Finite Group Databasebeta

← C13×#18444 #15704783

Subgroups — C13×#18444 #15704783

Order 3328.

908 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3560C211yesmaximal, characteristic
2C13×#3234C211yesmaximal, characteristic, complemented
3C13×#3232C211yesmaximal, characteristic, complemented
4C13×#2664C211yesmaximal, characteristic, complemented
5C13×#1618C211yesmaximal, characteristic, complemented
6C13×#1616C211yesmaximal, characteristic, complemented
7C13×#1615C211yesmaximal, characteristic, complemented
8C13×#1613C211yesmaximal, characteristic, complemented
9C13×#1612C211yesmaximal, characteristic, complemented
10C13×#1610C211yesmaximal, characteristic, complemented
11C13×#1609C211yesmaximal, characteristic, complemented
12C13×#1607C211yesmaximal, characteristic, complemented
13C13×#1509C211yesmaximal, characteristic, complemented
14C13×#1502C211yesmaximal, characteristic, complemented
15C13×#1473C211yesmaximal, characteristic, complemented
16C13×#563—21no—
17C13×#560—21no—
18C13×#553—21no—
19C13×#553—21no—
20C13×#551—21no—
21C13×#547—21no—
22C13×#546—21no—
23C13×#546—21no—
24C13×#542—21no—
25C13×#539—21no—
26C13×#539C2211yescharacteristic
27C13×#538—21no—
28C13×#538—21no—
29C13×#538C2211yescharacteristic
30C13×#537C2211yescharacteristic
31C13×#534C2211yescharacteristic
32C13×#532C2211yescharacteristic
33C13×#529C2211yescharacteristic
34C2×C13×#126C2211yescharacteristic
35C2×C13×#125C2211yescharacteristic, complemented
36C13×#501—21no—
37C13×#499—21no—
38C13×#490—21no—
39C13×#488—21no—
40C13×#484C2211yescharacteristic, complemented
41C13×#483C2211yescharacteristic, complemented
42C13×#481C2211yescharacteristic
43C13×#481C2211yescharacteristic
44C13×#481C2211yescharacteristic, complemented
45C13×#480C2211yescharacteristic
46C13×#480C2211yescharacteristic
47C13×#480C2211yescharacteristic, complemented
48C13×#479—21no—
49C13×#478—21no—
50C13×#478—21no—
51C13×#478—21no—
52C13×#432C2211yescharacteristic, complemented
53C13×#431C2211yescharacteristic, complemented
54C13×#400C2211yescharacteristic, complemented
55C13×#399C2211yescharacteristic
56C13×#398—21no—
57C13×#398C2211yescharacteristic, complemented
58C13×#397C2211yescharacteristic
59C13×#396—21no—
60C13×#389—21no—
61C13×#388—21no—
62C4×C13×C4⋊C4C2211yescharacteristic, complemented
63C13×#328C2211yescharacteristic, complemented
64C13×#328C2211yescharacteristic, complemented
65C13×#327C2211yescharacteristic
66C13×#327C2211yescharacteristic
67C13×#327C2211yescharacteristic
68C13×#327C2211yescharacteristic
69C13×#327C2211yescharacteristic, complemented
70C13×#327C2211yescharacteristic, complemented
71C13×#324C2211yescharacteristic, complemented
72C13×#324C2211yescharacteristic, complemented
73C13×#323C2211yescharacteristic
74C13×#323C2211yescharacteristic
75C2×C13×#41—21no—
76C2×C13×#41—21no—
77C22×D4×C13—21no—
78C13×C4⋊Q8—21no—
79C13×C4⋊Q8D411yescharacteristic
80C13×#127D411yescharacteristic
81C13×#126—21no—
82C13×#126—21no—
83C13×#126—21no—
84C13×#126—21no—
85C13×#126—21no—
86C13×#126—21no—
87C13×#126—21no—
88C13×#126—21no—
89C13×#126—21no—
90C13×#125—21no—
91C13×#125—21no—
92C13×#125—21no—
93C13×#125—21no—
94C13×#125—21no—
95C13×#125—21no—
96C13×#125D411yescharacteristic
97C13×#124—21no—
98C13×#124—21no—
99C13×#124—21no—
100C13×#124—21no—
101C13×#124D411yescharacteristic
102C13×#123—21no—
103C13×#123—21no—
104C13×#123—21no—
105C13×#123—21no—
106C13×#123—21no—
107C13×#123—21no—
108C13×#123—21no—
109C13×#123—21no—
110C13×#123—21no—
