Finite Group Databasebeta

← C13×#18258 #15704597

Subgroups — C13×#18258 #15704597

Order 3328.

1276 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3538C211yesmaximal, characteristic, complemented
2C13×#3003C211yesmaximal, characteristic
3C2×C13×#450C211yesmaximal, characteristic, complemented
4C13×#2435C211yesmaximal, characteristic, complemented
5C13×#1599C214yesmaximal, complemented
6C13×#1597C214yesmaximal, complemented
7C13×#1508C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic, complemented
9C13×#1472C211yesmaximal, characteristic, complemented
10C23×D4×C13C2211yescharacteristic
11C2×C13×AGL(1,ℤ/8)—21no—
12C22×C13×SD16—21no—
13C13×#563—22no—
14C13×#552—21no—
15C13×#552—21no—
16C13×#551—22no—
17D4×Q8×C13—21no—
18D4×Q8×C13—21no—
19C13×#544—21no—
20C13×#544C2212yescomplemented
21C13×#541—21no—
22C13×#539—21no—
23C13×#539C2212yescomplemented
24C13×#536—21no—
25C2×C13×#124—21no—
26C13×#525C2211yescharacteristic
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C13×C22⋊Q8C2211yescharacteristic
29C13×#450—22no—
30C13×#450—21no—
31C13×#450C2214yes—
32C13×#450C2212yes—
33C13×#447—21no—
34C13×#447C2212yes—
35C13×#418—21no—
36C2×C13×#102—21no—
37C13×#407C2211yescharacteristic
38C2×C13×C22⋊C8C2211yescharacteristic
39C13×#394C2214yes—
40C13×#390—21no—
41C13×#379—22no—
42C4×C13×C22⋊C4C2211yescharacteristic
43C13×#328C2212yescomplemented
44C13×#328C2214yescomplemented
45C13×#327C2212yescomplemented
46C13×#324C2214yescomplemented
47C25×C13—21no—
48C2×C13×#41D411yescharacteristic
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×Q8×C13D411yescharacteristic
52C22×D4×C13—21no—
53C22×D4×C13—21no—
54C22×D4×C13—21no—
55C22×D4×C13—21no—
56C22×D4×C13—21no—
57C22×D4×C13—44no—
58C22×D4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C13×AGL(1,ℤ/8)—44no—
61C2×C13×SD16—24no—
62C2×C13×SD16—22no—
63C2×C13×SD16—44no—
64C2×C13×D8—22no—
65C2×C13×M16—21no—
66C22×C8×C13—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×#126—22no—
72C13×#126—22no—
73C13×#126—22no—
74C13×#126—22no—
75C13×#125—21no—
76C13×#125—22no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#124—22no—
81C13×#124—44no—
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—22no—
85C13×#123—21no—
86C13×#123—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—21no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—21no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8D412yes—
100C13×C22⋊Q8D411yescharacteristic
101C13×C22⋊Q8C2312yes—
102C13×C22⋊Q8C2311yescharacteristic
103C13×#121D411yescharacteristic
104C13×#121C2311yescharacteristic
105C13×#120—21no—
106C4×Q8×C13—21no—
107C4×Q8×C13—21no—
108C4×D4×C13—22no—
109C4×D4×C13—21no—
110C4×D4×C13—21no—
111C4×D4×C13—22no—
112C13×#117—21no—
113C13×#117—22no—
114C13×#117—22no—
115C13×#117D411yescharacteristic
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C13×C4⋊C4C2312yes—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—24no—
123C2×C13×C22⋊C4—24no—
124C2×C13×C22⋊C4D412yes—
125C2×C42×C13—21no—
126C13×#102—24no—
127C13×#102—22no—
128C13×#102—22no—
129C13×C22⋊C8—21no—
130C13×C22⋊C8—21no—
131C13×C22⋊C8C2312yes—
