Finite Group Databasebeta

← C13×#18467 #15704806

Subgroups — C13×#18467 #15704806

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3236C211yesmaximal, characteristic, complemented
3C13×#3232C211yesmaximal, characteristic, complemented
4C13×#2820C211yesmaximal, characteristic, complemented
5C13×#1618C212yesmaximal, complemented
6C13×#1614C212yesmaximal, complemented
7C13×#1612C212yesmaximal, complemented
8C13×#1608C212yesmaximal, complemented
9C13×#1518C211yesmaximal, characteristic, complemented
10C13×#1512C211yesmaximal, 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×#125C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C13×#501—21no—
29C13×#499—21no—
30C13×#491—21no—
31C13×#488—21no—
32C13×#484C2211yescharacteristic
33C13×#484C2212yes—
34C13×#483C2211yescharacteristic
35C13×#483C2212yes—
36C13×#481C2211yescharacteristic
37C13×#480C2211yescharacteristic
38C13×#479—21no—
39C13×#479—22no—
40C13×#478—21no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#399C2212yes—
44C13×#397C2212yes—
45C13×#396—22no—
46C13×#395—21no—
47C13×#394—21no—
48C13×#382C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#323C2212yes—
54C13×#323C2212yes—
55C2×C13×#41—21no—
56C22×Q8×C13—21no—
57C22×Q8×C13D411yescharacteristic
58C22×D4×C13D411yescharacteristic
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8D411yescharacteristic
62C13×C4⋊Q8D411yescharacteristic
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—22no—
66C13×#126—21no—
67C13×#125—21no—
68C13×#125—21no—
69C13×#125—21no—
70C13×#125—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×C13D411yescharacteristic
105C4×Q8×C13D412yes—
106C4×D4×C13—21no—
107C4×D4×C13—22no—
108C4×D4×C13—21no—
109C4×D4×C13—22no—
110C4×D4×C13D411yescharacteristic
111C13×#117—22no—
112C13×#117—21no—
113C13×#117—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—22no—
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C4⋊C4C2311yescharacteristic
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4D412yes—
124C2×C13×C22⋊C4C2312yes—
125C2×C42×C13C2311yescharacteristic
126C13×#107—21no—
127C13×#107—21no—
128C13×#107—22no—
129C13×#106—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—22no—
138C13×#102—21no—
139C13×#102—21no—
140C13×C22⋊C8C2312yes—
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2311yescharacteristic
143C13×#97—21no—
144C4×C8×C13—21no—
145C13×#95—21no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18467C1311yesmaximal, 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—81no—
156C2×Q8×C13—82no—
157C2×Q8×C13C2×D411yescharacteristic
158C2×Q8×C13C2×D412yes—
159C2×D4×C13—21no—
160C2×D4×C13—22no—
161C2×D4×C13—22no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—81no—
165C2×D4×C13C2×D411yescharacteristic
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—21no—
170C22×C4×C13—22no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2411yescharacteristic
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—41no—
198C13×C4⋊C4—41no—
199C13×C4⋊C4—41no—
200C13×C4⋊C4—41no—
201C13×C4⋊C4—81no—
202C13×C4⋊C4—82no—
203C13×C4⋊C4C2×D411yescharacteristic
204C13×C4⋊C4C2×D411yescharacteristic
205C13×C4⋊C4C2×D412yes—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—21no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—82no—
222C13×C22⋊C4—82no—
223C42×C13—22no—
224C42×C13—22no—
225C42×C13—21no—
226C42×C13C2×D411yescharacteristic
227C42×C13C2×D411yescharacteristic
228C42×C13C2×D411yescharacteristic
229C42×C13C2×D411yescharacteristic
230#3561C2×C1311yescharacteristic
231#3236C2×C1311yescharacteristic, complemented
