Finite Group Databasebeta

← C13×#19068 #15705407

Subgroups — C13×#19068 #15705407

Order 3328.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3545C211yesmaximal, characteristic, complemented
2C13×#3219C211yesmaximal, characteristic, complemented
3C13×#3213C211yesmaximal, characteristic, complemented
4C13×#3171C211yesmaximal, characteristic, complemented
5C13×#1664C211yesmaximal, characteristic, complemented
6C13×#1662C211yesmaximal, characteristic, complemented
7C13×#1661C211yesmaximal, characteristic, complemented
8C13×#1659C211yesmaximal, characteristic, complemented
9C13×#1657C211yesmaximal, characteristic, complemented
10C13×#1656C211yesmaximal, characteristic, complemented
11C13×#1656C211yesmaximal, characteristic, complemented
12C13×#1655C211yesmaximal, characteristic, complemented
13C13×#1535C211yesmaximal, characteristic, complemented
14C13×#1529C211yesmaximal, characteristic, complemented
15C13×#1527C211yesmaximal, characteristic, complemented
16C13×#563C2211yescharacteristic
17C13×#562C2211yescharacteristic
18C13×#562C2211yescharacteristic
19C13×H(3,𝔽4)C2211yescharacteristic
20C13×#555—21no—
21C13×#551—21no—
22C13×#551—21no—
23C13×#551—21no—
24C13×#546—21no—
25C13×#546—21no—
26C13×#542—21no—
27C13×#542—21no—
28C13×#538—21no—
29C13×#538—21no—
30C13×#536—21no—
31C13×#534—21no—
32C13×#532C2211yescharacteristic, complemented
33C13×#529C2211yescharacteristic
34C13×#529C2211yescharacteristic
35C2×C13×#124C2211yescharacteristic
36C13×#501C2211yescharacteristic, complemented
37C13×#497C2211yescharacteristic, complemented
38C13×#496C2211yescharacteristic
39C13×#496C2211yescharacteristic, complemented
40C13×#496C2211yescharacteristic, complemented
41C13×#496C2211yescharacteristic, complemented
42C13×#491C2211yescharacteristic, complemented
43C13×#490C2211yescharacteristic, complemented
44C13×#490C2211yescharacteristic, complemented
45C13×#489C2211yescharacteristic
46C13×#489C2211yescharacteristic, complemented
47C13×#489C2211yescharacteristic, complemented
48C13×#469—21no—
49C13×#468—21no—
50C13×#464—21no—
51C13×#463—21no—
52C13×#463—21no—
53C13×#463—21no—
54C13×#452—21no—
55C13×#449—21no—
56C13×#448—21no—
57C13×#447—21no—
58C4×C13×SD16—21no—
59C4×C13×D8—21no—
60C13×#432C2211yescharacteristic, complemented
61C13×#432C2211yescharacteristic, complemented
62C4×C13×M16C2211yescharacteristic, complemented
63C13×#330C2211yescharacteristic, complemented
64C13×#330C2211yescharacteristic, complemented
65C13×#330C2211yescharacteristic, complemented
66C13×#330C2211yescharacteristic, complemented
67C13×#329C2211yescharacteristic
68C13×#329C2211yescharacteristic
69C13×#329C2211yescharacteristic, complemented
70C13×#329C2211yescharacteristic, complemented
71C13×#329C2211yescharacteristic, complemented
72C13×#329C2211yescharacteristic, complemented
73C13×#329C2211yescharacteristic, complemented
74C13×#329C2211yescharacteristic, complemented
75C2×C13×#41—21no—
76C2×C13×#41—21no—
77C22×Q8×C13D411yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13D411yescharacteristic
80C2×C13×Q16—21no—
81C2×C13×SD16—21no—
82C2×C13×SD16—21no—
