD16C2213yes—
69C4×C13×SD16C2213yes—
70C4×C13×D8C2213yes—
71C4×C13×D8C2213yes—
72C13×#432C2213yes—
73C13×#431C2213yes—
74C13×2−1+4—48no—
75C2×C13×#41—21no—
76C2×C13×#41—23no—
77C2×C13×#41—21no—
78C2×C13×#41—23no—
79C2×C13×#41—23no—
80C2×C13×#41C2313yes—
81C22×Q8×C13—23no—
82C22×Q8×C13—21no—
83C22×Q8×C13D411yescharacteristic
84C2×C13×SD16C2313yes—
85C2×C13×SD16C2313yes—
86C2×C13×SD16C2316yes—
87C2×C13×D8C2313yes—
88C2×C13×D8C2313yes—
89C2×C13×D8C2316yes—
90C13×C4⋊Q8C2313yes—
91C13×C4⋊Q8C2313yes—
92C13×C4⋊Q8C2313yes—
93C13×#127C2313yes—
94C13×#127C2313yes—
95C13×#127C2313yes—
96C13×#126—26no—
97C13×#125—23no—
98C13×#124—23no—
99C13×#124—23no—
100C13×#124—23no—
101C13×#124C2316yes—
102C13×#123—26no—
103C13×C22⋊Q8—23no—
104C13×C22⋊Q8—23no—
105C13×C22⋊Q8—23no—
106C13×C22⋊Q8—26no—
107C13×#121—23no—
108C13×#121—23no—
109C13×#121—23no—
110C13×#121—23no—
111C13×#121—23no—
112C13×#121—23no—
113C13×#121—23no—
114C13×#121—26no—
115C13×#121C2313yes—
116C13×#121C2311yescharacteristic
117C4×Q8×C13—21no—
118C4×Q8×C13D411yescharacteristic
119C4×Q8×C13D413yes—
120C4×Q8×C13C2313yes—
121C4×Q8×C13C2313yes—
122C4×Q8×C13C2311yescharacteristic
123C4×Q8×C13C2313yes—
124C4×D4×C13—23no—
125C4×D4×C13—23no—
126C4×D4×C13—23no—
127C4×D4×C13—23no—
128C4×D4×C13—23no—
129C4×D4×C13—23no—
130C4×D4×C13—23no—
131C4×D4×C13C2313yes—
132C4×D4×C13C2313yes—
133C4×D4×C13C2313yes—
134C4×D4×C13C2316yes—
135C4×D4×C13C2313yes—
136C13×#117—23no—
137C13×#117—23no—
138C13×#117C2311yescharacteristic
139C2×C13×C4⋊C4D413yes—
140C2×C42×C13—23no—
141C2×C42×C13C2313yes—
142C13×#107C2311yescharacteristic
143C13×#107C2313yes—
144C13×#106C2311yescharacteristic
145C13×#106C2313yes—
146C13×C4⋊C8C2313yes—
147C13×C4⋊C8C2313yes—
148C13×C4⋊C8C2313yes—
149C13×C4⋊C8C2313yes—
150C13×#103C2313yes—
151C13×#103C2313yes—
152C13×#103C2316yes—
153C13×#102C2311yescharacteristic
154C13×#102C2313yes—
155C13×#102C2313yes—
156C13×#102C2313yes—
157C13×#102C2311yescharacteristic
158C13×#102C2313yes—
159C13×#102C2316yes—
160C13×C22⋊C8C2311yescharacteristic
161C13×C22⋊C8C2313yes—
162C13×#97C2316yes—
163C4×C8×C13C2313yes—
164C4×C8×C13C2313yes—
165#61903C1311yesmaximal, characteristic, direct product factor, Sylow
166C13×#41—43no—
167C13×#41—43no—
168C13×#41—412no—
169C13×#41—412no—
170C13×#41—412no—
171C13×#41—44no—
172C13×#41—44no—
173C2×Q8×C13—24no—
174C2×Q8×C13—23no—
175C2×Q8×C13—23no—
176C2×Q8×C13—412no—
177C2×Q8×C13—44no—
178C2×Q8×C13C2×D413yes—
179C2×Q8×C13C2×D411yescharacteristic
180C2×Q8×C13C2413yes—
181C2×D4×C13—23no—
182C2×D4×C13—21no—
183C2×D4×C13—23no—
184C2×D4×C13—23no—
185C2×D4×C13—23no—
186C2×D4×C13—23no—
187C2×D4×C13—23no—