111C13×#123—21no—
112C13×#123—21no—
113C13×#123—21no—
114C13×C22⋊Q8—21no—
115C13×C22⋊Q8—21no—
116C13×C22⋊Q8—21no—
117C13×C22⋊Q8—21no—
118C13×C22⋊Q8—21no—
119C13×C22⋊Q8—21no—
120C13×C22⋊Q8—21no—
121C13×C22⋊Q8C2311yescharacteristic
122C13×#121—21no—
123C13×#121—21no—
124C13×#121—21no—
125C13×#121—21no—
126C13×#121—21no—
127C13×#121—21no—
128C13×#121—21no—
129C13×#121—21no—
130C13×#121—21no—
131C13×#121—21no—
132C13×#121—21no—
133C13×#121—21no—
134C13×#121C2311yescharacteristic
135C13×#121C2311yescharacteristic
136C13×#121C2311yescharacteristic
137C13×#120—21no—
138C13×#120—21no—
139C13×#120—21no—
140C13×#120—21no—
141C13×#120—21no—
142C4×Q8×C13D411yescharacteristic
143C4×D4×C13—21no—
144C4×D4×C13—21no—
145C4×D4×C13—21no—
146C4×D4×C13—21no—
147C4×D4×C13—21no—
148C4×D4×C13—21no—
149C4×D4×C13—21no—
150C4×D4×C13—21no—
151C4×D4×C13D411yescharacteristic
152C4×D4×C13D411yescharacteristic
153C4×D4×C13D411yescharacteristic
154C13×#117—21no—
155C13×#117—21no—
156C2×C13×C4⋊C4—21no—
157C2×C13×C4⋊C4—21no—
158C2×C13×C4⋊C4—21no—
159C2×C13×C4⋊C4—21no—
160C2×C13×C4⋊C4—21no—
161C2×C13×C4⋊C4—21no—
162C2×C13×C4⋊C4D411yescharacteristic
163C2×C13×C4⋊C4D411yescharacteristic
164C2×C13×C4⋊C4C2311yescharacteristic
165C2×C13×C4⋊C4C2311yescharacteristic
166C2×C13×C4⋊C4C2311yescharacteristic
167C2×C13×C22⋊C4—21no—
168C2×C13×C22⋊C4—21no—
169C2×C13×C22⋊C4—21no—
170C2×C13×C22⋊C4—21no—
171C2×C13×C22⋊C4D411yescharacteristic
172C2×C13×C22⋊C4D411yescharacteristic
173C2×C13×C22⋊C4C2311yescharacteristic
174C2×C42×C13—21no—
175C2×C42×C13C2311yescharacteristic
176C13×#107—21no—
177C13×#107—21no—
178C13×#107—21no—
179C13×#107—21no—
180C13×#106—21no—
181C13×#106—21no—
182C13×#106—21no—
183C13×#106—21no—
184C13×C4⋊C8—21no—
185C13×C4⋊C8—21no—
186C13×#103—21no—
187C13×#103—21no—
188C13×#102—21no—
189C13×#102—21no—
190C13×#102—21no—
191C13×#102—21no—
192C13×#102—21no—
193C13×#102—21no—
194C13×C22⋊C8C2311yescharacteristic
195C13×C22⋊C8C2311yescharacteristic
196C13×C22⋊C8C2311yescharacteristic
197C13×C22⋊C8C2311yescharacteristic
198C13×#97—21no—
199C4×C8×C13—21no—
200C13×#95—21no—
201C13×#95—21no—
202C13×#95—21no—
203C13×#95—21no—
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#18444C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13C2×D411yescharacteristic
209C13×#41—81no—
210C13×#41—81no—
211C13×#41—81no—
212C13×#41—81no—
213C2×Q8×C13—21no—
214C2×Q8×C13—21no—
215C2×Q8×C13C2×D411yescharacteristic
216C2×D4×C13—21no—
217C2×D4×C13—21no—
218C2×D4×C13—21no—
219C2×D4×C13—21no—
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—81no—
229C2×D4×C13—81no—
230C2×D4×C13C2×D411yescharacteristic
231C2×D4×C13C2×D411yescharacteristic
232C2×D4×C13C2×D411yescharacteristic
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13C2×D411yescharacteristic
246C22×C4×C13C2×D411yescharacteristic
247C22×C4×C13C2×D411yescharacteristic
248C22×C4×C13C2×D411yescharacteristic
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2411yescharacteristic
251C2×C8×C13—21no—
252C2×C8×C13—21no—
253C2×C8×C13—21no—
254C2×C8×C13—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—42no—
277C13×C4⋊C4—42no—
278C13×C4⋊C4—41no—
279C13×C4⋊C4—41no—
280C13×C4⋊C4—41no—
281C13×C4⋊C4—41no—
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—21no—
309C13×C22⋊C4—21no—
310C13×C22⋊C4—21no—
311C13×C22⋊C4—21no—
312C13×C22⋊C4—42no—
313C13×C22⋊C4—81no—
314C42×C13—21no—
315C42×C13—21no—
316C42×C13—21no—
317C42×C13—81no—
318C42×C13C2×D411yescharacteristic
319C42×C13C2×D411yescharacteristic
