Finite Group Databasebeta

← C13×#18278 #15704617

Subgroups — C13×#18278 #15704617

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic, complemented
2C13×#3110C211yesmaximal, characteristic, complemented
3C13×#3105C211yesmaximal, characteristic
4C13×#2562C211yesmaximal, characteristic, complemented
5C13×#1617C212yesmaximal, complemented
6C13×#1615C212yesmaximal, complemented
7C13×#1599C212yesmaximal, complemented
8C13×#1597C212yesmaximal
9C13×#1509C211yesmaximal, characteristic, complemented
10C13×#1503C211yesmaximal, characteristic, complemented
11C13×#1470C211yesmaximal, characteristic, complemented
12C13×#564—21no—
13C13×#563—21no—
14C13×#557—21no—
15C13×#554—21no—
16C13×#552—21no—
17C13×#552—21no—
18C13×#552—22no—
19C13×#544—21no—
20C13×#544C2212yes—
21C13×#541—21no—
22C13×#541—22no—
23C13×#539C2212yes—
24C13×#533C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C13×#484C2211yescharacteristic
29C13×#484C2212yes—
30C13×#481C2211yescharacteristic
31C13×#478—21no—
32C13×#474—21no—
33C13×#463—21no—
34C13×#461—21no—
35C13×#450C2211yescharacteristic
36C13×#450C2212yes—
37C13×#447C2211yescharacteristic
38C13×#440—22no—
39C4×C13×SD16—21no—
40C4×C13×D8—21no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#400C2212yes—
44C13×#394C2212yes—
45C13×#388—22no—
46C13×#380—21no—
47C13×#380—21no—
48C4×C13×C4⋊C4C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C22×D4×C13C2311yescharacteristic
56C23×C4×C13—21no—
57C2×C13×SD16—21no—
58C2×C13×SD16—22no—
59C2×C13×D8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8—22no—
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8D411yescharacteristic
64C13×C4⋊Q8D411yescharacteristic
65C13×#126—22no—
66C13×#126—22no—
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—21no—
70C13×#125—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—22no—
76C13×#125—22no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#125—21no—
80C13×#125—21no—
81C13×#125—21no—
82C13×#125—21no—
83C13×#125—21no—
84C13×#125D411yescharacteristic
85C13×#124D411yescharacteristic
86C13×#123—22no—
87C13×#123—21no—
88C13×#123—22no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8C2311yescharacteristic
97C13×C22⋊Q8C2312yes—
98C13×#121C2311yescharacteristic
99C4×Q8×C13—21no—
100C4×Q8×C13—22no—
101C4×Q8×C13—21no—
102C4×Q8×C13—21no—
103C4×Q8×C13D411yescharacteristic
104C4×Q8×C13D412yes—
105C4×D4×C13—21no—
106C4×D4×C13—22no—
107C4×D4×C13—21no—
108C4×D4×C13—21no—
109C4×D4×C13—21no—
110C4×D4×C13—21no—
111C4×D4×C13D411yescharacteristic
112C13×#117—22no—
113C13×#117—21no—
114C13×#117—21no—
115C13×#117—22no—
116C13×#117—21no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4D411yescharacteristic
120C2×C13×C4⋊C4D411yescharacteristic
121C2×C13×C4⋊C4D412yes—
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C4⋊C4C2312yes—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—22no—
127C2×C42×C13—21no—
128C2×C42×C13C2311yescharacteristic
129C13×#107—21no—
130C13×#107—22no—
131C13×#106—21no—
132C13×C4⋊C8—21no—
133C13×C4⋊C8—21no—
134C13×#103—21no—
135C13×#103—22no—
136C13×#102—21no—
137C13×#102—21no—
138C13×#102—21no—
139C13×#102—22no—
140C13×C22⋊C8C2312yes—
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2311yescharacteristic
143C13×#97—21no—
144C4×C8×C13—21no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18278C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13—21no—
150C2×Q8×C13—22no—
151C2×Q8×C13—21no—
152C2×Q8×C13C2×D412yes—
153C2×Q8×C13C2×D411yescharacteristic
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—42no—
158C2×D4×C13C2×D411yescharacteristic
159C22×C4×C13—22no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—22no—
163C22×C4×C13—42no—
164C22×C4×C13—42no—
165C22×C4×C13—41no—
166C22×C4×C13—41no—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2411yescharacteristic
172C13×SD16—42no—
173C13×SD16—44no—