83C2×C13×SD16—21no—
84C2×C13×SD16—21no—
85C2×C13×SD16—21no—
86C2×C13×D8—21no—
87C2×C13×D8—21no—
88C2×C13×D8—21no—
89C2×C13×D8—21no—
90C2×C13×M16—21no—
91C13×C4⋊Q8—21no—
92C13×C4⋊Q8—21no—
93C13×C4⋊Q8C2311yescharacteristic
94C13×#127C2311yescharacteristic
95C13×#126—21no—
96C13×#126—21no—
97C13×#126—21no—
98C13×#126—21no—
99C13×#126—21no—
100C13×#126—21no—
101C13×#125C2311yescharacteristic
102C13×#125C2311yescharacteristic
103C13×#124—21no—
104C13×#124—21no—
105C13×#124—21no—
106C13×#124—21no—
107C13×#124—21no—
108C13×#124—21no—
109C13×#124—21no—
110C13×#124—21no—
111C13×#124—21no—
112C13×#124D411yescharacteristic
113C13×#124D411yescharacteristic
114C13×#124C2311yescharacteristic
115C13×#124C2311yescharacteristic
116C13×#124C2311yescharacteristic
117C13×#124C2311yescharacteristic
118C13×#123—21no—
119C13×#123—21no—
120C13×#123—21no—
121C13×#123—21no—
122C13×#123—21no—
123C13×#123—21no—
124C13×#123—21no—
125C13×#123—21no—
126C13×#123—21no—
127C13×#123—21no—
128C13×#123—21no—
129C13×#123—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⋊Q8—21no—
137C13×C22⋊Q8—21no—
138C13×C22⋊Q8D411yescharacteristic
139C13×C22⋊Q8D411yescharacteristic
140C13×#121—21no—
141C13×#121—21no—
142C13×#121—21no—
143C13×#121—21no—
144C13×#121—21no—
145C13×#121—21no—
146C13×#121—21no—
147C13×#121—21no—
148C13×#121—21no—
149C13×#121—21no—
150C13×#121D411yescharacteristic
151C13×#121D411yescharacteristic
152C13×#120—21no—
153C13×#120—21no—
154C13×#120—21no—
155C13×#120—21no—
156C13×#120—21no—
157C13×#120—21no—
158C4×Q8×C13D411yescharacteristic
159C4×Q8×C13D411yescharacteristic
160C4×D4×C13—21no—
161C4×D4×C13—21no—
162C4×D4×C13—21no—
163C4×D4×C13—21no—
164C4×D4×C13—21no—
165C4×D4×C13—21no—
166C4×D4×C13—21no—
167C4×D4×C13—21no—
168C4×D4×C13D411yescharacteristic
169C4×D4×C13D411yescharacteristic
170C13×#117—21no—
171C13×#117—21no—
172C13×#117—21no—
173C13×#117—21no—
174C13×#117—21no—
175C2×C13×C22⋊C4—21no—
176C2×C13×C22⋊C4—21no—
177C2×C13×C22⋊C4—21no—
178C2×C13×C22⋊C4—21no—
179C2×C13×C22⋊C4—21no—
180C2×C42×C13C2311yescharacteristic
181C13×#107—21no—
182C13×#106—21no—
183C13×C4⋊C8—21no—
184C13×C4⋊C8—21no—
185C13×#103—21no—
186C13×#103—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×#102—21no—
196C13×#102—21no—
197C13×C22⋊C8—21no—
198C13×C22⋊C8—21no—
199C13×#97C2311yescharacteristic
200C13×#97C2311yescharacteristic
201C13×#97C2311yescharacteristic
202C13×#97C2311yescharacteristic
203C13×#97C2311yescharacteristic
204C13×#97C2311yescharacteristic
205C4×C8×C13—21no—
206#19068C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C13×#41—82no—
210C13×#41—81no—
211C13×#41—81no—
212C2×Q8×C13—21no—
213C2×Q8×C13—21no—
214C2×Q8×C13—21no—
215C2×Q8×C13—81no—
216C2×Q8×C13C2×D411yescharacteristic
217C2×Q8×C13C2×D411yescharacteristic
218C2×Q8×C13C2×D411yescharacteristic
219C2×Q8×C13C2×D411yescharacteristic
220C2×D4×C13—21no—
221C2×D4×C13—21no—
222C2×D4×C13—21no—
223C2×D4×C13—21no—
224C2×D4×C13—21no—
225C2×D4×C13—21no—
226C2×D4×C13—21no—
227C2×D4×C13—21no—
228C2×D4×C13—21no—
229C2×D4×C13—21no—
230C2×D4×C13—21no—
231C2×D4×C13—21no—
232C2×D4×C13—21no—
233C2×D4×C13—41no—