320C42×C13C2×D411yescharacteristic
321C42×C13C2×D411yescharacteristic
322#3560C2×C1311yescharacteristic
323#3234C2×C1311yescharacteristic, complemented
324#3232C2×C1311yescharacteristic, complemented
325#2664C2×C1311yescharacteristic, complemented
326#1618C2×C1311yescharacteristic, complemented
327#1616C2×C1311yescharacteristic, complemented
328#1615C2×C1311yescharacteristic, complemented
329#1613C2×C1311yescharacteristic, complemented
330#1612C2×C1311yescharacteristic, complemented
331#1610C2×C1311yescharacteristic, complemented
332#1609C2×C1311yescharacteristic, complemented
333#1607C2×C1311yescharacteristic, complemented
334#1509C2×C1311yescharacteristic, complemented
335#1502C2×C1311yescharacteristic, complemented
336#1473C2×C1311yescharacteristic, complemented
337C23×C13—21no—
338C23×C13—21no—
339C23×C13—21no—
340C23×C13—21no—
341C23×C13—21no—
342C23×C13—21no—
343C23×C13—41no—
344C23×C13—41no—
345C23×C13—81no—
346C23×C13—81no—
347C23×C13—81no—
348C23×C13C22×D411yescharacteristic
349Q8×C13—41no—
350Q8×C13—81no—
351Q8×C13—81no—
352D4×C13—41no—
353D4×C13—41no—
354D4×C13—41no—
355D4×C13—41no—
356D4×C13—41no—
357D4×C13—41no—
358D4×C13—41no—
359D4×C13—41no—
360D4×C13—41no—
361D4×C13—81no—
362D4×C13—81no—
363D4×C13—81no—
364D4×C13—81no—
365D4×C13—81no—
366D4×C13—81no—
367D4×C13—81no—
368D4×C13—81no—
369D4×C13—81no—
370C2×C4×C13—21no—
371C2×C4×C13—21no—
372C2×C4×C13—22no—
373C2×C4×C13—21no—
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—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
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—81no—
400C2×C4×C13—81no—
401C2×C4×C13—81no—
402C2×C4×C13—81no—
403C2×C4×C13—81no—
404C2×C4×C13—81no—
405C2×C4×C13—81no—
406C2×C4×C13#12011yescharacteristic
407C2×C4×C13#12011yescharacteristic
408C2×C4×C13#12011yescharacteristic
409C2×C4×C13#12011yescharacteristic
410C2×C4×C13C22×D411yescharacteristic
411C2×C4×C13C22×D411yescharacteristic
412C8×C13—41no—
413C8×C13—41no—
414C8×C13—41no—
415C8×C13—41no—
416#563—21no—
417#560—21no—
418#553—21no—
419#553—21no—
420#551—21no—
421#547—21no—
422#546—21no—
423#546—21no—
424#542—21no—
425#539—21no—
426#539C22×C1311yescharacteristic
427#538—21no—
428#538—21no—
429#538C22×C1311yescharacteristic
430#537C22×C1311yescharacteristic
431#534C22×C1311yescharacteristic
432#532C22×C1311yescharacteristic
433#529C22×C1311yescharacteristic
434C2×#126C22×C1311yescharacteristic
435C2×#125C22×C1311yescharacteristic, complemented
436#501—21no—
437#499—21no—
438#490—21no—
439#488—21no—
440#484C22×C1311yescharacteristic, complemented
441#483C22×C1311yescharacteristic, complemented
442#481C22×C1311yescharacteristic
443#481C22×C1311yescharacteristic
444#481C22×C1311yescharacteristic, complemented
445#480C22×C1311yescharacteristic
446#480C22×C1311yescharacteristic
447#480C22×C1311yescharacteristic, complemented
448#479—21no—
449#478—21no—
450#478—21no—
451#478—21no—
452#432C22×C1311yescharacteristic, complemented
453#431C22×C1311yescharacteristic, complemented
454#400C22×C1311yescharacteristic, complemented
455#399C22×C1311yescharacteristic
456#398—21no—
457#398C22×C1311yescharacteristic, complemented
458#397C22×C1311yescharacteristic
459#396—21no—
460#389—21no—
461#388—21no—
462C4×C4⋊C4C22×C1311yescharacteristic, complemented
463#328C22×C1311yescharacteristic, complemented
464#328C22×C1311yescharacteristic, complemented
465#327C22×C1311yescharacteristic
466#327C22×C1311yescharacteristic
467#327C22×C1311yescharacteristic
468#327C22×C1311yescharacteristic