232#3232C2×C1311yescharacteristic, complemented
233#2820C2×C1311yescharacteristic, complemented
234#1618C2×C1312yescomplemented
235#1614C2×C1312yescomplemented
236#1612C2×C1312yescomplemented
237#1608C2×C1312yescomplemented
238#1518C2×C1311yescharacteristic, complemented
239#1512C2×C1311yescharacteristic, complemented
240#1469C2×C1311yescharacteristic, complemented
241C23×C13—22no—
242C23×C13—21no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—42no—
246C23×C13—42no—
247C23×C13C22×D411yescharacteristic
248Q8×C13—42no—
249Q8×C13—42no—
250Q8×C13—41no—
251Q8×C13—42no—
252Q8×C13—81no—
253Q8×C13—82no—
254D4×C13—42no—
255D4×C13—41no—
256D4×C13—41no—
257D4×C13—41no—
258D4×C13—81no—
259D4×C13—82no—
260D4×C13—82no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—42no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—42no—
280C2×C4×C13—41no—
281C2×C4×C13—82no—
282C2×C4×C13—82no—
283C2×C4×C13—82no—
284C2×C4×C13#12011yescharacteristic
285C2×C4×C13#12011yescharacteristic
286C2×C4×C13#12011yescharacteristic
287C2×C4×C13#12011yescharacteristic
288C2×C4×C13C22×D411yescharacteristic
289C2×C4×C13C22×D411yescharacteristic
290C8×C13—41no—
291C8×C13—41no—
292C8×C13—42no—
293#563—21no—
294#562—21no—
295#556—21no—
296#551—22no—
297D4×Q8—21no—
298#548—21no—
299#546—21no—
300#543C22×C1312yes—
301#542—21no—
302#542—22no—
303#538C22×C1312yes—
304#536—21no—
305#533C22×C1311yescharacteristic
306#529C22×C1311yescharacteristic
307C2×#125C22×C1311yescharacteristic
308C2×#124C22×C1311yescharacteristic
309#501—21no—
310#499—21no—
311#491—21no—
312#488—21no—
313#484C22×C1311yescharacteristic
314#484C22×C1312yes—
315#483C22×C1311yescharacteristic
316#483C22×C1312yes—
317#481C22×C1311yescharacteristic
318#480C22×C1311yescharacteristic
319#479—21no—
320#479—22no—
321#478—21no—
322#432C22×C1311yescharacteristic
323#431C22×C1311yescharacteristic
324#399C22×C1312yes—
325#397C22×C1312yes—
326#396—22no—
327#395—21no—
328#394—21no—
329#382C22×C1311yescharacteristic
330#328C22×C1312yes—
331#328C22×C1312yes—
332#328C22×C1312yes—
333#327C22×C1312yes—
334#323C22×C1312yes—
335#323C22×C1312yes—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—41no—
339C22×C13—42no—
340C22×C13—41no—
341C22×C13—42no—
342C22×C13—42no—
343C22×C13—41no—
344C22×C13—82no—
345C22×C13—82no—
346C22×C13C2×#12011yescharacteristic
347C22×C13#57711yescharacteristic
348C22×C13#57811yescharacteristic
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—42no—
358C4×C13—42no—
359C4×C13—41no—
360C4×C13—42no—
361C4×C13—82no—
362C4×C13—81no—
363C4×C13—81no—
364C2×#41—21no—
365C22×Q8—21no—
366C22×Q8D4×C1311yescharacteristic
367C22×D4D4×C1311yescharacteristic
368C4⋊Q8—21no—
369C4⋊Q8—22no—
370C4⋊Q8D4×C1311yescharacteristic
371C4⋊Q8D4×C1311yescharacteristic
372#126—22no—
373#126—22no—
374#126—22no—
375#126—21no—
376#125—21no—
377#125—21no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125D4×C1311yescharacteristic
382#124—21no—
383#124—22no—
384#124—22no—
385#124—21no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124D4×C1311yescharacteristic
390#123—22no—
391#123—22no—
392#123—22no—
393#123—21no—
394#123—22no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8C23×C1311yescharacteristic
405C22⋊Q8C23×C1312yes—
406#121—21no—
407#121—22no—
408#121—22no—
409#121C23×C1311yescharacteristic
410#120—22no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8D4×C1311yescharacteristic
414C4×Q8D4×C1312yes—
415C4×D4—21no—
416C4×D4—22no—
417C4×D4—21no—
418C4×D4—22no—
419C4×D4D4×C1311yescharacteristic
420#117—22no—
421#117—21no—
