Finite Group Databasebeta

← C13×#61846 #15748185

Subgroups — C13×#61846 #15748185

Order 3328.

1664 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3502C211yesmaximal, characteristic, complemented
2Q8×C13×#41C211yesmaximal, characteristic
3C13×#3387C213yesmaximal, complemented
4C13×#3385C213yesmaximal, complemented
5Q8×C13×Q16C211yesmaximal, characteristic, complemented
6Q8×C13×SD16C211yesmaximal, characteristic, complemented
7C13×#3374C213yesmaximal, complemented
8C13×#3372C213yesmaximal, complemented
9C13×#3363C211yesmaximal, characteristic, complemented
10C13×#3359C211yesmaximal, characteristic, complemented
11C13×#3237C213yesmaximal, complemented
12C13×#3231C213yesmaximal, complemented
13C13×#3116C213yesmaximal
14C13×#3107C213yesmaximal
15C13×#2984C211yesmaximal, characteristic, complemented
16Q82×C13C2211yescharacteristic
17Q82×C13C2211yescharacteristic
18Q82×C13C2213yes—
19C13×#557—21no—
20C13×#557—23no—
21C13×#557C2211yescharacteristic
22C13×#557C2213yes—
23C13×#557C2213yes—
24C13×#554—23no—
25C13×#554C2213yes—
26D4×Q8×C13—21no—
27D4×Q8×C13C2211yescharacteristic
28C13×#544—23no—
29C13×#533—23no—
30C13×#533C2213yes—
31C13×#533C2213yes—
32C13×#533C2213yes—
33C13×#519—21no—
34C4×C13×#41C2213yes—
35C2×C4×Q8×C13—21no—
36C2×C4×Q8×C13C2211yescharacteristic
37C13×#501C2216yes—
38C13×#500C2213yes—
39C13×#498C2213yes—
40C13×#491C2216yes—
41C13×#487C2213yes—
42C13×#487C2213yes—
43C13×#485C2213yes—
44C13×#485C2213yes—
45C13×#485C2216yes—
46C13×#479C2216yes—
47C13×#479C2216yes—
48C13×#477C2213yes—
49C13×#477C2213yes—
50C13×#477C2213yes—
51C13×#476C2213yes—
52C13×#475C2213yes—
53C13×#475C2213yes—
54C13×#475C2213yes—
55C13×#474C2213yes—
56C13×#462C2213yes—
57C13×#462C2213yes—
58C13×#461C2213yes—
59C13×#461C2213yes—
60C13×#452C2211yescharacteristic
61C13×#452C2213yes—
62C13×#446C2213yes—
63C13×#446C2213yes—
64C8×Q8×C13C2211yescharacteristic
65C8×Q8×C13C2211yescharacteristic
66C13×#441C2216yes—
67C13×#440C2216yes—
68C4×C13×Q16C2213yes—
69C4×C13×Q16C2213yes—
70C4×C13×SD16C2213yes—
71C4×C13×SD16C2213yes—
72C13×#432C2213yes—
73C13×#431C2213yes—
74C2×C13×#41C2311yescharacteristic
75C22×Q8×C13—21no—
76C22×Q8×C13D411yescharacteristic
77C2×C13×Q16C2311yescharacteristic
78C2×C13×Q16C2313yes—
79C2×C13×SD16C2311yescharacteristic
80C2×C13×SD16C2313yes—
81C13×C4⋊Q8—23no—
82C13×C4⋊Q8—23no—
83C13×C4⋊Q8—23no—
84C13×C4⋊Q8—26no—
85C13×C4⋊Q8—23no—
86C13×C4⋊Q8C2313yes—
87C13×C4⋊Q8C2313yes—
88C13×C4⋊Q8C2313yes—
89C13×C4⋊Q8C2313yes—
90C13×C4⋊Q8C2313yes—
91C13×C4⋊Q8C2313yes—
92C13×#125—26no—
93C13×#125—23no—
94C13×#125—26no—
95C13×#125—23no—
96C13×#125—23no—
97C13×#125—23no—
98C13×#125C2316yes—
99C13×C22⋊Q8—23no—
100C13×C22⋊Q8—23no—
101C13×C22⋊Q8—23no—
102C13×C22⋊Q8—23no—
103C13×C22⋊Q8—23no—
104C13×C22⋊Q8—23no—
105C13×C22⋊Q8—26no—
106C13×C22⋊Q8C2311yescharacteristic
107C13×C22⋊Q8C2313yes—
108C4×Q8×C13—21no—
109C4×Q8×C13—23no—
