Finite Group Databasebeta

← C13×#18282 #15704621

Subgroups — C13×#18282 #15704621

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3564C211yesmaximal, characteristic, complemented
2C13×#3114C211yesmaximal, characteristic, complemented
3C13×#3101C211yesmaximal, characteristic, complemented
4C13×#2603C211yesmaximal, characteristic, complemented
5C13×#1612C211yesmaximal, characteristic, complemented
6C13×#1611C211yesmaximal, characteristic, complemented
7C13×#1609C211yesmaximal, characteristic, complemented
8C13×#1608C211yesmaximal, characteristic, complemented
9C13×#1600C211yesmaximal, characteristic
10C13×#1599C211yesmaximal, characteristic, complemented
11C13×#1597C211yesmaximal, characteristic, complemented
12C13×#1596C211yesmaximal, characteristic, complemented
13C13×#1506C211yesmaximal, characteristic, complemented
14C13×#1500C211yesmaximal, characteristic, complemented
15C13×#1473C211yesmaximal, characteristic, complemented
16C13×#563—21no—
17C13×#563—21no—
18C13×#556—21no—
19C13×#554—21no—
20C13×#552—21no—
21C13×#552—21no—
22C13×#551—21no—
23C13×#551—21no—
24C13×#544C2211yescharacteristic
25C13×#543C2211yescharacteristic
26C13×#542—21no—
27C13×#541—21no—
28C13×#541—21no—
29C13×#539—21no—
30C13×#539C2211yescharacteristic
31C13×#538C2211yescharacteristic
32C13×#533C2211yescharacteristic
33C13×#529C2211yescharacteristic
34C2×C13×#126C2211yescharacteristic
35C2×C4×D4×C13C2211yescharacteristic
36C13×#483C2211yescharacteristic
37C13×#483C2211yescharacteristic
38C13×#483C2211yescharacteristic
39C13×#480C2211yescharacteristic
40C13×#478—21no—
41C13×#476—21no—
42C13×#463—21no—
43C13×#461—21no—
44C13×#450C2211yescharacteristic
45C13×#450C2211yescharacteristic
46C13×#450C2211yescharacteristic
47C13×#447C2211yescharacteristic
48C13×#442—21no—
49C13×#440—21no—
50C4×C13×SD16—21no—
51C4×C13×SD16—21no—
52C13×#432C2211yescharacteristic
53C13×#431C2211yescharacteristic
54C13×#398C2211yescharacteristic
55C13×#397C2211yescharacteristic
56C13×#394C2211yescharacteristic
57C13×#392C2211yescharacteristic
58C13×#390—21no—
59C13×#388—21no—
60C13×#386—21no—
61C13×#385—21no—
62C13×#376C2211yescharacteristic
63C13×#328C2211yescharacteristic
64C13×#328C2211yescharacteristic
65C13×#328C2211yescharacteristic
66C13×#328C2211yescharacteristic
67C13×#328C2211yescharacteristic
68C13×#328C2211yescharacteristic
69C13×#327C2211yescharacteristic
70C13×#327C2211yescharacteristic
71C13×#324C2211yescharacteristic
72C13×#324C2211yescharacteristic
73C13×#323C2211yescharacteristic
74C13×#323C2211yescharacteristic
75C22×D4×C13—21no—
76C22×D4×C13C2311yescharacteristic
77C23×C4×C13—21no—
78C2×C13×SD16—21no—
79C2×C13×SD16—21no—
80C2×C13×SD16—21no—
81C2×C13×D8—21no—
82C13×C4⋊Q8—21no—
83C13×C4⋊Q8—21no—
84C13×C4⋊Q8—21no—
85C13×C4⋊Q8D411yescharacteristic, complemented
86C13×C4⋊Q8D411yescharacteristic, complemented
87C13×#126—21no—
88C13×#126—21no—
89C13×#126—21no—
90C13×#126—21no—
91C13×#126—21no—
92C13×#126—21no—
93C13×#126—21no—
94C13×#126—21no—
95C13×#126—21no—
96C13×#126—21no—
97C13×#126—21no—
