Finite Group Databasebeta

← C13×#18275 #15704614

Subgroups — C13×#18275 #15704614

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3113C211yesmaximal, characteristic, complemented
3C13×#3108C211yesmaximal, characteristic, complemented
4C13×#2592C211yesmaximal, characteristic, complemented
5C13×#1612C212yesmaximal, complemented
6C13×#1608C212yesmaximal, complemented
7C13×#1606C212yesmaximal, complemented
8C13×#1602C212yesmaximal, complemented
9C13×#1509C211yesmaximal, characteristic, complemented
10C13×#1503C211yesmaximal, characteristic, complemented
11C13×#1469C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#562—21no—
14C13×#556—21no—
15C13×#551—22no—
16D4×Q8×C13—21no—
17C13×#548—21no—
18C13×#546—21no—
19C13×#543C2212yes—
20C13×#542—21no—
21C13×#542—22no—
22C13×#538C2212yes—
23C13×#536—21no—
24C13×#533C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#124C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C13×#483C2211yescharacteristic
29C13×#483C2212yes—
30C13×#480C2211yescharacteristic
31C13×#479—21no—
32C13×#475—21no—
33C13×#464—21no—
34C13×#462—21no—
35C13×#451C2211yescharacteristic
36C13×#451C2212yes—
37C13×#448C2211yescharacteristic
38C13×#441—22no—
39C4×C13×Q16—21no—
40C4×C13×SD16—21no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#397C2212yes—
44C13×#393C2212yes—
45C13×#391—21no—
46C13×#390—21no—
47C13×#388—22no—
48C4×C13×C4⋊C4C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#323C2212yes—
54C13×#323C2212yes—
55C2×C13×#41—21no—
56C22×Q8×C13—21no—
57C22×Q8×C13D411yescharacteristic
58C22×Q8×C13C2311yescharacteristic
59C22×D4×C13D411yescharacteristic
60C2×C13×Q16—21no—
61C2×C13×Q16—22no—
62C2×C13×SD16—21no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8D411yescharacteristic
66C13×C4⋊Q8D411yescharacteristic
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—22no—
70C13×#126—21no—
71C13×#125—21no—
72C13×#125D411yescharacteristic
73C13×#124—21no—
74C13×#124—22no—
75C13×#124—22no—
76C13×#124—21no—
77C13×#124—21no—
78C13×#124—21no—
79C13×#124—21no—
80C13×#124D411yescharacteristic
81C13×#123—22no—
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—21no—
85C13×#123—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8C2311yescharacteristic
96C13×C22⋊Q8C2312yes—
97C13×#121—21no—
98C13×#121—22no—
99C13×#121—22no—
100C13×#121C2311yescharacteristic
101C13×#120—22no—
102C4×Q8×C13—21no—
103C4×Q8×C13—21no—
104C4×Q8×C13—21no—
105C4×Q8×C13—21no—
106C4×Q8×C13—21no—
107C4×Q8×C13—21no—
108C4×Q8×C13D411yescharacteristic
109C4×Q8×C13D412yes—
110C4×D4×C13—21no—
111C4×D4×C13—22no—
112C4×D4×C13—21no—
113C4×D4×C13—22no—
114C4×D4×C13D411yescharacteristic
115C13×#117—22no—
116C13×#117—21no—
117C13×#117—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4D412yes—
125C2×C13×C22⋊C4C2312yes—
126C2×C42×C13—21no—
127C2×C42×C13—21no—
128C2×C42×C13C2311yescharacteristic
129C13×#107—21no—
130C13×#106—21no—
131C13×#106—22no—
132C13×C4⋊C8—21no—
133C13×C4⋊C8—21no—
134C13×#103—21no—
135C13×#103—22no—
136C13×#103—21no—
137C13×#103—21no—
138C13×#103—22no—
139C13×#102—21no—
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#18275C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13C2×D412yes—
150C13×#41—82no—
151C2×Q8×C13—22no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—42no—
158C2×Q8×C13—42no—
159C2×Q8×C13—82no—
160C2×Q8×C13C2×D411yescharacteristic
161C2×Q8×C13C2×D412yes—
162C2×D4×C13—21no—
163C2×D4×C13—22no—
164C2×D4×C13—22no—
165C2×D4×C13—21no—
166C2×D4×C13—21no—
167C2×D4×C13—42no—
168C2×D4×C13C2×D411yescharacteristic
169C22×C4×C13—21no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—21no—
174C22×C4×C13—22no—
175C22×C4×C13—21no—
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2411yescharacteristic
180C13×Q16—42no—
181C13×Q16—44no—
182C13×SD16—42no—
183C2×C8×C13—21no—
184C2×C8×C13—21no—
185C2×C8×C13—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—42no—
202C13×C4⋊C4—41no—
203C13×C4⋊C4—41no—
204C13×C4⋊C4C2×D411yescharacteristic
205C13×C4⋊C4C2×D412yes—
206C13×C4⋊C4C2×D411yescharacteristic