110C4×Q8×C13—21no—
111C4×Q8×C13—23no—
112C4×Q8×C13—21no—
113C4×Q8×C13—23no—
114C4×Q8×C13—23no—
115C4×Q8×C13—23no—
116C4×Q8×C13—23no—
117C4×Q8×C13—23no—
118C4×Q8×C13D411yescharacteristic
119C4×Q8×C13D413yes—
120C4×Q8×C13C2313yes—
121C4×Q8×C13C2313yes—
122C4×Q8×C13C2313yes—
123C4×Q8×C13C2316yes—
124C4×Q8×C13C2313yes—
125C4×Q8×C13C2311yescharacteristic
126C4×Q8×C13C2313yes—
127C4×D4×C13—23no—
128C4×D4×C13—23no—
129C4×D4×C13C2313yes—
130C4×D4×C13C2313yes—
131C13×#117—23no—
132C13×#117—23no—
133C13×#117—23no—
134C13×#117C2313yes—
135C2×C13×C4⋊C4—23no—
136C2×C13×C4⋊C4D413yes—
137C2×C42×C13—23no—
138C2×C42×C13C2313yes—
139C13×#107C2313yes—
140C13×#107C2313yes—
141C13×#107C2316yes—
142C13×#106C2313yes—
143C13×#106C2313yes—
144C13×#106C2316yes—
145C13×C4⋊C8C2313yes—
146C13×C4⋊C8C2313yes—
147C13×C4⋊C8C2313yes—
148C13×C4⋊C8C2313yes—
149C13×#103C2313yes—
150C13×#103C2313yes—
151C13×#103C2311yescharacteristic
152C13×#103C2313yes—
153C13×#103C2313yes—
154C13×#103C2313yes—
155C13×#103C2316yes—
156C13×#103C2316yes—
157C13×#102C2311yescharacteristic
158C13×#102C2313yes—
159C13×C22⋊C8C2311yescharacteristic
160C13×C22⋊C8C2313yes—
161C13×#97C2316yes—
162C4×C8×C13C2313yes—
163C4×C8×C13C2313yes—
164#61846C1311yesmaximal, characteristic, direct product factor, Sylow
165C13×#41—22no—
166C13×#41—22no—
167C2×Q8×C13—24no—
168C2×Q8×C13—23no—
169C2×Q8×C13—23no—
170C2×Q8×C13—23no—
171C2×Q8×C13—23no—
172C2×Q8×C13—44no—
173C2×Q8×C13C2×D413yes—
174C2×Q8×C13C2×D411yescharacteristic
175C2×Q8×C13C2411yescharacteristic
176C2×Q8×C13C2413yes—
177C2×Q8×C13C2411yescharacteristic
178C2×D4×C13—21no—
179C2×D4×C13C2411yescharacteristic
180C22×C4×C13—21no—
181C22×C4×C13—23no—
182C22×C4×C13—23no—
183C22×C4×C13C2×D413yes—
184C22×C4×C13C2×D413yes—
185C22×C4×C13C2411yescharacteristic
186C13×Q16—22no—
187C13×Q16—26no—
188C13×SD16—22no—
189C13×SD16—26no—
190C2×C8×C13C2411yescharacteristic
191C2×C8×C13C2411yescharacteristic
192C2×C8×C13C2413yes—
193C2×C8×C13C2413yes—
194C13×C4⋊C4—26no—
195C13×C4⋊C4—23no—
196C13×C4⋊C4—23no—
197C13×C4⋊C4—23no—
198C13×C4⋊C4—23no—
199C13×C4⋊C4—23no—
200C13×C4⋊C4—23no—
201C13×C4⋊C4—23no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—23no—
204C13×C4⋊C4—23no—
205C13×C4⋊C4—26no—
206C13×C4⋊C4—23no—
207C13×C4⋊C4—23no—
208C13×C4⋊C4—26no—
209C13×C4⋊C4—23no—
210C13×C4⋊C4—23no—
211C13×C4⋊C4C2×D413yes—
212C13×C4⋊C4C2×D416yes—
213C13×C4⋊C4C2×D413yes—
214C13×C4⋊C4C2411yescharacteristic
215C13×C4⋊C4C2413yes—
216C13×C4⋊C4C2413yes—
217C13×C4⋊C4C2413yes—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—23no—
220C13×C22⋊C4—23no—
221C13×C22⋊C4—23no—
222C13×C22⋊C4—23no—
223C42×C13—23no—
224C42×C13—23no—
225C42×C13—23no—
226C42×C13—26no—
227C42×C13—23no—
228C42×C13—23no—
229C42×C13C2×D413yes—
230C42×C13C2×D413yes—
231C42×C13C2413yes—
232C42×C13C2413yes—
233#3502C2×C1311yescharacteristic, complemented
234Q8×#41C2×C1311yescharacteristic