174C13×D8—42no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—42no—
206C13×C4⋊C4C2×D411yescharacteristic
207C13×C4⋊C4C2×D411yescharacteristic
208C13×C4⋊C4C2×D412yes—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—21no—
214C13×C22⋊C4—21no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—44no—
219C13×C22⋊C4—41no—
220C13×C22⋊C4—41no—
221C13×C22⋊C4—82no—
222C42×C13—22no—
223C42×C13—22no—
224C42×C13—22no—
225C42×C13—22no—
226C42×C13—21no—
227C42×C13—81no—
228C42×C13C2×D411yescharacteristic
229C42×C13C2×D411yescharacteristic
230C42×C13C2×D411yescharacteristic
231C42×C13C2×D411yescharacteristic
232#3563C2×C1311yescharacteristic, complemented
233#3110C2×C1311yescharacteristic, complemented
234#3105C2×C1311yescharacteristic
235#2562C2×C1311yescharacteristic, complemented
236#1617C2×C1312yescomplemented
237#1615C2×C1312yescomplemented
238#1599C2×C1312yescomplemented
239#1597C2×C1312yes—
240#1509C2×C1311yescharacteristic, complemented
241#1503C2×C1311yescharacteristic, complemented
242#1470C2×C1311yescharacteristic, complemented
243C23×C13—22no—
244C23×C13—21no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13C22×D411yescharacteristic
252Q8×C13—41no—
253Q8×C13—42no—
254Q8×C13—42no—
255Q8×C13—82no—
256D4×C13—22no—
257D4×C13—22no—
258D4×C13—41no—
259D4×C13—41no—
260D4×C13—41no—
261D4×C13—41no—
262D4×C13—41no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—41no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—42no—
284C2×C4×C13—82no—
285C2×C4×C13—82no—
286C2×C4×C13—82no—
287C2×C4×C13#12011yescharacteristic
288C2×C4×C13#12011yescharacteristic
289C2×C4×C13#12011yescharacteristic
290C2×C4×C13#12011yescharacteristic
291C2×C4×C13C22×D411yescharacteristic
292C2×C4×C13C22×D411yescharacteristic
293C8×C13—41no—
294C8×C13—41no—
295C8×C13—42no—
296#564—21no—
297#563—21no—
298#557—21no—
299#554—21no—
300#552—21no—
301#552—21no—
302#552—22no—
303#544—21no—
304#544C22×C1312yes—
305#541—21no—
306#541—22no—
307#539C22×C1312yes—
308#533C22×C1311yescharacteristic
309#529C22×C1311yescharacteristic
310C2×#125C22×C1311yescharacteristic
311C2×C4×D4C22×C1311yescharacteristic
312#484C22×C1311yescharacteristic
313#484C22×C1312yes—
314#481C22×C1311yescharacteristic
315#478—21no—
316#474—21no—
317#463—21no—
318#461—21no—
319#450C22×C1311yescharacteristic
320#450C22×C1312yes—
321#447C22×C1311yescharacteristic
322#440—22no—
323C4×SD16—21no—
324C4×D8—21no—
325#432C22×C1311yescharacteristic
326#431C22×C1311yescharacteristic
327#400C22×C1312yes—
328#394C22×C1312yes—
329#388—22no—
330#380—21no—
331#380—21no—
332C4×C4⋊C4C22×C1311yescharacteristic
333#328C22×C1312yes—
334#328C22×C1312yes—
335#328C22×C1312yes—
336#327C22×C1312yes—
337#324C22×C1312yes—
338#324C22×C1312yes—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—42no—
342C22×C13—42no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—42no—
347C22×C13—81no—
348C22×C13—81no—
349C22×C13—81no—
350C22×C13—81no—
351C22×C13C2×#12011yescharacteristic
352C22×C13#57711yescharacteristic
353C22×C13#57811yescharacteristic
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—21no—
358C4×C13—21no—
359C4×C13—42no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—42no—
363C4×C13—42no—
364C4×C13—42no—
365C4×C13—41no—
366C4×C13—82no—
367C4×C13—81no—
368C4×C13#45412yes—
369C22×D4C23×C1311yescharacteristic
370C23×C4—21no—
371C2×SD16—21no—
372C2×SD16—22no—
373C2×D8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8D4×C1311yescharacteristic
378C4⋊Q8D4×C1311yescharacteristic
379#126—22no—
380#126—22no—
381#126—22no—
382#126—22no—
383#126—21no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—21no—
389#125—22no—
390#125—22no—
391#125—22no—
392#125—22no—
393#125—21no—
394#125—21no—
395#125—21no—
396#125—21no—
397#125—21no—
398#125D4×C1311yescharacteristic
399#124D4×C1311yescharacteristic
400#123—22no—
401#123—21no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—21no—
409C22⋊Q8—22no—
