Finite Group Databasebeta

← C13×#18277 #15704616

Subgroups — C13×#18277 #15704616

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic
2C13×#3112C211yesmaximal, characteristic, complemented
3C13×#3108C211yesmaximal, characteristic, complemented
4C13×#2584C211yesmaximal, characteristic, complemented
5C13×#1610C212yesmaximal, complemented
6C13×#1609C212yesmaximal, complemented
7C13×#1604C212yesmaximal, complemented
8C13×#1603C212yesmaximal, complemented
9C13×#1509C211yesmaximal, characteristic, complemented
10C13×#1502C211yesmaximal, characteristic, complemented
11C13×#1470C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#562—21no—
14C13×#554—21no—
15C13×#553—21no—
16C13×#553—21no—
17C13×#547—22no—
18C13×#547—21no—
19C13×#544—21no—
20C13×#540—21no—
21C13×#539—22no—
22C13×#539C2212yes—
23C13×#537C2212yes—
24C13×#532C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C13×#483C2211yescharacteristic
29C13×#480C2211yescharacteristic
30C13×#480C2212yes—
31C13×#479—21no—
32C13×#477—21no—
33C13×#464—21no—
34C13×#460—21no—
35C13×#451C2211yescharacteristic
36C13×#448C2211yescharacteristic
37C13×#448C2212yes—
38C13×#440—22no—
39C4×C13×Q16—21no—
40C4×C13×SD16—21no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#398C2212yes—
44C13×#395C2212yes—
45C13×#389—21no—
46C13×#389—22no—
47C13×#389—21no—
48C4×C13×C4⋊C4C2211yescharacteristic
49C13×#328C2212yes—
50C13×#327C2212yes—
51C13×#327C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C2×C13×#41—21no—
56C2×C13×#41—22no—
57C22×Q8×C13C2311yescharacteristic
58C2×C13×Q16—21no—
59C2×C13×SD16—21no—
60C2×C13×SD16—22no—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8D411yescharacteristic
64C13×#127D411yescharacteristic
65C13×#126—22no—
66C13×#126—22no—
67C13×#126—21no—
68C13×#125—21no—
69C13×#125—22no—
70C13×#125—21no—
71C13×#125—21no—
72C13×#125—21no—
73C13×#125—21no—
74C13×#125D411yescharacteristic
75C13×#124—21no—
76C13×#124D411yescharacteristic
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—21no—
83C13×#123—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8C2311yescharacteristic
91C13×#121—21no—
92C13×#121—22no—
93C13×#121—21no—
94C13×#121—22no—
95C13×#121—22no—
96C13×#121—21no—
97C13×#121—22no—
98C13×#121C2311yescharacteristic
99C13×#121C2312yes—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×Q8×C13—21no—
103C4×Q8×C13—21no—
104C4×Q8×C13D411yescharacteristic
105C4×D4×C13—22no—
106C4×D4×C13—21no—
107C4×D4×C13—21no—
108C4×D4×C13—21no—
109C4×D4×C13—22no—
110C4×D4×C13—21no—
111C4×D4×C13D411yescharacteristic
112C4×D4×C13D412yes—
113C13×#117—21no—
114C13×#117—21no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—22no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—22no—
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4D412yes—
123C2×C13×C4⋊C4D411yescharacteristic
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C4⋊C4C2312yes—
126C2×C42×C13—21no—
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—21no—
136C13×#103—21no—
137C13×#103—22no—
138C13×#102—21no—
139C13×#102—22no—
140C13×C22⋊C8C2311yescharacteristic
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2312yes—
143C13×#97—21no—
144C4×C8×C13—21no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18277C1311yesmaximal, characteristic, direct product factor, Sylow
149C13×#41—81no—
150C13×#41—81no—
151C13×#41—82no—
152C13×#41—82no—
153C2×Q8×C13—22no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—42no—
158C2×Q8×C13C2×D411yescharacteristic
159C2×D4×C13—21no—
160C2×D4×C13—22no—
161C2×D4×C13—22no—
162C2×D4×C13—22no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13C2×D411yescharacteristic
166C2×D4×C13C2×D412yes—
167C22×C4×C13—22no—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—21no—
173C22×C4×C13—22no—
174C22×C4×C13—21no—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2411yescharacteristic
180C13×Q16—42no—
181C13×SD16—44no—
182C13×SD16—42no—
183C2×C8×C13—21no—
184C2×C8×C13—21no—
185C2×C8×C13—22no—