98C13×#126—21no—
99C13×#126—21no—
100C13×#125—21no—
101C13×#125—21no—
102C13×#125—21no—
103C13×#125—21no—
104C13×#125—21no—
105C13×#125—21no—
106C13×#125—21no—
107C13×#125—21no—
108C13×#125—21no—
109C13×#125D411yescharacteristic, complemented
110C13×#124—21no—
111C13×#124—21no—
112C13×#124—21no—
113C13×#124D411yescharacteristic, complemented
114C13×#123—21no—
115C13×#123—21no—
116C13×#123—21no—
117C13×#123—21no—
118C13×#123—21no—
119C13×#123—21no—
120C13×#123—21no—
121C13×#123—21no—
122C13×C22⋊Q8—21no—
123C13×C22⋊Q8—21no—
124C13×C22⋊Q8—21no—
125C13×C22⋊Q8—21no—
126C13×C22⋊Q8—21no—
127C13×C22⋊Q8—21no—
128C13×C22⋊Q8—21no—
129C13×C22⋊Q8—21no—
130C13×C22⋊Q8—21no—
131C13×C22⋊Q8—21no—
132C13×C22⋊Q8—21no—
133C13×C22⋊Q8—21no—
134C13×C22⋊Q8—21no—
135C13×C22⋊Q8—21no—
136C13×C22⋊Q8C2311yescharacteristic
137C13×C22⋊Q8C2311yescharacteristic
138C13×C22⋊Q8C2311yescharacteristic
139C13×#121—21no—
140C13×#121C2311yescharacteristic
141C13×#120—21no—
142C4×Q8×C13—21no—
143C4×Q8×C13—21no—
144C4×Q8×C13—21no—
145C4×Q8×C13D411yescharacteristic, complemented
146C4×Q8×C13D411yescharacteristic, complemented
147C4×Q8×C13D411yescharacteristic, complemented
148C4×D4×C13—21no—
149C4×D4×C13—21no—
150C4×D4×C13—21no—
151C4×D4×C13—21no—
152C4×D4×C13—21no—
153C4×D4×C13—21no—
154C4×D4×C13—21no—
155C4×D4×C13—21no—
156C4×D4×C13—21no—
157C4×D4×C13D411yescharacteristic, complemented
158C13×#117—21no—
159C13×#117—21no—
160C13×#117—21no—
161C13×#117—21no—
162C13×#117—21no—
163C13×#117—21no—
164C2×C13×C4⋊C4—21no—
165C2×C13×C4⋊C4—21no—
166C2×C13×C4⋊C4D411yescharacteristic
167C2×C13×C4⋊C4D411yescharacteristic
168C2×C13×C4⋊C4C2311yescharacteristic
169C2×C13×C4⋊C4C2311yescharacteristic
170C2×C13×C22⋊C4—21no—
171C2×C13×C22⋊C4—21no—
172C2×C13×C22⋊C4—21no—
173C2×C13×C22⋊C4—21no—
174C2×C13×C22⋊C4—21no—
175C2×C13×C22⋊C4—21no—
176C2×C13×C22⋊C4D411yescharacteristic
177C2×C13×C22⋊C4D411yescharacteristic
178C2×C13×C22⋊C4C2311yescharacteristic
179C2×C42×C13—21no—
180C2×C42×C13C2311yescharacteristic
181C13×#107—21no—
182C13×#106—21no—
183C13×#106—21no—
184C13×#106—21no—
185C13×C4⋊C8—21no—
186C13×C4⋊C8—21no—
187C13×#103—21no—
188C13×#103—21no—
189C13×#103—21no—
190C13×#102—21no—
191C13×#102—21no—
192C13×#102—21no—
193C13×#102—21no—
194C13×#102—21no—
195C13×C22⋊C8C2311yescharacteristic
196C13×C22⋊C8C2311yescharacteristic
197C13×C22⋊C8C2311yescharacteristic
198C13×C22⋊C8C2311yescharacteristic
199C13×#97—21no—
200C4×C8×C13—21no—
201C13×#95—21no—
202C13×#95—21no—
203C13×#95—21no—
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#18282C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13C2×D411yescharacteristic
209C2×Q8×C13—21no—
210C2×Q8×C13—21no—
211C2×Q8×C13—21no—
212C2×Q8×C13C2×D411yescharacteristic
213C2×Q8×C13C2×D411yescharacteristic
214C2×Q8×C13C2×D411yescharacteristic
215C2×D4×C13—21no—
216C2×D4×C13—21no—
217C2×D4×C13—21no—
218C2×D4×C13—21no—
219C2×D4×C13—21no—
220C2×D4×C13—42no—
221C2×D4×C13—42no—
222C2×D4×C13—42no—
223C2×D4×C13—81no—
224C2×D4×C13C2×D411yescharacteristic
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—41no—