235#3387C2×C1313yescomplemented
236#3385C2×C1313yescomplemented
237Q8×Q16C2×C1311yescharacteristic, complemented
238Q8×SD16C2×C1311yescharacteristic, complemented
239#3374C2×C1313yescomplemented
240#3372C2×C1313yescomplemented
241#3363C2×C1311yescharacteristic, complemented
242#3359C2×C1311yescharacteristic, complemented
243#3237C2×C1313yescomplemented
244#3231C2×C1313yescomplemented
245#3116C2×C1313yes—
246#3107C2×C1313yes—
247#2984C2×C1311yescharacteristic, complemented
248C23×C13—21no—
249C23×C13C22×D411yescharacteristic
250Q8×C13—26no—
251Q8×C13—21no—
252Q8×C13—21no—
253Q8×C13—23no—
254Q8×C13—21no—
255Q8×C13—23no—
256Q8×C13—46no—
257Q8×C13—83no—
258Q8×C13—83no—
259Q8×C13—83no—
260Q8×C13#13714yes—
261Q8×C132−1+412yes—
262D4×C13—24no—
263D4×C13—21no—
264D4×C132−1+412yes—
265C2×C4×C13—24no—
266C2×C4×C13—21no—
267C2×C4×C13—26no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—23no—
271C2×C4×C13—21no—
272C2×C4×C13—23no—
273C2×C4×C13—21no—
274C2×C4×C13—23no—
275C2×C4×C13—23no—
276C2×C4×C13—43no—
277C2×C4×C13—46no—
278C2×C4×C13—83no—
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C22×D413yes—
281C2×C4×C13C22×D413yes—
282C2×C4×C13C22×D413yes—
283C2×C4×C13C22×D413yes—
284C2×C4×C13C2511yescharacteristic
285C8×C13—21no—
286C8×C13—23no—
287C8×C13—21no—
288C8×C13—23no—
289Q82C22×C1311yescharacteristic
290Q82C22×C1311yescharacteristic
291Q82C22×C1313yes—
292#557—21no—
293#557—23no—
294#557C22×C1311yescharacteristic
295#557C22×C1313yes—
296#557C22×C1313yes—
297#554—23no—
298#554C22×C1313yes—
299D4×Q8—21no—
300D4×Q8C22×C1311yescharacteristic
301#544—23no—
302#533—23no—
303#533C22×C1313yes—
304#533C22×C1313yes—
305#533C22×C1313yes—
306#519—21no—
307C4×#41C22×C1313yes—
308C2×C4×Q8—21no—
309C2×C4×Q8C22×C1311yescharacteristic
310#501C22×C1316yes—
311#500C22×C1313yes—
312#498C22×C1313yes—
313#491C22×C1316yes—
314#487C22×C1313yes—
315#487C22×C1313yes—
316#485C22×C1313yes—
317#485C22×C1313yes—
318#485C22×C1316yes—
319#479C22×C1316yes—
320#479C22×C1316yes—
321#477C22×C1313yes—
322#477C22×C1313yes—
323#477C22×C1313yes—
324#476C22×C1313yes—
325#475C22×C1313yes—
326#475C22×C1313yes—
327#475C22×C1313yes—
328#474C22×C1313yes—
329#462C22×C1313yes—
330#462C22×C1313yes—
331#461C22×C1313yes—
332#461C22×C1313yes—
333#452C22×C1311yescharacteristic
334#452C22×C1313yes—
335#446C22×C1313yes—
336#446C22×C1313yes—
337C8×Q8C22×C1311yescharacteristic
338C8×Q8C22×C1311yescharacteristic
339#441C22×C1316yes—
340#440C22×C1316yes—
341C4×Q16C22×C1313yes—
342C4×Q16C22×C1313yes—
343C4×SD16C22×C1313yes—
344C4×SD16C22×C1313yes—
345#432C22×C1313yes—
346#431C22×C1313yes—
347C22×C13—21no—
348C22×C13—21no—
349C22×C13—22no—
350C22×C13—21no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13C23×D411yescharacteristic
354C4×C13—23no—
355C4×C13—23no—
356C4×C13—21no—
357C4×C13—22no—
358C4×C13—23no—
359C4×C13—43no—
360C4×C13—41no—