469#327C22×C1311yescharacteristic, complemented
470#327C22×C1311yescharacteristic, complemented
471#324C22×C1311yescharacteristic, complemented
472#324C22×C1311yescharacteristic, complemented
473#323C22×C1311yescharacteristic
474#323C22×C1311yescharacteristic
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—41no—
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—81no—
490C22×C13—81no—
491C22×C13—162no—
492C22×C13C2×#12011yescharacteristic
493C22×C13#57611yescharacteristic
494C22×C13#57711yescharacteristic
495C4×C13—21no—
496C4×C13—21no—
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—21no—
501C4×C13—42no—
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—
511C4×C13—81no—
512C4×C13—81no—
513C2×#41—21no—
514C2×#41—21no—
515C22×D4—21no—
516C4⋊Q8—21no—
517C4⋊Q8D4×C1311yescharacteristic
518#127D4×C1311yescharacteristic
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#126—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125—21no—
532#125—21no—
533#125—21no—
534#125D4×C1311yescharacteristic
535#124—21no—
536#124—21no—
537#124—21no—
538#124—21no—
539#124D4×C1311yescharacteristic
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8C23×C1311yescharacteristic
560#121—21no—
561#121—21no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121C23×C1311yescharacteristic
573#121C23×C1311yescharacteristic
574#121C23×C1311yescharacteristic
575#120—21no—
576#120—21no—
577#120—21no—
578#120—21no—
579#120—21no—
580C4×Q8D4×C1311yescharacteristic
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4D4×C1311yescharacteristic
590C4×D4D4×C1311yescharacteristic
591C4×D4D4×C1311yescharacteristic
592#117—21no—
593#117—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4D4×C1311yescharacteristic
601C2×C4⋊C4D4×C1311yescharacteristic
602C2×C4⋊C4C23×C1311yescharacteristic
603C2×C4⋊C4C23×C1311yescharacteristic
604C2×C4⋊C4C23×C1311yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C1311yescharacteristic
610C2×C22⋊C4D4×C1311yescharacteristic
611C2×C22⋊C4C23×C1311yescharacteristic
612C2×C42—21no—
613C2×C42C23×C1311yescharacteristic
614#107—21no—
615#107—21no—
616#107—21no—
617#107—21no—
618#106—21no—
619#106—21no—
620#106—21no—
621#106—21no—
622C4⋊C8—21no—
623C4⋊C8—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—
632C22⋊C8C23×C1311yescharacteristic
633C22⋊C8C23×C1311yescharacteristic
634C22⋊C8C23×C1311yescharacteristic
635C22⋊C8C23×C1311yescharacteristic
636#97—21no—
637C4×C8—21no—
638#95—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—81no—
649C2×C13—81no—
650C2×C13#301211yescharacteristic
651C2×C13#301811yescharacteristic
652C2×C13#302811yescharacteristic
653C24—21no—
654C24C2×D4×C1311yescharacteristic
655#41—81no—
656#41—81no—
657#41—81no—
658#41—81no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8C2×D4×C1311yescharacteristic
662C2×D4—21no—
663C2×D4—21no—
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—81no—
675C2×D4—81no—
676C2×D4C2×D4×C1311yescharacteristic
677C2×D4C2×D4×C1311yescharacteristic
678C2×D4C2×D4×C1311yescharacteristic
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4C2×D4×C1311yescharacteristic
692C22×C4C2×D4×C1311yescharacteristic
693C22×C4C2×D4×C1311yescharacteristic
694C22×C4C2×D4×C1311yescharacteristic
695C22×C4C2×D4×C1311yescharacteristic
696C22×C4C24×C1311yescharacteristic
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—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—42no—
723C4⋊C4—42no—