234C2×D4×C13—81no—
235C2×D4×C13—82no—
236C2×D4×C13C2×D411yescharacteristic
237C2×D4×C13C2×D411yescharacteristic
238C2×D4×C13C2×D411yescharacteristic
239C2×D4×C13C2×D411yescharacteristic
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—41no—
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2×D411yescharacteristic
251C22×C4×C13C2×D411yescharacteristic
252C13×Q16—81no—
253C13×SD16—42no—
254C13×SD16—81no—
255C13×SD16—81no—
256C13×SD16—81no—
257C13×SD16—81no—
258C13×D8—42no—
259C13×D8—81no—
260C13×D8—81no—
261C13×D8—81no—
262C13×M16—42no—
263C2×C8×C13—21no—
264C2×C8×C13—21no—
265C2×C8×C13—21no—
266C2×C8×C13—21no—
267C2×C8×C13—21no—
268C2×C8×C13—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—21no—
283C13×C4⋊C4—21no—
284C13×C4⋊C4—21no—
285C13×C4⋊C4C2×D411yescharacteristic
286C13×C4⋊C4C2×D411yescharacteristic
287C13×C4⋊C4C2×D411yescharacteristic
288C13×C4⋊C4C2×D411yescharacteristic
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—21no—
309C13×C22⋊C4—21no—
310C13×C22⋊C4—21no—
311C13×C22⋊C4—21no—
312C13×C22⋊C4—21no—
313C13×C22⋊C4—21no—
314C13×C22⋊C4—21no—
315C13×C22⋊C4—21no—
316C13×C22⋊C4—21no—
317C13×C22⋊C4—41no—
318C13×C22⋊C4—41no—
319C42×C13—21no—
320C42×C13—21no—
321C42×C13—21no—
322C42×C13—21no—
323C42×C13C2×D411yescharacteristic
324C42×C13C2×D411yescharacteristic
325C42×C13C2×D411yescharacteristic
326C42×C13C2411yescharacteristic
327#3545C2×C1311yescharacteristic, complemented
328#3219C2×C1311yescharacteristic, complemented
329#3213C2×C1311yescharacteristic, complemented
330#3171C2×C1311yescharacteristic, complemented
331#1664C2×C1311yescharacteristic, complemented
332#1662C2×C1311yescharacteristic, complemented
333#1661C2×C1311yescharacteristic, complemented
334#1659C2×C1311yescharacteristic, complemented
335#1657C2×C1311yescharacteristic, complemented
336#1656C2×C1311yescharacteristic, complemented
337#1656C2×C1311yescharacteristic, complemented
338#1655C2×C1311yescharacteristic, complemented
339#1535C2×C1311yescharacteristic, complemented
340#1529C2×C1311yescharacteristic, complemented
341#1527C2×C1311yescharacteristic, complemented
342C23×C13—21no—
343C23×C13—21no—
344C23×C13—21no—
345C23×C13—21no—
346C23×C13—42no—
347C23×C13—41no—
348C23×C13—81no—
349C23×C13—81no—
350C23×C13—81no—
351C23×C13—81no—
352C23×C13—81no—
353C23×C13#12011yescharacteristic
354Q8×C13—41no—
355Q8×C13—41no—
356Q8×C13—41no—
357Q8×C13—41no—
358Q8×C13—41no—
359Q8×C13—41no—
360Q8×C13—81no—
361Q8×C13—81no—
362D4×C13—41no—
363D4×C13—41no—
364D4×C13—41no—
365D4×C13—41no—
366D4×C13—41no—
367D4×C13—41no—
368D4×C13—41no—
369D4×C13—41no—
370D4×C13—41no—
371D4×C13—41no—
372D4×C13—42no—
373D4×C13—42no—
374D4×C13—81no—
375D4×C13—81no—
376D4×C13—81no—
377D4×C13—81no—
378D4×C13—81no—
379D4×C13—81no—
380D4×C13—81no—
381D4×C13—81no—
382D4×C13—82no—
383C2×C4×C13—21no—
384C2×C4×C13—21no—
385C2×C4×C13—21no—
386C2×C4×C13—21no—
387C2×C4×C13—21no—
388C2×C4×C13—21no—
389C2×C4×C13—21no—
390C2×C4×C13—21no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—42no—
395C2×C4×C13—41no—
396C2×C4×C13—81no—
397C2×C4×C13—81no—
398C2×C4×C13—82no—