410C22⋊Q8C23×C1311yescharacteristic
411C22⋊Q8C23×C1312yes—
412#121C23×C1311yescharacteristic
413C4×Q8—21no—
414C4×Q8—22no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8D4×C1311yescharacteristic
418C4×Q8D4×C1312yes—
419C4×D4—21no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4D4×C1311yescharacteristic
426#117—22no—
427#117—21no—
428#117—21no—
429#117—22no—
430#117—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C1311yescharacteristic
434C2×C4⋊C4D4×C1312yes—
435C2×C4⋊C4D4×C1311yescharacteristic
436C2×C4⋊C4C23×C1311yescharacteristic
437C2×C4⋊C4C23×C1312yes—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C42—21no—
442C2×C42C23×C1311yescharacteristic
443#107—21no—
444#107—22no—
445#106—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448#103—21no—
449#103—22no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—22no—
454C22⋊C8C23×C1312yes—
455C22⋊C8C23×C1311yescharacteristic
456C22⋊C8C23×C1311yescharacteristic
457#97—21no—
458C4×C8—21no—
459#95—22no—
460#95—22no—
461#95C23×C1312yes—
462C2×C13—21no—
463C2×C13—21no—
464C2×C13—81no—
465C2×C13—82no—
466C2×C13#301311yescharacteristic
467C2×C13C2×#45411yescharacteristic
468C2×C13#302511yescharacteristic
469C24—21no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8C2×D4×C1312yes—
473C2×Q8C2×D4×C1311yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4C2×D4×C1311yescharacteristic
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C2×D4×C1312yes—
488C22×C4C2×D4×C1311yescharacteristic
489C22×C4C2×D4×C1311yescharacteristic
490C22×C4C2×D4×C1312yes—
491C22×C4C24×C1311yescharacteristic
492SD16—42no—
493SD16—44no—
494D8—42no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4C2×D4×C1311yescharacteristic
527C4⋊C4C2×D4×C1311yescharacteristic
528C4⋊C4C2×D4×C1312yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—44no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—82no—
542C42—22no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—21no—
547C42—81no—
548C42C2×D4×C1311yescharacteristic
549C42C2×D4×C1311yescharacteristic
550C42C2×D4×C1311yescharacteristic
551C42C2×D4×C1311yescharacteristic
552C13#1827811yescharacteristic, direct product factor, Sylow
553C23—22no—
554C23—21no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C22×D4×C1311yescharacteristic
562Q8—41no—
563Q8—42no—
564Q8—42no—
565Q8—82no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4C13×#12011yescharacteristic
598C2×C4C13×#12011yescharacteristic
599C2×C4C13×#12011yescharacteristic
600C2×C4C13×#12011yescharacteristic
601C2×C4C22×D4×C1311yescharacteristic
602C2×C4C22×D4×C1311yescharacteristic
603C8—41no—
604C8—41no—
605C8—42no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22C2×C13×#12011yescharacteristic
619C22C13×#57711yescharacteristic
620C22C13×#57811yescharacteristic
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—41no—
628C4—41no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—41no—
633C4—82no—
634C4—81no—
635C4C13×#45412yes—
636C2—21no—
637C2—21no—
638C2—82no—
639C2—81no—
640C2C13×#301311yescharacteristic
641C2C2×C13×#45411yescharacteristic
642C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#447C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3563C2semidirect
2. C13×#3110C2semidirect
4. C13×#2562C2semidirect
5. C13×#1617C2semidirect
6. C13×#1615C2semidirect
7. C13×#1599C2semidirect
9. C13×#1509C2semidirect
10. C13×#1503C2semidirect
11. C13×#1470C2semidirect
148. #18278C13direct (N × H)
232. #3563C2×C13semidirect
233. #3110C2×C13semidirect
235. #2562C2×C13semidirect
236. #1617C2×C13semidirect
237. #1615C2×C13semidirect
238. #1599C2×C13semidirect
240. #1509C2×C13semidirect
241. #1503C2×C13semidirect
242. #1470C2×C13semidirect
552. C13#18278direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#31102
C13×#31052
C13×#25622
C13×#16172
C13×#16152
C13×#15992
C13×#15972
C13×#15092
C13×#15032
C13×#14702
#1827813