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—21no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—44no—
223C13×C22⋊C4—82no—
224C42×C13—22no—
225C42×C13—22no—
226C42×C13—21no—
227C42×C13—41no—
228C42×C13—41no—
229C42×C13—81no—
230C42×C13C2×D411yescharacteristic
231C42×C13C2×D411yescharacteristic
232C42×C13C2×D411yescharacteristic
233C42×C13C2×D411yescharacteristic
234#3561C2×C1311yescharacteristic
235#3113C2×C1311yescharacteristic, complemented
236#3108C2×C1311yescharacteristic, complemented
237#2592C2×C1311yescharacteristic, complemented
238#1612C2×C1312yescomplemented
239#1608C2×C1312yescomplemented
240#1606C2×C1312yescomplemented
241#1602C2×C1312yescomplemented
242#1509C2×C1311yescharacteristic, complemented
243#1503C2×C1311yescharacteristic, complemented
244#1469C2×C1311yescharacteristic, complemented
245C23×C13—22no—
246C23×C13—21no—
247C23×C13—22no—
248C23×C13—22no—
249C23×C13—42no—
250C23×C13—42no—
251C23×C13C22×D411yescharacteristic
252Q8×C13—22no—
253Q8×C13—22no—
254Q8×C13—41no—
255Q8×C13—41no—
256Q8×C13—41no—
257Q8×C13—42no—
258Q8×C13—42no—
259Q8×C13—42no—
260Q8×C13—81no—
261Q8×C13—82no—
262D4×C13—41no—
263D4×C13—41no—
264D4×C13—41no—
265D4×C13—42no—
266D4×C13—81no—
267D4×C13—82no—
268D4×C13—82no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—21no—
274C2×C4×C13—22no—
275C2×C4×C13—21no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—21no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—41no—
287C2×C4×C13—42no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—82no—
291C2×C4×C13—82no—
292C2×C4×C13—82no—
293C2×C4×C13#12011yescharacteristic
294C2×C4×C13#12011yescharacteristic
295C2×C4×C13#12011yescharacteristic
296C2×C4×C13#12011yescharacteristic
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C13C22×D411yescharacteristic
299C8×C13—41no—
300C8×C13—41no—
301C8×C13—42no—
302#563—21no—
303#562—21no—
304#556—21no—
305#551—22no—
306D4×Q8—21no—
307#548—21no—
308#546—21no—
309#543C22×C1312yes—
310#542—21no—
311#542—22no—
312#538C22×C1312yes—
313#536—21no—
314#533C22×C1311yescharacteristic
315#529C22×C1311yescharacteristic
316C2×#124C22×C1311yescharacteristic
317C2×C4×Q8C22×C1311yescharacteristic
318#483C22×C1311yescharacteristic
319#483C22×C1312yes—
320#480C22×C1311yescharacteristic
321#479—21no—
322#475—21no—
323#464—21no—
324#462—21no—
325#451C22×C1311yescharacteristic
326#451C22×C1312yes—
327#448C22×C1311yescharacteristic
328#441—22no—
329C4×Q16—21no—
330C4×SD16—21no—
331#432C22×C1311yescharacteristic
332#431C22×C1311yescharacteristic
333#397C22×C1312yes—
334#393C22×C1312yes—
335#391—21no—
336#390—21no—
337#388—22no—
338C4×C4⋊C4C22×C1311yescharacteristic
339#328C22×C1312yes—
340#328C22×C1312yes—
341#328C22×C1312yes—
342#327C22×C1312yes—
343#323C22×C1312yes—
344#323C22×C1312yes—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13—41no—
348C22×C13—42no—
349C22×C13—41no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13—41no—
353C22×C13—82no—
354C22×C13—82no—
355C22×C13C2×#12011yescharacteristic
356C22×C13#57711yescharacteristic
357C22×C13#57811yescharacteristic
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—21no—
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13—42no—
368C4×C13—41no—
369C4×C13—42no—
370C4×C13—82no—
371C4×C13—81no—
372C4×C13#45512yes—
373C2×#41—21no—
374C22×Q8—21no—
375C22×Q8D4×C1311yescharacteristic
376C22×Q8C23×C1311yescharacteristic
377C22×D4D4×C1311yescharacteristic
378C2×Q16—21no—
379C2×Q16—22no—
380C2×SD16—21no—
381C4⋊Q8—21no—
382C4⋊Q8—22no—
383C4⋊Q8D4×C1311yescharacteristic
384C4⋊Q8D4×C1311yescharacteristic
385#126—22no—
386#126—22no—
387#126—22no—
388#126—21no—
389#125—21no—
390#125D4×C1311yescharacteristic
391#124—21no—
392#124—22no—
393#124—22no—
394#124—21no—
395#124—21no—
396#124—21no—
397#124—21no—
398#124D4×C1311yescharacteristic
399#123—22no—
400#123—22no—
401#123—22no—
402#123—21no—
403#123—22no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—21no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8C23×C1311yescharacteristic
414C22⋊Q8C23×C1312yes—
415#121—21no—
416#121—22no—