724C4⋊C4—41no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—81no—
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—42no—
759C22⋊C4—81no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—81no—
764C42C2×D4×C1311yescharacteristic
765C42C2×D4×C1311yescharacteristic
766C42C2×D4×C1311yescharacteristic
767C42C2×D4×C1311yescharacteristic
768C13#1844411yescharacteristic, direct product factor, Sylow
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—41no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23C22×D4×C1311yescharacteristic
781Q8—41no—
782Q8—81no—
783Q8—81no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—81no—
794D4—81no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
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—41no—
816C2×C4—41no—
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—41no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C13×#12011yescharacteristic
839C2×C4C13×#12011yescharacteristic
840C2×C4C13×#12011yescharacteristic
841C2×C4C13×#12011yescharacteristic
842C2×C4C22×D4×C1311yescharacteristic
843C2×C4C22×D4×C1311yescharacteristic
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C22—21no—
849C22—21no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22C2×C13×#12011yescharacteristic
866C22C13×#57611yescharacteristic
867C22C13×#57711yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—21no—
887C2—21no—
888C2—81no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2C13×#301211yescharacteristic
893C2C13×#301811yescharacteristic
894C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3560C2
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×#3234C2semidirect
3. C13×#3232C2semidirect
4. C13×#2664C2semidirect
5. C13×#1618C2semidirect
6. C13×#1616C2semidirect
7. C13×#1615C2semidirect
8. C13×#1613C2semidirect
9. C13×#1612C2semidirect
10. C13×#1610C2semidirect
11. C13×#1609C2semidirect
12. C13×#1607C2semidirect
13. C13×#1509C2semidirect
14. C13×#1502C2semidirect
15. C13×#1473C2semidirect
35. C2×C13×#125C22semidirect
40. C13×#484C22semidirect
41. C13×#483C22semidirect
44. C13×#481C22semidirect
47. C13×#480C22semidirect
52. C13×#432C22semidirect
53. C13×#431C22semidirect
54. C13×#400C22semidirect
57. C13×#398C22semidirect
62. C4×C13×C4⋊C4C22semidirect
63. C13×#328C22semidirect
64. C13×#328C22semidirect
69. C13×#327C22semidirect
70. C13×#327C22semidirect
71. C13×#324C22semidirect
72. C13×#324C22semidirect
206. #18444C13direct (N × H)
323. #3234C2×C13semidirect
324. #3232C2×C13semidirect
325. #2664C2×C13semidirect
326. #1618C2×C13semidirect
327. #1616C2×C13semidirect
328. #1615C2×C13semidirect
329. #1613C2×C13semidirect
330. #1612C2×C13semidirect
331. #1610C2×C13semidirect
332. #1609C2×C13semidirect
333. #1607C2×C13semidirect
334. #1509C2×C13semidirect
335. #1502C2×C13semidirect
336. #1473C2×C13semidirect
435. C2×#125C22×C13semidirect
440. #484C22×C13semidirect
441. #483C22×C13semidirect
444. #481C22×C13semidirect
447. #480C22×C13semidirect
452. #432C22×C13semidirect
453. #431C22×C13semidirect
454. #400C22×C13semidirect
457. #398C22×C13semidirect
462. C4×C4⋊C4C22×C13semidirect
463. #328C22×C13semidirect
464. #328C22×C13semidirect
469. #327C22×C13semidirect
470. #327C22×C13semidirect
471. #324C22×C13semidirect
472. #324C22×C13semidirect
768. C13#18444direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35602
C13×#32342
C13×#32322
C13×#26642
C13×#16182
C13×#16162
C13×#16152
C13×#16132
C13×#16122
C13×#16102
C13×#16092
C13×#16072
C13×#15092
C13×#15022
C13×#14732
#1844413