188C2×D4×C13—23no—
189C2×D4×C13—23no—
190C2×D4×C13C2413yes—
191C2×D4×C13C2411yescharacteristic
192C2×D4×C13C2413yes—
193C22×C4×C13—23no—
194C22×C4×C13—23no—
195C22×C4×C13—26no—
196C22×C4×C13—23no—
197C22×C4×C13—23no—
198C22×C4×C13—23no—
199C22×C4×C13C2×D413yes—
200C22×C4×C13C2×D413yes—
201C22×C4×C13C2411yescharacteristic
202C13×SD16—43no—
203C13×SD16—46no—
204C13×SD16—43no—
205C13×D8—43no—
206C13×D8—46no—
207C13×D8—43no—
208C2×C8×C13C2411yescharacteristic
209C2×C8×C13C2411yescharacteristic
210C2×C8×C13C2413yes—
211C2×C8×C13C2413yes—
212C13×C4⋊C4—23no—
213C13×C4⋊C4—23no—
214C13×C4⋊C4—23no—
215C13×C4⋊C4—23no—
216C13×C4⋊C4—23no—
217C13×C4⋊C4—23no—
218C13×C4⋊C4C2×D413yes—
219C13×C4⋊C4C2×D413yes—
220C13×C4⋊C4C2×D416yes—
221C13×C4⋊C4C2411yescharacteristic
222C13×C4⋊C4C2411yescharacteristic
223C13×C4⋊C4C2411yescharacteristic
224C13×C4⋊C4C2413yes—
225C13×C22⋊C4—21no—
226C13×C22⋊C4—26no—
227C13×C22⋊C4—23no—
228C13×C22⋊C4—23no—
229C13×C22⋊C4—21no—
230C13×C22⋊C4—23no—
231C13×C22⋊C4—26no—
232C13×C22⋊C4—26no—
233C13×C22⋊C4—23no—
234C13×C22⋊C4—23no—
235C42×C13—21no—
236C42×C13—23no—
237C42×C13—23no—
238C42×C13C2×D413yes—
239C42×C13C2×D413yes—
240C42×C13C2413yes—
241C42×C13C2413yes—
242#3497C2×C1311yescharacteristic, complemented
243#3480C2×C1311yescharacteristic, complemented
244#3399C2×C1313yescomplemented
245#3397C2×C1313yescomplemented
246#3392C2×C1311yescharacteristic, complemented
247#3391C2×C1311yescharacteristic, complemented
248#3373C2×C1313yescomplemented
249#3367C2×C1313yescomplemented
250#3359C2×C1311yescharacteristic, complemented
251#3358C2×C1311yescharacteristic, complemented
252#3214C2×C1313yescomplemented
253#3207C2×C1313yescomplemented
254#3115C2×C1313yescomplemented
255#3106C2×C1313yescomplemented
256#2984C2×C1311yescharacteristic, complemented
257C23×C13—23no—
258C23×C13—21no—
259C23×C13—23no—
260C23×C13C22×D411yescharacteristic
261Q8×C13—26no—
262Q8×C13—23no—
263Q8×C13—23no—
264Q8×C13—46no—
265Q8×C13—46no—
266Q8×C13AGL(1,ℤ/8)14yes—
267D4×C13—21no—
268D4×C13—23no—
269D4×C13—23no—
270D4×C13—23no—
271D4×C13—23no—
272D4×C13—21no—
273D4×C13—46no—
274D4×C13—46no—
275D4×C13—46no—
276D4×C13—42no—
277D4×C13—46no—
278D4×C13—46no—
279D4×C13—83no—
280D4×C13—83no—
281D4×C13—83no—
282C2×C4×C13—26no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—23no—
288C2×C4×C13—23no—
289C2×C4×C13—21no—
290C2×C4×C13—43no—
291C2×C4×C13—412no—
292C2×C4×C13—46no—
293C2×C4×C13—46no—
294C2×C4×C13—46no—
295C2×C4×C13—46no—
296C2×C4×C13—83no—
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C13C22×D413yes—
299C2×C4×C13C22×D413yes—
300C2×C4×C13C22×D413yes—
301C2×C4×C13C22×D413yes—