361C4×C13—43no—
362C4×C13—43no—
363C4×C13—41no—
364C4×C13—43no—
365C4×C13C2×#13716yes—
366C4×C13C2×2−1+411yescharacteristic
367C4×C13C2×2−1+411yescharacteristic
368C2×#41C23×C1311yescharacteristic
369C22×Q8—21no—
370C22×Q8D4×C1311yescharacteristic
371C2×Q16C23×C1311yescharacteristic
372C2×Q16C23×C1313yes—
373C2×SD16C23×C1311yescharacteristic
374C2×SD16C23×C1313yes—
375C4⋊Q8—23no—
376C4⋊Q8—23no—
377C4⋊Q8—23no—
378C4⋊Q8—26no—
379C4⋊Q8—23no—
380C4⋊Q8C23×C1313yes—
381C4⋊Q8C23×C1313yes—
382C4⋊Q8C23×C1313yes—
383C4⋊Q8C23×C1313yes—
384C4⋊Q8C23×C1313yes—
385C4⋊Q8C23×C1313yes—
386#125—26no—
387#125—23no—
388#125—26no—
389#125—23no—
390#125—23no—
391#125—23no—
392#125C23×C1316yes—
393C22⋊Q8—23no—
394C22⋊Q8—23no—
395C22⋊Q8—23no—
396C22⋊Q8—23no—
397C22⋊Q8—23no—
398C22⋊Q8—23no—
399C22⋊Q8—26no—
400C22⋊Q8C23×C1311yescharacteristic
401C22⋊Q8C23×C1313yes—
402C4×Q8—21no—
403C4×Q8—23no—
404C4×Q8—21no—
405C4×Q8—23no—
406C4×Q8—21no—
407C4×Q8—23no—
408C4×Q8—23no—
409C4×Q8—23no—
410C4×Q8—23no—
411C4×Q8—23no—
412C4×Q8D4×C1311yescharacteristic
413C4×Q8D4×C1313yes—
414C4×Q8C23×C1313yes—
415C4×Q8C23×C1313yes—
416C4×Q8C23×C1313yes—
417C4×Q8C23×C1313yes—
418C4×Q8C23×C1316yes—
419C4×Q8C23×C1311yescharacteristic
420C4×Q8C23×C1313yes—
421C4×D4—23no—
422C4×D4—23no—
423C4×D4C23×C1313yes—
424C4×D4C23×C1313yes—
425#117—23no—
426#117—23no—
427#117—23no—
428#117C23×C1313yes—
429C2×C4⋊C4—23no—
430C2×C4⋊C4D4×C1313yes—
431C2×C42—23no—
432C2×C42C23×C1313yes—
433#107C23×C1313yes—
434#107C23×C1313yes—
435#107C23×C1316yes—
436#106C23×C1313yes—
437#106C23×C1313yes—
438#106C23×C1316yes—
439C4⋊C8C23×C1313yes—
440C4⋊C8C23×C1313yes—
441C4⋊C8C23×C1313yes—
442C4⋊C8C23×C1313yes—
443#103C23×C1313yes—
444#103C23×C1313yes—
445#103C23×C1311yescharacteristic
446#103C23×C1313yes—
447#103C23×C1313yes—
448#103C23×C1313yes—
449#103C23×C1316yes—
450#103C23×C1316yes—
451#102C23×C1311yescharacteristic
452#102C23×C1313yes—
453C22⋊C8C23×C1311yescharacteristic
454C22⋊C8C23×C1313yes—
455#97C23×C1316yes—
456C4×C8C23×C1313yes—
457C4×C8C23×C1313yes—
458C2×C13—41no—
459C2×C13—42no—
460C2×C13#348611yescharacteristic
461C2×C13C22×#13711yescharacteristic
462C2×C13#358411yescharacteristic
463#41—22no—
464#41—22no—
465C2×Q8—24no—
466C2×Q8—23no—
467C2×Q8—23no—
468C2×Q8—23no—
469C2×Q8—23no—
470C2×Q8—44no—
471C2×Q8C2×D4×C1313yes—
472C2×Q8C2×D4×C1311yescharacteristic
473C2×Q8C24×C1311yescharacteristic
474C2×Q8C24×C1313yes—
475C2×Q8C24×C1311yescharacteristic
476C2×D4—21no—
477C2×D4C24×C1311yescharacteristic
478C22×C4—21no—
479C22×C4—23no—
480C22×C4—23no—
481C22×C4C2×D4×C1313yes—
482C22×C4C2×D4×C1313yes—
483C22×C4C24×C1311yescharacteristic
484Q16—22no—
485Q16—26no—
486SD16—22no—
487SD16—26no—
488C2×C8C24×C1311yescharacteristic
489C2×C8C24×C1311yescharacteristic
490C2×C8C24×C1313yes—
491C2×C8C24×C1313yes—
492C4⋊C4—26no—
493C4⋊C4—23no—
494C4⋊C4—23no—
495C4⋊C4—23no—
496C4⋊C4—23no—