399C2×C4×C13—81no—
400C2×C4×C13—81no—
401C2×C4×C13—81no—
402C2×C4×C13—81no—
403C2×C4×C13—81no—
404C2×C4×C13#12011yescharacteristic
405C2×C4×C13#12011yescharacteristic
406C2×C4×C13#12011yescharacteristic
407C2×C4×C13C22×D411yescharacteristic
408C2×C4×C13C22×D411yescharacteristic
409C2×C4×C13C22×D411yescharacteristic
410C8×C13—22no—
411C8×C13—41no—
412C8×C13—41no—
413C8×C13—41no—
414C8×C13—41no—
415C8×C13—41no—
416#563C22×C1311yescharacteristic
417#562C22×C1311yescharacteristic
418#562C22×C1311yescharacteristic
419H(3,𝔽4)C22×C1311yescharacteristic
420#555—21no—
421#551—21no—
422#551—21no—
423#551—21no—
424#546—21no—
425#546—21no—
426#542—21no—
427#542—21no—
428#538—21no—
429#538—21no—
430#536—21no—
431#534—21no—
432#532C22×C1311yescharacteristic, complemented
433#529C22×C1311yescharacteristic
434#529C22×C1311yescharacteristic
435C2×#124C22×C1311yescharacteristic
436#501C22×C1311yescharacteristic, complemented
437#497C22×C1311yescharacteristic, complemented
438#496C22×C1311yescharacteristic
439#496C22×C1311yescharacteristic, complemented
440#496C22×C1311yescharacteristic, complemented
441#496C22×C1311yescharacteristic, complemented
442#491C22×C1311yescharacteristic, complemented
443#490C22×C1311yescharacteristic, complemented
444#490C22×C1311yescharacteristic, complemented
445#489C22×C1311yescharacteristic
446#489C22×C1311yescharacteristic, complemented
447#489C22×C1311yescharacteristic, complemented
448#469—21no—
449#468—21no—
450#464—21no—
451#463—21no—
452#463—21no—
453#463—21no—
454#452—21no—
455#449—21no—
456#448—21no—
457#447—21no—
458C4×SD16—21no—
459C4×D8—21no—
460#432C22×C1311yescharacteristic, complemented
461#432C22×C1311yescharacteristic, complemented
462C4×M16C22×C1311yescharacteristic, complemented
463#330C22×C1311yescharacteristic, complemented
464#330C22×C1311yescharacteristic, complemented
465#330C22×C1311yescharacteristic, complemented
466#330C22×C1311yescharacteristic, complemented
467#329C22×C1311yescharacteristic
468#329C22×C1311yescharacteristic
469#329C22×C1311yescharacteristic, complemented
470#329C22×C1311yescharacteristic, complemented
471#329C22×C1311yescharacteristic, complemented
472#329C22×C1311yescharacteristic, complemented
473#329C22×C1311yescharacteristic, complemented
474#329C22×C1311yescharacteristic, complemented
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—41no—
479C22×C13—41no—
480C22×C13—41no—
481C22×C13—41no—
482C22×C13—41no—
483C22×C13—41no—
484C22×C13—41no—
485C22×C13—41no—
486C22×C13—41no—
487C22×C13—41no—
488C22×C13—41no—
489C22×C13—41no—
490C22×C13—81no—
491C22×C13—81no—
492C22×C13—81no—
493C22×C13—162no—
494C22×C13—162no—
495C22×C13C2×#12011yescharacteristic
496C4×C13—21no—
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—21no—
501C4×C13—21no—
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—81no—
511C2×#41—21no—
512C2×#41—21no—
513C22×Q8D4×C1311yescharacteristic
514C22×D4—21no—
515C22×D4D4×C1311yescharacteristic
516C2×Q16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×D8—21no—
523C2×D8—21no—
524C2×D8—21no—
525C2×D8—21no—
526C2×M16—21no—
527C4⋊Q8—21no—