302C2×C4×C13C2511yescharacteristic
303C8×C13—21no—
304C8×C13—23no—
305C8×C13—23no—
306C8×C13—21no—
307C2×2−1+4—21no—
308#559C22×C1313yes—
309#557C22×C1311yescharacteristic
310#556C22×C1313yes—
311#553—23no—
312#550C22×C1311yescharacteristic
313#550C22×C1311yescharacteristic
314#550C22×C1313yes—
315D4×Q8C22×C1311yescharacteristic
316D4×Q8C22×C1313yes—
317#548—21no—
318#548—21no—
319#548—23no—
320#537—23no—
321#532C22×C1313yes—
322#532C22×C1313yes—
323#532C22×C1313yes—
324#529—23no—
325C4×#41—21no—
326C4×#41C22×C1313yes—
327C2×C4×Q8C22×C1311yescharacteristic
328#496C22×C1316yes—
329#493C22×C1313yes—
330#492C22×C1313yes—
331#489C22×C1316yes—
332#487C22×C1313yes—
333#486C22×C1313yes—
334#482C22×C1311yescharacteristic
335#482C22×C1313yes—
336#477C22×C1313yes—
337#476C22×C1313yes—
338#475C22×C1313yes—
339#474C22×C1313yes—
340#463C22×C1316yes—
341#463C22×C1316yes—
342#461C22×C1313yes—
343#461C22×C1313yes—
344#460C22×C1313yes—
345#460C22×C1313yes—
346#459C22×C1313yes—
347#459C22×C1313yes—
348#459C22×C1313yes—
349#459C22×C1313yes—
350#449C22×C1313yes—
351#449C22×C1313yes—
352#449C22×C1316yes—
353#446C22×C1313yes—
354#446C22×C1313yes—
355C8×Q8C22×C1311yescharacteristic
356C8×Q8C22×C1311yescharacteristic
357#442C22×C1316yes—
358#440C22×C1316yes—
359C4×SD16C22×C1313yes—
360C4×SD16C22×C1313yes—
361C4×D8C22×C1313yes—
362C4×D8C22×C1313yes—
363#432C22×C1313yes—
364#431C22×C1313yes—
365C22×C13—21no—
366C22×C13—21no—
367C22×C13—21no—
368C22×C13—43no—
369C22×C13—41no—
370C22×C13—43no—
371C22×C13—43no—
372C22×C13—41no—
373C22×C13—43no—
374C22×C13—43no—
375C22×C13—41no—
376C22×C13—43no—
377C22×C13C23×D411yescharacteristic
378C4×C13—23no—
379C4×C13—23no—
380C4×C13—21no—
381C4×C13—23no—
382C4×C13—41no—
383C4×C13—43no—
384C4×C13—41no—
385C4×C13—43no—
386C4×C13—41no—
387C4×C13C2×AGL(1,ℤ/8)16yes—
388C4×C13#58511yescharacteristic
389C4×C13#58511yescharacteristic
3902−1+4—48no—
391C2×#41—21no—
392C2×#41—23no—
393C2×#41—21no—
394C2×#41—23no—
395C2×#41—23no—
396C2×#41C23×C1313yes—
397C22×Q8—23no—
398C22×Q8—21no—
399C22×Q8D4×C1311yescharacteristic
400C2×SD16C23×C1313yes—
401C2×SD16C23×C1313yes—
402C2×SD16C23×C1316yes—
403C2×D8C23×C1313yes—
404C2×D8C23×C1313yes—
405C2×D8C23×C1316yes—
406C4⋊Q8C23×C1313yes—
407C4⋊Q8C23×C1313yes—
408C4⋊Q8C23×C1313yes—
409#127C23×C1313yes—
410#127C23×C1313yes—
411#127C23×C1313yes—
412#126—26no—
413#125—23no—
414#124—23no—
415#124—23no—
416#124—23no—
417#124C23×C1316yes—
418#123—26no—
419C22⋊Q8—23no—
420C22⋊Q8—23no—
421C22⋊Q8—23no—
422C22⋊Q8—26no—
423#121—23no—
424#121—23no—
425#121—23no—
426#121—23no—
427#121—23no—
428#121—23no—
429#121—23no—
430#121—26no—