234C22×C4×C13—41no—
235C22×C4×C13—81no—
236C22×C4×C13—81no—
237C22×C4×C13C2×D411yescharacteristic
238C22×C4×C13C2×D411yescharacteristic
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D411yescharacteristic
241C22×C4×C13C2×D411yescharacteristic
242C22×C4×C13C2411yescharacteristic
243C13×SD16—42no—
244C13×SD16—42no—
245C13×SD16—42no—
246C13×D8—42no—
247C2×C8×C13—21no—
248C2×C8×C13—21no—
249C2×C8×C13—21no—
250C2×C8×C13—21no—
251C13×C4⋊C4—21no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4—21no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—21no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4—21no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4—21no—
261C13×C4⋊C4—21no—
262C13×C4⋊C4—21no—
263C13×C4⋊C4—21no—
264C13×C4⋊C4—21no—
265C13×C4⋊C4—21no—
266C13×C4⋊C4—21no—
267C13×C4⋊C4—21no—
268C13×C4⋊C4—21no—
269C13×C4⋊C4—21no—
270C13×C4⋊C4—21no—
271C13×C4⋊C4—21no—
272C13×C4⋊C4—21no—
273C13×C4⋊C4—21no—
274C13×C4⋊C4—21no—
275C13×C4⋊C4—21no—
276C13×C4⋊C4—21no—
277C13×C4⋊C4—21no—
278C13×C4⋊C4—21no—
279C13×C4⋊C4—21no—
280C13×C4⋊C4—21no—
281C13×C4⋊C4—21no—
282C13×C4⋊C4—81no—
283C13×C4⋊C4C2×D411yescharacteristic
284C13×C4⋊C4C2×D411yescharacteristic
285C13×C4⋊C4C2×D411yescharacteristic
286C13×C4⋊C4C2×D411yescharacteristic
287C13×C22⋊C4—21no—
288C13×C22⋊C4—21no—
289C13×C22⋊C4—21no—
290C13×C22⋊C4—21no—
291C13×C22⋊C4—21no—
292C13×C22⋊C4—21no—
293C13×C22⋊C4—21no—
294C13×C22⋊C4—21no—
295C13×C22⋊C4—21no—
296C13×C22⋊C4—21no—
297C13×C22⋊C4—21no—
298C13×C22⋊C4—21no—
299C13×C22⋊C4—21no—
300C13×C22⋊C4—21no—
301C13×C22⋊C4—21no—
302C13×C22⋊C4—21no—
303C13×C22⋊C4—21no—
304C13×C22⋊C4—21no—
305C13×C22⋊C4—21no—
306C13×C22⋊C4—21no—
307C13×C22⋊C4—21no—
308C13×C22⋊C4—42no—
309C13×C22⋊C4—42no—
310C13×C22⋊C4—41no—
311C13×C22⋊C4—41no—
312C13×C22⋊C4—81no—
313C13×C22⋊C4—81no—
314C42×C13—21no—
315C42×C13—21no—
316C42×C13—21no—
317C42×C13—21no—
318C42×C13—21no—
319C42×C13—21no—
320C42×C13—21no—
321C42×C13—42no—
322C42×C13C2×D411yescharacteristic
323C42×C13C2×D411yescharacteristic
324C42×C13C2×D411yescharacteristic
325C42×C13C2×D411yescharacteristic
326#3564C2×C1311yescharacteristic, complemented
327#3114C2×C1311yescharacteristic, complemented
328#3101C2×C1311yescharacteristic, complemented
329#2603C2×C1311yescharacteristic, complemented
330#1612C2×C1311yescharacteristic, complemented
331#1611C2×C1311yescharacteristic, complemented
332#1609C2×C1311yescharacteristic, complemented
333#1608C2×C1311yescharacteristic, complemented
334#1600C2×C1311yescharacteristic
335#1599C2×C1311yescharacteristic, complemented
336#1597C2×C1311yescharacteristic, complemented
337#1596C2×C1311yescharacteristic, complemented
338#1506C2×C1311yescharacteristic, complemented
339#1500C2×C1311yescharacteristic, complemented
340#1473C2×C1311yescharacteristic, complemented
341C23×C13—22no—
342C23×C13—21no—
343C23×C13—21no—
344C23×C13—21no—
345C23×C13—21no—
346C23×C13—41no—
347C23×C13—41no—
348C23×C13—41no—
349C23×C13—41no—
350C23×C13—41no—
351C23×C13—41no—
352C23×C13—41no—
353C23×C13—41no—