528C4⋊Q8—21no—
529C4⋊Q8C23×C1311yescharacteristic
530#127C23×C1311yescharacteristic
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#125C23×C1311yescharacteristic
538#125C23×C1311yescharacteristic
539#124—21no—
540#124—21no—
541#124—21no—
542#124—21no—
543#124—21no—
544#124—21no—
545#124—21no—
546#124—21no—
547#124—21no—
548#124D4×C1311yescharacteristic
549#124D4×C1311yescharacteristic
550#124C23×C1311yescharacteristic
551#124C23×C1311yescharacteristic
552#124C23×C1311yescharacteristic
553#124C23×C1311yescharacteristic
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—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⋊Q8D4×C1311yescharacteristic
575C22⋊Q8D4×C1311yescharacteristic
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121D4×C1311yescharacteristic
587#121D4×C1311yescharacteristic
588#120—21no—
589#120—21no—
590#120—21no—
591#120—21no—
592#120—21no—
593#120—21no—
594C4×Q8D4×C1311yescharacteristic
595C4×Q8D4×C1311yescharacteristic
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4D4×C1311yescharacteristic
605C4×D4D4×C1311yescharacteristic
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C42C23×C1311yescharacteristic
617#107—21no—
618#106—21no—
619C4⋊C8—21no—
620C4⋊C8—21no—
621#103—21no—
622#103—21no—
623#103—21no—
624#103—21no—
625#103—21no—
626#102—21no—
627#102—21no—
628#102—21no—
629#102—21no—
630#102—21no—
631#102—21no—
632#102—21no—
633C22⋊C8—21no—
634C22⋊C8—21no—
635#97C23×C1311yescharacteristic
636#97C23×C1311yescharacteristic
637#97C23×C1311yescharacteristic
638#97C23×C1311yescharacteristic
639#97C23×C1311yescharacteristic
640#97C23×C1311yescharacteristic
641C4×C8—21no—
642C2×C13—41no—
643C2×C13—81no—
644C2×C13—81no—
645C2×C13—81no—
646C2×C13—81no—
647C2×C13—161no—
648C2×C13#301811yescharacteristic
649C2×C13#301911yescharacteristic
650C2×C13#302111yescharacteristic
651C24—21no—
652C24—21no—
653#41—82no—
654#41—81no—
655#41—81no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—81no—
660C2×Q8C2×D4×C1311yescharacteristic
661C2×Q8C2×D4×C1311yescharacteristic
662C2×Q8C2×D4×C1311yescharacteristic
663C2×Q8C2×D4×C1311yescharacteristic
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—41no—
678C2×D4—81no—
679C2×D4—82no—
680C2×D4C2×D4×C1311yescharacteristic
681C2×D4C2×D4×C1311yescharacteristic
682C2×D4C2×D4×C1311yescharacteristic
683C2×D4C2×D4×C1311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—41no—
693C22×C4C2×D4×C1311yescharacteristic
694C22×C4C2×D4×C1311yescharacteristic
695C22×C4C2×D4×C1311yescharacteristic
696Q16—81no—
697SD16—42no—
698SD16—81no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702D8—42no—
703D8—81no—
704D8—81no—
705D8—81no—
706M16—42no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—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—21no—
728C4⋊C4—21no—
729C4⋊C4C2×D4×C1311yescharacteristic
730C4⋊C4C2×D4×C1311yescharacteristic
731C4⋊C4C2×D4×C1311yescharacteristic
732C4⋊C4C2×D4×C1311yescharacteristic
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—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C1311yescharacteristic
768C42C2×D4×C1311yescharacteristic