431#121C23×C1311yescharacteristic
432#121C23×C1313yes—
433C4×Q8—21no—
434C4×Q8D4×C1311yescharacteristic
435C4×Q8D4×C1313yes—
436C4×Q8C23×C1313yes—
437C4×Q8C23×C1313yes—
438C4×Q8C23×C1311yescharacteristic
439C4×Q8C23×C1313yes—
440C4×D4—23no—
441C4×D4—23no—
442C4×D4—23no—
443C4×D4—23no—
444C4×D4—23no—
445C4×D4—23no—
446C4×D4—23no—
447C4×D4C23×C1313yes—
448C4×D4C23×C1313yes—
449C4×D4C23×C1313yes—
450C4×D4C23×C1313yes—
451C4×D4C23×C1316yes—
452#117—23no—
453#117—23no—
454#117C23×C1311yescharacteristic
455C2×C4⋊C4D4×C1313yes—
456C2×C42—23no—
457C2×C42C23×C1313yes—
458#107C23×C1311yescharacteristic
459#107C23×C1313yes—
460#106C23×C1311yescharacteristic
461#106C23×C1313yes—
462C4⋊C8C23×C1313yes—
463C4⋊C8C23×C1313yes—
464C4⋊C8C23×C1313yes—
465C4⋊C8C23×C1313yes—
466#103C23×C1313yes—
467#103C23×C1313yes—
468#103C23×C1316yes—
469#102C23×C1311yescharacteristic
470#102C23×C1313yes—
471#102C23×C1313yes—
472#102C23×C1313yes—
473#102C23×C1311yescharacteristic
474#102C23×C1313yes—
475#102C23×C1316yes—
476C22⋊C8C23×C1311yescharacteristic
477C22⋊C8C23×C1313yes—
478#97C23×C1316yes—
479C4×C8C23×C1313yes—
480C4×C8C23×C1313yes—
481C2×C13—41no—
482C2×C13—83no—
483C2×C13—81no—
484C2×C13—83no—
485C2×C13#348711yescharacteristic
486C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
487C2×C13#358411yescharacteristic
488#41—43no—
489#41—43no—
490#41—412no—
491#41—412no—
492#41—412no—
493#41—44no—
494#41—44no—
495C2×Q8—24no—
496C2×Q8—23no—
497C2×Q8—23no—
498C2×Q8—412no—
499C2×Q8—44no—
500C2×Q8C2×D4×C1313yes—
501C2×Q8C2×D4×C1311yescharacteristic
502C2×Q8C24×C1313yes—
503C2×D4—23no—
504C2×D4—21no—
505C2×D4—23no—
506C2×D4—23no—
507C2×D4—23no—
508C2×D4—23no—
509C2×D4—23no—
510C2×D4—23no—
511C2×D4—23no—
512C2×D4C24×C1313yes—
513C2×D4C24×C1311yescharacteristic
514C2×D4C24×C1313yes—
515C22×C4—23no—
516C22×C4—23no—
517C22×C4—26no—
518C22×C4—23no—
519C22×C4—23no—
520C22×C4—23no—
521C22×C4C2×D4×C1313yes—
522C22×C4C2×D4×C1313yes—
523C22×C4C24×C1311yescharacteristic
524SD16—43no—
525SD16—46no—
526SD16—43no—
527D8—43no—
528D8—46no—
529D8—43no—
530C2×C8C24×C1311yescharacteristic
531C2×C8C24×C1311yescharacteristic
532C2×C8C24×C1313yes—
533C2×C8C24×C1313yes—
534C4⋊C4—23no—
535C4⋊C4—23no—
536C4⋊C4—23no—
537C4⋊C4—23no—
538C4⋊C4—23no—
539C4⋊C4—23no—
540C4⋊C4C2×D4×C1313yes—
541C4⋊C4C2×D4×C1313yes—
542C4⋊C4C2×D4×C1316yes—
543C4⋊C4C24×C1311yescharacteristic
544C4⋊C4C24×C1311yescharacteristic
545C4⋊C4C24×C1311yescharacteristic
546C4⋊C4C24×C1313yes—
547C22⋊C4—21no—
548C22⋊C4—26no—
549C22⋊C4—23no—
550C22⋊C4—23no—
551C22⋊C4—21no—
552C22⋊C4—23no—
553C22⋊C4—26no—
554C22⋊C4—26no—
555C22⋊C4—23no—
556C22⋊C4—23no—