354C23×C13C22×D411yescharacteristic
355Q8×C13—41no—
356Q8×C13—41no—
357Q8×C13—41no—
358Q8×C13—81no—
359Q8×C13—81no—
360Q8×C13—81no—
361D4×C13—22no—
362D4×C13—22no—
363D4×C13—41no—
364D4×C13—41no—
365D4×C13—41no—
366D4×C13—41no—
367D4×C13—41no—
368D4×C13—81no—
369D4×C13—81no—
370D4×C13—84no—
371C2×C4×C13—21no—
372C2×C4×C13—21no—
373C2×C4×C13—22no—
374C2×C4×C13—21no—
375C2×C4×C13—21no—
376C2×C4×C13—21no—
377C2×C4×C13—21no—
378C2×C4×C13—21no—
379C2×C4×C13—21no—
380C2×C4×C13—21no—
381C2×C4×C13—21no—
382C2×C4×C13—21no—
383C2×C4×C13—21no—
384C2×C4×C13—21no—
385C2×C4×C13—21no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—81no—
399C2×C4×C13—82no—
400C2×C4×C13—82no—
401C2×C4×C13—81no—
402C2×C4×C13—81no—
403C2×C4×C13—81no—
404C2×C4×C13—81no—
405C2×C4×C13#12011yescharacteristic
406C2×C4×C13#12011yescharacteristic
407C2×C4×C13#12011yescharacteristic
408C2×C4×C13#12011yescharacteristic
409C2×C4×C13C22×D411yescharacteristic
410C2×C4×C13C22×D411yescharacteristic
411C8×C13—41no—
412C8×C13—41no—
413C8×C13—41no—
414C8×C13—41no—
415#563—21no—
416#563—21no—
417#556—21no—
418#554—21no—
419#552—21no—
420#552—21no—
421#551—21no—
422#551—21no—
423#544C22×C1311yescharacteristic
424#543C22×C1311yescharacteristic
425#542—21no—
426#541—21no—
427#541—21no—
428#539—21no—
429#539C22×C1311yescharacteristic
430#538C22×C1311yescharacteristic
431#533C22×C1311yescharacteristic
432#529C22×C1311yescharacteristic
433C2×#126C22×C1311yescharacteristic
434C2×C4×D4C22×C1311yescharacteristic
435#483C22×C1311yescharacteristic
436#483C22×C1311yescharacteristic
437#483C22×C1311yescharacteristic
438#480C22×C1311yescharacteristic
439#478—21no—
440#476—21no—
441#463—21no—
442#461—21no—
443#450C22×C1311yescharacteristic
444#450C22×C1311yescharacteristic
445#450C22×C1311yescharacteristic
446#447C22×C1311yescharacteristic
447#442—21no—
448#440—21no—
449C4×SD16—21no—
450C4×SD16—21no—
451#432C22×C1311yescharacteristic
452#431C22×C1311yescharacteristic
453#398C22×C1311yescharacteristic
454#397C22×C1311yescharacteristic
455#394C22×C1311yescharacteristic
456#392C22×C1311yescharacteristic
457#390—21no—
458#388—21no—
459#386—21no—
460#385—21no—
461#376C22×C1311yescharacteristic
462#328C22×C1311yescharacteristic
463#328C22×C1311yescharacteristic
464#328C22×C1311yescharacteristic
465#328C22×C1311yescharacteristic
466#328C22×C1311yescharacteristic
467#328C22×C1311yescharacteristic
468#327C22×C1311yescharacteristic
469#327C22×C1311yescharacteristic
470#324C22×C1311yescharacteristic
471#324C22×C1311yescharacteristic
472#323C22×C1311yescharacteristic
473#323C22×C1311yescharacteristic
474C22×C13—21no—
475C22×C13—21no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—41no—
479C22×C13—41no—
480C22×C13—41no—
481C22×C13—41no—
482C22×C13—41no—
483C22×C13—41no—
484C22×C13—42no—
485C22×C13—81no—
486C22×C13—81no—
487C22×C13—81no—
488C22×C13—81no—
489C22×C13—81no—
490C22×C13—81no—
491C22×C13C2×#12011yescharacteristic
492C22×C13#57711yescharacteristic
493C22×C13#57711yescharacteristic
494C4×C13—21no—
495C4×C13—21no—