186C13×C4⋊C4—24no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—44no—
207C13×C4⋊C4—41no—
208C13×C4⋊C4—41no—
209C13×C4⋊C4—82no—
210C13×C4⋊C4C2×D411yescharacteristic
211C13×C4⋊C4C2×D412yes—
212C13×C4⋊C4C2×D411yescharacteristic
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—22no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—21no—
224C13×C22⋊C4—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#3559C2×C1311yescharacteristic
235#3112C2×C1311yescharacteristic, complemented
236#3108C2×C1311yescharacteristic, complemented
237#2584C2×C1311yescharacteristic, complemented
238#1610C2×C1312yescomplemented
239#1609C2×C1312yescomplemented
240#1604C2×C1312yescomplemented
241#1603C2×C1312yescomplemented
242#1509C2×C1311yescharacteristic, complemented
243#1502C2×C1311yescharacteristic, complemented
244#1470C2×C1311yescharacteristic, complemented
245C23×C13—21no—
246C23×C13—22no—
247C23×C13C22×D411yescharacteristic
248Q8×C13—22no—
249Q8×C13—22no—
250Q8×C13—41no—
251Q8×C13—41no—
252Q8×C13—41no—
253Q8×C13—81no—
254Q8×C13—82no—
255D4×C13—42no—
256D4×C13—41no—
257D4×C13—42no—
258D4×C13—41no—
259D4×C13—42no—
260D4×C13—41no—
261D4×C13—42no—
262D4×C13—81no—
263D4×C13—82no—
264D4×C13—82no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—24no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—21no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—41no—
279C2×C4×C13—42no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—82no—
289C2×C4×C13—82no—
290C2×C4×C13—82no—
291C2×C4×C13—82no—
292C2×C4×C13#12011yescharacteristic
293C2×C4×C13#12011yescharacteristic
294C2×C4×C13#12011yescharacteristic
295C2×C4×C13#12011yescharacteristic
296C2×C4×C13C22×D411yescharacteristic
297C2×C4×C13C22×D411yescharacteristic
298C8×C13—42no—
299C8×C13—41no—
300C8×C13—41no—
301#563—21no—
302#562—21no—
303#554—21no—
304#553—21no—
305#553—21no—
306#547—22no—
307#547—21no—
308#544—21no—
309#540—21no—
310#539—22no—
311#539C22×C1312yes—
312#537C22×C1312yes—
313#532C22×C1311yescharacteristic
314#529C22×C1311yescharacteristic
315C2×#125C22×C1311yescharacteristic
316C2×C4×Q8C22×C1311yescharacteristic
317#483C22×C1311yescharacteristic
318#480C22×C1311yescharacteristic
319#480C22×C1312yes—
320#479—21no—
321#477—21no—
322#464—21no—
323#460—21no—
324#451C22×C1311yescharacteristic
325#448C22×C1311yescharacteristic
326#448C22×C1312yes—
327#440—22no—
328C4×Q16—21no—
329C4×SD16—21no—
330#432C22×C1311yescharacteristic
331#431C22×C1311yescharacteristic
332#398C22×C1312yes—
333#395C22×C1312yes—
334#389—21no—
335#389—22no—
336#389—21no—
337C4×C4⋊C4C22×C1311yescharacteristic
338#328C22×C1312yes—
339#327C22×C1312yes—
340#327C22×C1312yes—
341#327C22×C1312yes—
342#324C22×C1312yes—
343#324C22×C1312yes—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—42no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—41no—
352C22×C13C2×#12011yescharacteristic
353C22×C13#57611yescharacteristic
354C22×C13#57711yescharacteristic
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—21no—
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—44no—
361C4×C13—42no—
362C4×C13—42no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13—41no—
368C4×C13—81no—
369C4×C13#45612yes—
370C2×#41—21no—
371C2×#41—22no—
372C22×Q8C23×C1311yescharacteristic
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16—22no—
376C4⋊Q8—21no—
377C4⋊Q8—22no—
378C4⋊Q8D4×C1311yescharacteristic
379#127D4×C1311yescharacteristic
380#126—22no—
381#126—22no—
382#126—21no—
383#125—21no—
384#125—22no—
385#125—21no—
386#125—21no—
387#125—21no—
388#125—21no—
389#125D4×C1311yescharacteristic
390#124—21no—
391#124D4×C1311yescharacteristic
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—21no—
398#123—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8C23×C1311yescharacteristic
406#121—21no—
407#121—22no—
408#121—21no—
409#121—22no—
410#121—22no—
411#121—21no—
412#121—22no—
413#121C23×C1311yescharacteristic