132C13×C22⋊C8C2312yes—
133C13×#95C2312yes—
134#18258C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13—22no—
136C24×C13—44no—
137C24×C13—44no—
138C24×C13—41no—
139C24×C13—41no—
140C24×C13—82no—
141C24×C13C2×D411yescharacteristic
142C13×#41—42no—
143C2×Q8×C13—22no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—42no—
148C2×Q8×C13—42no—
149C2×Q8×C13—82no—
150C2×Q8×C13C2×D412yes—
151C2×Q8×C13C2×D411yescharacteristic
152C2×D4×C13—24no—
153C2×D4×C13—24no—
154C2×D4×C13—24no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13—42no—
161C2×D4×C13—42no—
162C2×D4×C13—42no—
163C2×D4×C13—44no—
164C2×D4×C13—44no—
165C2×D4×C13—44no—
166C2×D4×C13—41no—
167C2×D4×C13—41no—
168C2×D4×C13C2×D411yescharacteristic
169C22×C4×C13—21no—
170C22×C4×C13—22no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—22no—
174C22×C4×C13—42no—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2411yescharacteristic
183C13×SD16—48no—
184C13×SD16—44no—
185C13×D8—44no—
186C13×M16—42no—
187C2×C8×C13—22no—
188C2×C8×C13—22no—
189C2×C8×C13—42no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—22no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—22no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4C2×D412yes—
208C13×C4⋊C4C2×D411yescharacteristic
209C13×C4⋊C4C2×D411yescharacteristic
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—42no—
223C13×C22⋊C4—48no—
224C13×C22⋊C4—84no—
225C42×C13—22no—
226C42×C13—22no—
227C42×C13—22no—
228C42×C13—21no—
229C42×C13—42no—
230#3538C2×C1311yescharacteristic, complemented
231#3003C2×C1311yescharacteristic
232C2×#450C2×C1311yescharacteristic, complemented
233#2435C2×C1311yescharacteristic, complemented
234#1599C2×C1314yescomplemented
235#1597C2×C1314yescomplemented
236#1508C2×C1311yescharacteristic, complemented
237#1501C2×C1311yescharacteristic, complemented
238#1472C2×C1311yescharacteristic, complemented
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—24no—
242C23×C13—21no—
243C23×C13—41no—
244C23×C13—44no—
245C23×C13—44no—
246C23×C13—42no—
247C23×C13—44no—
248C23×C13—42no—
249C23×C13—44no—
250C23×C13—82no—
251C23×C13—82no—
252C23×C13—82no—
253C23×C13—816no—
254C23×C13—82no—
255C23×C13#12011yescharacteristic
256C23×C13#12011yescharacteristic
257C23×C13C22×D411yescharacteristic
258Q8×C13—42no—
259Q8×C13—41no—
260Q8×C13—42no—
261Q8×C13—42no—
262Q8×C13—81no—
263Q8×C13—82no—
264D4×C13—24no—
265D4×C13—24no—
266D4×C13—42no—
267D4×C13—42no—
268D4×C13—44no—
269D4×C13—41no—
270D4×C13—42no—
271D4×C13—42no—
272D4×C13—44no—
273D4×C13—81no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—21no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—24no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—81no—
295C2×C4×C13—82no—
296C2×C4×C13#12011yescharacteristic
297C2×C4×C13#12011yescharacteristic
298C2×C4×C13C22×D411yescharacteristic
299C2×C4×C13C22×D411yescharacteristic
300C8×C13—42no—
301C8×C13—42no—
302C23×D4C22×C1311yescharacteristic
303C2×AGL(1,ℤ/8)—21no—
304C22×SD16—21no—
305#563—22no—
306#552—21no—
307#552—21no—
308#551—22no—
309D4×Q8—21no—
310D4×Q8—21no—
311#544—21no—
312#544C22×C1312yescomplemented