417#121—22no—
418#121C23×C1311yescharacteristic
419#120—22no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8D4×C1311yescharacteristic
427C4×Q8D4×C1312yes—
428C4×D4—21no—
429C4×D4—22no—
430C4×D4—21no—
431C4×D4—22no—
432C4×D4D4×C1311yescharacteristic
433#117—22no—
434#117—21no—
435#117—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4C23×C1311yescharacteristic
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4D4×C1312yes—
443C2×C22⋊C4C23×C1312yes—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42C23×C1311yescharacteristic
447#107—21no—
448#106—21no—
449#106—22no—
450C4⋊C8—21no—
451C4⋊C8—21no—
452#103—21no—
453#103—22no—
454#103—21no—
455#103—21no—
456#103—22no—
457#102—21no—
458C22⋊C8C23×C1312yes—
459C22⋊C8C23×C1311yescharacteristic
460C22⋊C8C23×C1311yescharacteristic
461#97—21no—
462C4×C8—21no—
463#95—22no—
464#95—22no—
465#95C23×C1312yes—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13—81no—
469C2×C13—82no—
470C2×C13#301311yescharacteristic
471C2×C13C2×#45511yescharacteristic
472C2×C13#302511yescharacteristic
473C24C2×D4×C1312yes—
474#41—82no—
475C2×Q8—22no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—82no—
484C2×Q8C2×D4×C1311yescharacteristic
485C2×Q8C2×D4×C1312yes—
486C2×D4—21no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—42no—
492C2×D4C2×D4×C1311yescharacteristic
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4C2×D4×C1311yescharacteristic
501C22×C4C2×D4×C1311yescharacteristic
502C22×C4C2×D4×C1312yes—
503C22×C4C24×C1311yescharacteristic
504Q16—42no—
505Q16—44no—
506SD16—42no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4C2×D4×C1311yescharacteristic
529C4⋊C4C2×D4×C1312yes—
530C4⋊C4C2×D4×C1311yescharacteristic
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—44no—
547C22⋊C4—82no—
548C42—22no—
549C42—22no—
550C42—21no—
551C42—41no—
552C42—41no—
553C42—81no—
554C42C2×D4×C1311yescharacteristic
555C42C2×D4×C1311yescharacteristic
556C42C2×D4×C1311yescharacteristic
557C42C2×D4×C1311yescharacteristic
558C13#1827511yescharacteristic, direct product factor, Sylow
559C23—22no—
560C23—21no—
561C23—22no—
562C23—22no—
563C23—42no—
564C23—42no—
565C23C22×D4×C1311yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—41no—
569Q8—42no—
570Q8—41no—
571Q8—41no—
572Q8—42no—
573Q8—42no—
574Q8—81no—
575Q8—82no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—42no—
580D4—81no—
581D4—82no—
582D4—82no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4C13×#12011yescharacteristic
608C2×C4C13×#12011yescharacteristic
609C2×C4C13×#12011yescharacteristic
610C2×C4C13×#12011yescharacteristic
611C2×C4C22×D4×C1311yescharacteristic
612C2×C4C22×D4×C1311yescharacteristic
613C8—41no—
614C8—41no—
615C8—42no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—42no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—41no—
624C22—82no—
625C22—82no—
626C22C2×C13×#12011yescharacteristic
627C22C13×#57711yescharacteristic
628C22C13×#57811yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—41no—
640C4—42no—
641C4—82no—
642C4—81no—
643C4C13×#45512yes—
644C2—21no—
645C2—21no—
646C2—82no—
647C2—81no—
648C2C13×#301311yescharacteristic
649C2C2×C13×#45511yescharacteristic
650C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3561C2
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
2. C13×#3113C2semidirect
3. C13×#3108C2semidirect
4. C13×#2592C2semidirect
5. C13×#1612C2semidirect
6. C13×#1608C2semidirect
7. C13×#1606C2semidirect
8. C13×#1602C2semidirect
9. C13×#1509C2semidirect
10. C13×#1503C2semidirect
11. C13×#1469C2semidirect
148. #18275C13direct (N × H)
235. #3113C2×C13semidirect
236. #3108C2×C13semidirect
237. #2592C2×C13semidirect
238. #1612C2×C13semidirect
239. #1608C2×C13semidirect
240. #1606C2×C13semidirect
241. #1602C2×C13semidirect
242. #1509C2×C13semidirect
243. #1503C2×C13semidirect
244. #1469C2×C13semidirect
558. C13#18275direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35612
C13×#31132
C13×#31082
C13×#25922
C13×#16122
C13×#16082
C13×#16062
C13×#16022
C13×#15092
C13×#15032
C13×#14692
#1827513