496C4×C13—21no—
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—42no—
501C4×C13—41no—
502C4×C13—41no—
503C4×C13—41no—
504C4×C13—41no—
505C4×C13—41no—
506C4×C13—41no—
507C4×C13—41no—
508C4×C13—41no—
509C4×C13—41no—
510C4×C13—41no—
511C4×C13—81no—
512C4×C13—81no—
513C22×D4—21no—
514C22×D4C23×C1311yescharacteristic
515C23×C4—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×D8—21no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522C4⋊Q8—21no—
523C4⋊Q8D4×C1311yescharacteristic, complemented
524C4⋊Q8D4×C1311yescharacteristic, complemented
525#126—21no—
526#126—21no—
527#126—21no—
528#126—21no—
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#125—21no—
539#125—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125D4×C1311yescharacteristic, complemented
548#124—21no—
549#124—21no—
550#124—21no—
551#124D4×C1311yescharacteristic, complemented
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8C23×C1311yescharacteristic
575C22⋊Q8C23×C1311yescharacteristic
576C22⋊Q8C23×C1311yescharacteristic
577#121—21no—
578#121C23×C1311yescharacteristic
579#120—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8D4×C1311yescharacteristic, complemented
584C4×Q8D4×C1311yescharacteristic, complemented
585C4×Q8D4×C1311yescharacteristic, complemented
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4D4×C1311yescharacteristic, complemented
596#117—21no—
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4D4×C1311yescharacteristic
605C2×C4⋊C4D4×C1311yescharacteristic
606C2×C4⋊C4C23×C1311yescharacteristic
607C2×C4⋊C4C23×C1311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4D4×C1311yescharacteristic
615C2×C22⋊C4D4×C1311yescharacteristic
616C2×C22⋊C4C23×C1311yescharacteristic
617C2×C42—21no—
618C2×C42C23×C1311yescharacteristic
619#107—21no—
620#106—21no—
621#106—21no—
622#106—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625#103—21no—
626#103—21no—
627#103—21no—
628#102—21no—
629#102—21no—
630#102—21no—
631#102—21no—
632#102—21no—
633C22⋊C8C23×C1311yescharacteristic
634C22⋊C8C23×C1311yescharacteristic
635C22⋊C8C23×C1311yescharacteristic
636C22⋊C8C23×C1311yescharacteristic
637#97—21no—
638C4×C8—21no—
639#95—21no—
640#95—21no—
641#95—21no—
642#95C23×C1311yescharacteristic
643#95C23×C1311yescharacteristic
644C2×C13—21no—
645C2×C13—21no—
646C2×C13—81no—
647C2×C13—81no—
648C2×C13—82no—
649C2×C13#301011yescharacteristic
650C2×C13#301811yescharacteristic
651C2×C13#302511yescharacteristic
652C24—21no—
653C24C2×D4×C1311yescharacteristic
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C1311yescharacteristic
658C2×Q8C2×D4×C1311yescharacteristic
659C2×Q8C2×D4×C1311yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—81no—
669C2×D4C2×D4×C1311yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—81no—
681C22×C4—81no—
682C22×C4C2×D4×C1311yescharacteristic
683C22×C4C2×D4×C1311yescharacteristic
684C22×C4C2×D4×C1311yescharacteristic
685C22×C4C2×D4×C1311yescharacteristic
686C22×C4C2×D4×C1311yescharacteristic
687C22×C4C24×C1311yescharacteristic
688SD16—42no—