313#541—21no—
314#539—21no—
315#539C22×C1312yescomplemented
316#536—21no—
317C2×#124—21no—
318#525C22×C1311yescharacteristic
319C2×C22⋊Q8C22×C1311yescharacteristic
320C2×C22⋊Q8C22×C1311yescharacteristic
321#450—22no—
322#450—21no—
323#450C22×C1314yes—
324#450C22×C1312yes—
325#447—21no—
326#447C22×C1312yes—
327#418—21no—
328C2×#102—21no—
329#407C22×C1311yescharacteristic
330C2×C22⋊C8C22×C1311yescharacteristic
331#394C22×C1314yes—
332#390—21no—
333#379—22no—
334C4×C22⋊C4C22×C1311yescharacteristic
335#328C22×C1314yescomplemented
336#328C22×C1312yescomplemented
337#327C22×C1312yescomplemented
338#324C22×C1314yescomplemented
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—44no—
347C22×C13—48no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—44no—
352C22×C13—84no—
353C22×C13—88no—
354C22×C13—88no—
355C22×C13—82no—
356C22×C13—82no—
357C22×C13#45412yes—
358C22×C13C2×#12011yescharacteristic
359C22×C13#57712yes—
360C4×C13—21no—
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—42no—
364C4×C13—41no—
365C4×C13—42no—
366C4×C13—41no—
367C4×C13—41no—
368C4×C13—42no—
369C4×C13—42no—
370C4×C13—82no—
371C4×C13B(4,𝔽2)12yes—
372C25—21no—
373C2×#41D4×C1311yescharacteristic
374C22×Q8—21no—
375C22×Q8D4×C1311yescharacteristic
376C22×Q8D4×C1311yescharacteristic
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—44no—
383C22×D4C23×C1312yes—
384C23×C4C23×C1311yescharacteristic
385AGL(1,ℤ/8)—44no—
386C2×SD16—24no—
387C2×SD16—22no—
388C2×SD16—44no—
389C2×D8—22no—
390C2×M16—21no—
391C22×C8—21no—
392C4⋊Q8—21no—
393C4⋊Q8—22no—
394C4⋊Q8—22no—
395C4⋊Q8—22no—
396#126—22no—
397#126—22no—
398#126—22no—
399#126—22no—
400#125—21no—
401#125—22no—
402#125—22no—
403#125—22no—
404#125—22no—
405#124—22no—
406#124—44no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—21no—
411#123—22no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8D4×C1312yes—
425C22⋊Q8D4×C1311yescharacteristic
426C22⋊Q8C23×C1312yes—
427C22⋊Q8C23×C1311yescharacteristic
428#121D4×C1311yescharacteristic
429#121C23×C1311yescharacteristic
430#120—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—22no—
437#117—21no—
438#117—22no—
439#117—22no—
440#117D4×C1311yescharacteristic
441C2×C4⋊C4—21no—
442C2×C4⋊C4D4×C1311yescharacteristic
443C2×C4⋊C4D4×C1311yescharacteristic
444C2×C4⋊C4C23×C1312yes—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4D4×C1312yes—
450C2×C42—21no—
451#102—24no—
452#102—22no—
453#102—22no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8C23×C1312yes—
457C22⋊C8C23×C1312yes—
458#95C23×C1312yes—
459C2×C13—22no—
460C2×C13—22no—
461C2×C13—41no—
462C2×C13—81no—
463C2×C13—84no—
464C2×C13#301011yescharacteristic
465C2×C13C2×#45411yescharacteristic
466C2×C13C2×B(4,𝔽2)11yescharacteristic
467C24—22no—
468C24—44no—
469C24—44no—
470C24—41no—
471C24—41no—
472C24—82no—
473C24C2×D4×C1311yescharacteristic
474#41—42no—
475C2×Q8—22no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—82no—
482C2×Q8C2×D4×C1312yes—
483C2×Q8C2×D4×C1311yescharacteristic
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4C2×D4×C1311yescharacteristic
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—42no—