557C42—21no—
558C42—23no—
559C42—23no—
560C42C2×D4×C1313yes—
561C42C2×D4×C1313yes—
562C42C24×C1313yes—
563C42C24×C1313yes—
564C13#6190311yescharacteristic, direct product factor, Sylow
565C23—23no—
566C23—23no—
567C23—21no—
568C23C22×D4×C1311yescharacteristic
569Q8—26no—
570Q8—23no—
571Q8—23no—
572Q8—46no—
573Q8—46no—
574Q8C13×AGL(1,ℤ/8)14yes—
575D4—21no—
576D4—23no—
577D4—23no—
578D4—23no—
579D4—23no—
580D4—21no—
581D4—46no—
582D4—46no—
583D4—46no—
584D4—42no—
585D4—46no—
586D4—46no—
587D4—83no—
588D4—83no—
589D4—83no—
590C2×C4—26no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—23no—
596C2×C4—23no—
597C2×C4—21no—
598C2×C4—43no—
599C2×C4—412no—
600C2×C4—46no—
601C2×C4—46no—
602C2×C4—46no—
603C2×C4—46no—
604C2×C4—83no—
605C2×C4C22×D4×C1311yescharacteristic
606C2×C4C22×D4×C1313yes—
607C2×C4C22×D4×C1313yes—
608C2×C4C22×D4×C1313yes—
609C2×C4C22×D4×C1313yes—
610C2×C4C25×C1311yescharacteristic
611C8—21no—
612C8—23no—
613C8—23no—
614C8—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—43no—
619C22—41no—
620C22—43no—
621C22—43no—
622C22—41no—
623C22—43no—
624C22—43no—
625C22—41no—
626C22—43no—
627C22C23×D4×C1311yescharacteristic
628C4—23no—
629C4—23no—
630C4—23no—
631C4—21no—
632C4—41no—
633C4—43no—
634C4—41no—
635C4—41no—
636C4—43no—
637C4C2×C13×AGL(1,ℤ/8)16yes—
638C4C13×#58511yescharacteristic
639C4C13×#58511yescharacteristic
640C2—41no—
641C2—83no—
642C2—81no—
643C2—83no—
644C2C13×#348711yescharacteristic
645C2C22×C13×AGL(1,ℤ/8)11yescharacteristic
646C2C13×#358411yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3497C2semidirect
2. C13×#3480C2semidirect
3. C13×#3399C2semidirect
4. C13×#3397C2semidirect
5. C13×#3392C2semidirect
6. C13×#3391C2semidirect
7. C13×#3373C2semidirect
8. C13×#3367C2semidirect
9. C13×#3359C2semidirect
10. C13×#3358C2semidirect
11. C13×#3214C2semidirect
12. C13×#3207C2semidirect
13. C13×#3115C2semidirect
14. C13×#3106C2semidirect
15. C13×#2984C2semidirect
165. #61903C13direct (N × H)
242. #3497C2×C13semidirect
243. #3480C2×C13semidirect
244. #3399C2×C13semidirect
245. #3397C2×C13semidirect
246. #3392C2×C13semidirect
247. #3391C2×C13semidirect
248. #3373C2×C13semidirect
249. #3367C2×C13semidirect
250. #3359C2×C13semidirect
251. #3358C2×C13semidirect
252. #3214C2×C13semidirect
253. #3207C2×C13semidirect
254. #3115C2×C13semidirect
255. #3106C2×C13semidirect
256. #2984C2×C13semidirect
564. C13#61903direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34972
C13×#34802
C13×#33992
C13×#33972
C13×#33922
C13×#33912
C13×#33732
C13×#33672
C13×#33592
C13×#33582
C13×#32142
C13×#32072
C13×#31152
C13×#31062
C13×#29842
#6190313