497C4⋊C4—23no—
498C4⋊C4—23no—
499C4⋊C4—23no—
500C4⋊C4—21no—
501C4⋊C4—23no—
502C4⋊C4—23no—
503C4⋊C4—26no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—26no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4C2×D4×C1313yes—
510C4⋊C4C2×D4×C1316yes—
511C4⋊C4C2×D4×C1313yes—
512C4⋊C4C24×C1311yescharacteristic
513C4⋊C4C24×C1313yes—
514C4⋊C4C24×C1313yes—
515C4⋊C4C24×C1313yes—
516C22⋊C4—21no—
517C22⋊C4—23no—
518C22⋊C4—23no—
519C22⋊C4—23no—
520C22⋊C4—23no—
521C42—23no—
522C42—23no—
523C42—23no—
524C42—26no—
525C42—23no—
526C42—23no—
527C42C2×D4×C1313yes—
528C42C2×D4×C1313yes—
529C42C24×C1313yes—
530C42C24×C1313yes—
531C13#6184611yescharacteristic, direct product factor, Sylow
532C23—21no—
533C23C22×D4×C1311yescharacteristic
534Q8—26no—
535Q8—21no—
536Q8—21no—
537Q8—23no—
538Q8—21no—
539Q8—23no—
540Q8—46no—
541Q8—83no—
542Q8—83no—
543Q8—83no—
544Q8C13×#13714yes—
545Q8C13×2−1+412yes—
546D4—24no—
547D4—21no—
548D4C13×2−1+412yes—
549C2×C4—24no—
550C2×C4—21no—
551C2×C4—26no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—23no—
555C2×C4—21no—
556C2×C4—23no—
557C2×C4—21no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—43no—
561C2×C4—46no—
562C2×C4—83no—
563C2×C4C22×D4×C1311yescharacteristic
564C2×C4C22×D4×C1313yes—
565C2×C4C22×D4×C1313yes—
566C2×C4C22×D4×C1313yes—
567C2×C4C22×D4×C1313yes—
568C2×C4C25×C1311yescharacteristic
569C8—21no—
570C8—23no—
571C8—21no—
572C8—23no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22C23×D4×C1311yescharacteristic
580C4—23no—
581C4—23no—
582C4—23no—
583C4—21no—
584C4—22no—
585C4—43no—
586C4—43no—
587C4—41no—
588C4—43no—
589C4—43no—
590C4—41no—
591C4C2×C13×#13716yes—
592C4C2×C13×2−1+411yescharacteristic
593C4C2×C13×2−1+411yescharacteristic
594C2—41no—
595C2—42no—
596C2C13×#348611yescharacteristic
597C2C22×C13×#13711yescharacteristic
598C2C13×#358411yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
prime radicalC2×C13×#41C23
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×#3502C2semidirect
3. C13×#3387C2semidirect
4. C13×#3385C2semidirect
5. Q8×C13×Q16C2semidirect
6. Q8×C13×SD16C2semidirect
7. C13×#3374C2semidirect
8. C13×#3372C2semidirect
9. C13×#3363C2semidirect
10. C13×#3359C2semidirect
11. C13×#3237C2semidirect
12. C13×#3231C2semidirect
15. C13×#2984C2semidirect
164. #61846C13direct (N × H)
233. #3502C2×C13semidirect
235. #3387C2×C13semidirect
236. #3385C2×C13semidirect
237. Q8×Q16C2×C13semidirect
238. Q8×SD16C2×C13semidirect
239. #3374C2×C13semidirect
240. #3372C2×C13semidirect
241. #3363C2×C13semidirect
242. #3359C2×C13semidirect
243. #3237C2×C13semidirect
244. #3231C2×C13semidirect
247. #2984C2×C13semidirect
531. C13#61846direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35022
Q8×C13×#412
C13×#33872
C13×#33852
Q8×C13×Q162
Q8×C13×SD162
C13×#33742
C13×#33722
C13×#33632
C13×#33592
C13×#32372
C13×#32312
C13×#31162
C13×#31072
C13×#29842
#6184613