689SD16—42no—
690SD16—42no—
691D8—42no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—81no—
728C4⋊C4C2×D4×C1311yescharacteristic
729C4⋊C4C2×D4×C1311yescharacteristic
730C4⋊C4C2×D4×C1311yescharacteristic
731C4⋊C4C2×D4×C1311yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—42no—
754C22⋊C4—42no—
755C22⋊C4—41no—
756C22⋊C4—41no—
757C22⋊C4—81no—
758C22⋊C4—81no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—42no—
767C42C2×D4×C1311yescharacteristic
768C42C2×D4×C1311yescharacteristic
769C42C2×D4×C1311yescharacteristic
770C42C2×D4×C1311yescharacteristic
771C13#1828211yescharacteristic, direct product factor, Sylow
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23C22×D4×C1311yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—81no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—81no—
800D4—81no—
801D4—84no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—81no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4C13×#12011yescharacteristic
837C2×C4C13×#12011yescharacteristic
838C2×C4C13×#12011yescharacteristic
839C2×C4C13×#12011yescharacteristic
840C2×C4C22×D4×C1311yescharacteristic
841C2×C4C22×D4×C1311yescharacteristic
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22C2×C13×#12011yescharacteristic
864C22C13×#57711yescharacteristic
865C22C13×#57711yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C2—21no—
886C2—21no—
887C2—82no—
888C2—81no—
889C2—81no—
890C2C13×#301011yescharacteristic
891C2C13×#301811yescharacteristic
892C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#1600C2
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×#3564C2semidirect
2. C13×#3114C2semidirect
3. C13×#3101C2semidirect
4. C13×#2603C2semidirect
5. C13×#1612C2semidirect
6. C13×#1611C2semidirect
7. C13×#1609C2semidirect
8. C13×#1608C2semidirect
10. C13×#1599C2semidirect
11. C13×#1597C2semidirect
12. C13×#1596C2semidirect
13. C13×#1506C2semidirect
14. C13×#1500C2semidirect
15. C13×#1473C2semidirect
85. C13×C4⋊Q8D4semidirect
86. C13×C4⋊Q8D4semidirect
109. C13×#125D4semidirect
113. C13×#124D4semidirect
145. C4×Q8×C13D4semidirect
146. C4×Q8×C13D4semidirect
147. C4×Q8×C13D4semidirect
157. C4×D4×C13D4semidirect
206. #18282C13direct (N × H)
326. #3564C2×C13semidirect
327. #3114C2×C13semidirect
328. #3101C2×C13semidirect
329. #2603C2×C13semidirect
330. #1612C2×C13semidirect
331. #1611C2×C13semidirect
332. #1609C2×C13semidirect
333. #1608C2×C13semidirect
335. #1599C2×C13semidirect
336. #1597C2×C13semidirect
337. #1596C2×C13semidirect
338. #1506C2×C13semidirect
339. #1500C2×C13semidirect
340. #1473C2×C13semidirect
523. C4⋊Q8D4×C13semidirect
524. C4⋊Q8D4×C13semidirect
547. #125D4×C13semidirect
551. #124D4×C13semidirect
583. C4×Q8D4×C13semidirect
584. C4×Q8D4×C13semidirect
585. C4×Q8D4×C13semidirect
595. C4×D4D4×C13semidirect
771. C13#18282direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35642
C13×#31142
C13×#31012
C13×#26032
C13×#16122
C13×#16112
C13×#16092
C13×#16082
C13×#16002
C13×#15992
C13×#15972
C13×#15962
C13×#15062
C13×#15002
C13×#14732
#1828213