422#117—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4C23×C1311yescharacteristic
428C2×C4⋊C4C23×C1311yescharacteristic
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4D4×C1312yes—
433C2×C22⋊C4C23×C1312yes—
434C2×C42C23×C1311yescharacteristic
435#107—21no—
436#107—21no—
437#107—22no—
438#106—21no—
439#106—21no—
440#106—22no—
441C4⋊C8—21no—
442C4⋊C8—21no—
443#103—21no—
444#103—22no—
445#103—21no—
446#103—22no—
447#102—21no—
448#102—21no—
449C22⋊C8C23×C1312yes—
450C22⋊C8C23×C1311yescharacteristic
451C22⋊C8C23×C1311yescharacteristic
452#97—21no—
453C4×C8—21no—
454#95—21no—
455#95—22no—
456#95C23×C1312yes—
457C2×C13—21no—
458C2×C13—21no—
459C2×C13—81no—
460C2×C13—82no—
461C2×C13#301311yescharacteristic
462C2×C13#301911yescharacteristic
463C2×C13#302811yescharacteristic
464C24C2×D4×C1312yes—
465#41—82no—
466C2×Q8—22no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—81no—
471C2×Q8—82no—
472C2×Q8C2×D4×C1311yescharacteristic
473C2×Q8C2×D4×C1312yes—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—81no—
480C2×D4C2×D4×C1311yescharacteristic
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4C2×D4×C1311yescharacteristic
489C22×C4C2×D4×C1312yes—
490C22×C4C2×D4×C1311yescharacteristic
491C22×C4C24×C1311yescharacteristic
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—81no—
517C4⋊C4—82no—
518C4⋊C4C2×D4×C1311yescharacteristic
519C4⋊C4C2×D4×C1311yescharacteristic
520C4⋊C4C2×D4×C1312yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—82no—
537C22⋊C4—82no—
538C42—22no—
539C42—22no—
540C42—21no—
541C42C2×D4×C1311yescharacteristic
542C42C2×D4×C1311yescharacteristic
543C42C2×D4×C1311yescharacteristic
544C42C2×D4×C1311yescharacteristic
545C13#1846711yescharacteristic, direct product factor, Sylow
546C23—22no—
547C23—21no—
548C23—22no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23C22×D4×C1311yescharacteristic
553Q8—41no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—81no—
558Q8—82no—
559D4—41no—
560D4—42no—
561D4—41no—
562D4—41no—
563D4—81no—
564D4—82no—
565D4—82no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4C13×#12011yescharacteristic
590C2×C4C13×#12011yescharacteristic
591C2×C4C13×#12011yescharacteristic
592C2×C4C13×#12011yescharacteristic
593C2×C4C22×D4×C1311yescharacteristic
594C2×C4C22×D4×C1311yescharacteristic
595C8—41no—
596C8—41no—
597C8—42no—
598C22—21no—
599C22—21no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—41no—
606C22—82no—
607C22—82no—
608C22C2×C13×#12011yescharacteristic
609C22C13×#57711yescharacteristic
610C22C13×#57811yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—42no—
620C4—42no—
621C4—41no—
622C4—42no—
623C4—82no—
624C4—81no—
625C4—81no—
626C2—21no—
627C2—21no—
628C2—82no—
629C2—81no—
630C2C13×#301311yescharacteristic
631C2C13×#301911yescharacteristic
632C2C13×#302811yescharacteristic
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×#3236C2semidirect
3. C13×#3232C2semidirect
4. C13×#2820C2semidirect
5. C13×#1618C2semidirect
6. C13×#1614C2semidirect
7. C13×#1612C2semidirect
8. C13×#1608C2semidirect
9. C13×#1518C2semidirect
10. C13×#1512C2semidirect
11. C13×#1469C2semidirect
148. #18467C13direct (N × H)
231. #3236C2×C13semidirect
232. #3232C2×C13semidirect
233. #2820C2×C13semidirect
234. #1618C2×C13semidirect
235. #1614C2×C13semidirect
236. #1612C2×C13semidirect
237. #1608C2×C13semidirect
238. #1518C2×C13semidirect
239. #1512C2×C13semidirect
240. #1469C2×C13semidirect
545. C13#18467direct (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×#32362
C13×#32322
C13×#28202
C13×#16182
C13×#16142
C13×#16122
C13×#16082
C13×#15182
C13×#15122
C13×#14692
#1846713