507C22×C4C2×D4×C1312yes—
508C22×C4C2×D4×C1311yescharacteristic
509C22×C4C2×D4×C1311yescharacteristic
510C22×C4C2×D4×C1311yescharacteristic
511C22×C4C2×D4×C1312yes—
512C22×C4C2×D4×C1311yescharacteristic
513C22×C4C2×D4×C1311yescharacteristic
514C22×C4C24×C1311yescharacteristic
515SD16—48no—
516SD16—44no—
517D8—44no—
518M16—42no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—42no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4C2×D4×C1312yes—
540C4⋊C4C2×D4×C1311yescharacteristic
541C4⋊C4C2×D4×C1311yescharacteristic
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—48no—
555C22⋊C4—42no—
556C22⋊C4—84no—
557C42—22no—
558C42—22no—
559C42—22no—
560C42—21no—
561C42—42no—
562C13#1825811yescharacteristic, direct product factor, Sylow
563C23—22no—
564C23—22no—
565C23—24no—
566C23—21no—
567C23—41no—
568C23—44no—
569C23—44no—
570C23—42no—
571C23—44no—
572C23—42no—
573C23—44no—
574C23—82no—
575C23—82no—
576C23—82no—
577C23—816no—
578C23—82no—
579C23C13×#12011yescharacteristic
580C23C13×#12011yescharacteristic
581C23C22×D4×C1311yescharacteristic
582Q8—42no—
583Q8—41no—
584Q8—42no—
585Q8—42no—
586Q8—81no—
587Q8—82no—
588D4—24no—
589D4—24no—
590D4—41no—
591D4—42no—
592D4—42no—
593D4—44no—
594D4—42no—
595D4—42no—
596D4—44no—
597D4—81no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—81no—
619C2×C4—82no—
620C2×C4C13×#12011yescharacteristic
621C2×C4C13×#12011yescharacteristic
622C2×C4C22×D4×C1311yescharacteristic
623C2×C4C22×D4×C1311yescharacteristic
624C8—42no—
625C8—42no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—44no—
634C22—48no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—44no—
639C22—84no—
640C22—88no—
641C22—88no—
642C22—82no—
643C22—82no—
644C22C13×#45412yes—
645C22C2×C13×#12011yescharacteristic
646C22C13×#57712yes—
647C4—21no—
648C4—21no—
649C4—21no—
650C4—42no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4C13×B(4,𝔽2)12yes—
659C2—22no—
660C2—22no—
661C2—41no—
662C2—84no—
663C2—81no—
664C2C13×#301011yescharacteristic
665C2C2×C13×#45411yescharacteristic
666C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3003C2
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
1. C13×#3538C2semidirect
3. C2×C13×#450C2semidirect
4. C13×#2435C2semidirect
5. C13×#1599C2semidirect
6. C13×#1597C2semidirect
7. C13×#1508C2semidirect
8. C13×#1501C2semidirect
9. C13×#1472C2semidirect
20. C13×#544C22semidirect
23. C13×#539C22semidirect
43. C13×#328C22semidirect
44. C13×#328C22semidirect
45. C13×#327C22semidirect
46. C13×#324C22semidirect
134. #18258C13direct (N × H)
230. #3538C2×C13semidirect
232. C2×#450C2×C13semidirect
233. #2435C2×C13semidirect
234. #1599C2×C13semidirect
235. #1597C2×C13semidirect
236. #1508C2×C13semidirect
237. #1501C2×C13semidirect
238. #1472C2×C13semidirect
312. #544C22×C13semidirect
315. #539C22×C13semidirect
335. #328C22×C13semidirect
336. #328C22×C13semidirect
337. #327C22×C13semidirect
338. #324C22×C13semidirect
562. C13#18258direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35382
C13×#30032
C2×C13×#4502
C13×#24352
C13×#15992
C13×#15972
C13×#15082
C13×#15012
C13×#14722
#1825813