769C42C2×D4×C1311yescharacteristic
770C42C24×C1311yescharacteristic
771C13#1906811yescharacteristic, direct product factor, Sylow
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C13×#12011yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4C13×#12011yescharacteristic
835C2×C4C13×#12011yescharacteristic
836C2×C4C13×#12011yescharacteristic
837C2×C4C22×D4×C1311yescharacteristic
838C2×C4C22×D4×C1311yescharacteristic
839C2×C4C22×D4×C1311yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×C13×#12011yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C13×#301811yescharacteristic
889C2C13×#301911yescharacteristic
890C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
LCSG ▷ C42 ▷ 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×#3545C2semidirect
2. C13×#3219C2semidirect
3. C13×#3213C2semidirect
4. C13×#3171C2semidirect
5. C13×#1664C2semidirect
6. C13×#1662C2semidirect
7. C13×#1661C2semidirect
8. C13×#1659C2semidirect
9. C13×#1657C2semidirect
10. C13×#1656C2semidirect
11. C13×#1656C2semidirect
12. C13×#1655C2semidirect
13. C13×#1535C2semidirect
14. C13×#1529C2semidirect
15. C13×#1527C2semidirect
32. C13×#532C22semidirect
36. C13×#501C22semidirect
37. C13×#497C22semidirect
39. C13×#496C22semidirect
40. C13×#496C22semidirect
41. C13×#496C22semidirect
42. C13×#491C22semidirect
43. C13×#490C22semidirect
44. C13×#490C22semidirect
46. C13×#489C22semidirect
47. C13×#489C22semidirect
60. C13×#432C22semidirect
61. C13×#432C22semidirect
62. C4×C13×M16C22semidirect
63. C13×#330C22semidirect
64. C13×#330C22semidirect
65. C13×#330C22semidirect
66. C13×#330C22semidirect
69. C13×#329C22semidirect
70. C13×#329C22semidirect
71. C13×#329C22semidirect
72. C13×#329C22semidirect
73. C13×#329C22semidirect
74. C13×#329C22semidirect
206. #19068C13direct (N × H)
327. #3545C2×C13semidirect
328. #3219C2×C13semidirect
329. #3213C2×C13semidirect
330. #3171C2×C13semidirect
331. #1664C2×C13semidirect
332. #1662C2×C13semidirect
333. #1661C2×C13semidirect
334. #1659C2×C13semidirect
335. #1657C2×C13semidirect
336. #1656C2×C13semidirect
337. #1656C2×C13semidirect
338. #1655C2×C13semidirect
339. #1535C2×C13semidirect
340. #1529C2×C13semidirect
341. #1527C2×C13semidirect
432. #532C22×C13semidirect
436. #501C22×C13semidirect
437. #497C22×C13semidirect
439. #496C22×C13semidirect
440. #496C22×C13semidirect
441. #496C22×C13semidirect
442. #491C22×C13semidirect
443. #490C22×C13semidirect
444. #490C22×C13semidirect
446. #489C22×C13semidirect
447. #489C22×C13semidirect
460. #432C22×C13semidirect
461. #432C22×C13semidirect
462. C4×M16C22×C13semidirect
463. #330C22×C13semidirect
464. #330C22×C13semidirect
465. #330C22×C13semidirect
466. #330C22×C13semidirect
469. #329C22×C13semidirect
470. #329C22×C13semidirect
471. #329C22×C13semidirect
472. #329C22×C13semidirect
473. #329C22×C13semidirect
474. #329C22×C13semidirect
771. C13#19068direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35452
C13×#32192
C13×#32132
C13×#31712
C13×#16642
C13×#16622
C13×#16612
C13×#16592
C13×#16572
C13×#16562
C13×#16552
C13×#15352
C13×#15292
C13×#15272
#1906813