414#121C23×C1312yes—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8D4×C1311yescharacteristic
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4D4×C1311yescharacteristic
427C4×D4D4×C1312yes—
428#117—21no—
429#117—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4D4×C1311yescharacteristic
437C2×C4⋊C4D4×C1312yes—
438C2×C4⋊C4D4×C1311yescharacteristic
439C2×C4⋊C4C23×C1311yescharacteristic
440C2×C4⋊C4C23×C1312yes—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C1311yescharacteristic
444#107—21no—
445#107—22no—
446#106—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—22no—
453#102—21no—
454#102—22no—
455C22⋊C8C23×C1311yescharacteristic
456C22⋊C8C23×C1311yescharacteristic
457C22⋊C8C23×C1312yes—
458#97—21no—
459C4×C8—21no—
460#95—22no—
461#95—22no—
462#95C23×C1312yes—
463C2×C13—21no—
464C2×C13—21no—
465C2×C13—81no—
466C2×C13—82no—
467C2×C13#301211yescharacteristic
468C2×C13C2×#45611yescharacteristic
469C2×C13#302511yescharacteristic
470#41—81no—
471#41—81no—
472#41—82no—
473#41—82no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—42no—
479C2×Q8C2×D4×C1311yescharacteristic
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×D4×C1311yescharacteristic
487C2×D4C2×D4×C1312yes—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4C2×D4×C1312yes—
497C22×C4C2×D4×C1311yescharacteristic
498C22×C4C2×D4×C1311yescharacteristic
499C22×C4C2×D4×C1312yes—
500C22×C4C24×C1311yescharacteristic
501Q16—42no—
502SD16—44no—
503SD16—42no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—24no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—44no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—82no—
531C4⋊C4C2×D4×C1311yescharacteristic
532C4⋊C4C2×D4×C1312yes—
533C4⋊C4C2×D4×C1311yescharacteristic
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—22no—
546C42—22no—
547C42—21no—
548C42—41no—
549C42—41no—
550C42—81no—
551C42C2×D4×C1311yescharacteristic
552C42C2×D4×C1311yescharacteristic
553C42C2×D4×C1311yescharacteristic
554C42C2×D4×C1311yescharacteristic
555C13#1827711yescharacteristic, direct product factor, Sylow
556C23—21no—
557C23—22no—
558C23C22×D4×C1311yescharacteristic
559Q8—22no—
560Q8—22no—
561Q8—41no—
562Q8—41no—
563Q8—41no—
564Q8—81no—
565Q8—82no—
566D4—42no—
567D4—41no—
568D4—42no—
569D4—41no—
570D4—42no—
571D4—41no—
572D4—42no—
573D4—81no—
574D4—82no—
575D4—82no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4C13×#12011yescharacteristic
604C2×C4C13×#12011yescharacteristic
605C2×C4C13×#12011yescharacteristic
606C2×C4C13×#12011yescharacteristic
607C2×C4C22×D4×C1311yescharacteristic
608C2×C4C22×D4×C1311yescharacteristic
609C8—42no—
610C8—41no—
611C8—41no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—41no—
616C22—41no—
617C22—42no—
618C22—42no—
619C22—41no—
620C22C2×C13×#12011yescharacteristic
621C22C13×#57611yescharacteristic
622C22C13×#57711yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—44no—
629C4—42no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—42no—
635C4—41no—
636C4—81no—
637C4C13×#45612yes—
638C2—21no—
639C2—21no—
640C2—81no—
641C2—82no—
642C2C13×#301211yescharacteristic
643C2C2×C13×#45611yescharacteristic
644C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3559C2
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×#3112C2semidirect
3. C13×#3108C2semidirect
4. C13×#2584C2semidirect
5. C13×#1610C2semidirect
6. C13×#1609C2semidirect
7. C13×#1604C2semidirect
8. C13×#1603C2semidirect
9. C13×#1509C2semidirect
10. C13×#1502C2semidirect
11. C13×#1470C2semidirect
148. #18277C13direct (N × H)
235. #3112C2×C13semidirect
236. #3108C2×C13semidirect
237. #2584C2×C13semidirect
238. #1610C2×C13semidirect
239. #1609C2×C13semidirect
240. #1604C2×C13semidirect
241. #1603C2×C13semidirect
242. #1509C2×C13semidirect
243. #1502C2×C13semidirect
244. #1470C2×C13semidirect
555. C13#18277direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#31122
C13×#31082
C13×#25842
C13×#16102
C13×#16092
C13×#16042
C13×#16032
C13×#15092
C13×#15022
C13×#14702
#1827713