Finite Group Databasebeta

← C13×#18463 #15704802

Subgroups — C13×#18463 #15704802

Order 3328.

930 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3560C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C13×#3206C211yesmaximal, characteristic, complemented
4C13×#2821C211yesmaximal, characteristic, complemented
5C13×#1606C212yesmaximal, complemented
6C13×#1604C212yesmaximal, complemented
7C13×#1603C212yesmaximal, complemented
8C13×#1601C212yesmaximal, complemented
9C13×#1521C211yesmaximal, characteristic, complemented
10C13×#1514C211yesmaximal, characteristic, complemented
11C13×#1473C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#560—21no—
14C13×#553—21no—
15C13×#553—21no—
16C13×#551—21no—
17C13×#547—21no—
18C13×#546—21no—
19C13×#546—21no—
20C13×#542—21no—
21C13×#539—21no—
22C13×#539C2211yescharacteristic
23C13×#538—21no—
24C13×#538—21no—
25C13×#538C2211yescharacteristic
26C13×#537C2211yescharacteristic
27C13×#534C2211yescharacteristic
28C13×#532C2211yescharacteristic
29C2×C13×C4⋊Q8C2211yescharacteristic, complemented
30C13×#529C2211yescharacteristic
31C2×C13×#126C2211yescharacteristic
32C13×#497—21no—
33C13×#492—21no—
34C13×#491—21no—
35C13×#487—21no—
36C13×#462—21no—
37C13×#461—21no—
38C13×#461—21no—
39C13×#461—21no—
40C13×#451C2212yescomplemented
41C13×#448C2212yes—
42C13×#448C2212yes—
43C13×#448C2212yescomplemented
44C13×#432C2211yescharacteristic, complemented
45C13×#431C2211yescharacteristic, complemented
46C13×#400—21no—
47C13×#399—21no—
48C13×#398—21no—
49C13×#397—21no—
50C13×#395C2212yescomplemented
51C13×#393C2212yes—
52C13×#383C2211yescharacteristic, complemented
53C13×#328C2212yescomplemented
54C13×#327C2212yes—
55C13×#327C2212yes—
56C13×#327C2212yescomplemented
57C13×#324C2212yescomplemented
58C13×#323C2212yes—
59C2×C13×#41—21no—
60C2×C13×#41—21no—
61C22×Q8×C13C2312yes—
62C22×D4×C13—21no—
63C2×C13×Q16—22no—
64C2×C13×SD16—22no—
65C2×C13×SD16—22no—
66C2×C13×SD16—22no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—21no—
69C13×C4⋊Q8—21no—
70C13×C4⋊Q8—21no—
71C13×C4⋊Q8—21no—
72C13×C4⋊Q8D411yescharacteristic
73C13×#127D411yescharacteristic
74C13×#126—21no—
75C13×#126—21no—
76C13×#126—21no—
77C13×#126—21no—
78C13×#126—21no—
79C13×#126—21no—
80C13×#126—21no—
81C13×#126—21no—
82C13×#126—21no—
83C13×#125—21no—
84C13×#125—21no—
85C13×#125D411yescharacteristic
86C13×#124—21no—
87C13×#124—21no—
88C13×#124—21no—
89C13×#124—21no—
90C13×#124D411yescharacteristic
91C13×#123—21no—
92C13×#123—21no—
93C13×#123—21no—
94C13×#123—21no—
95C13×#123—21no—
96C13×#123—21no—
97C13×#123—21no—
98C13×#123—21no—
99C13×#123—21no—
100C13×#123—21no—
101C13×#123—21no—
102C13×#123—21no—
103C13×C22⋊Q8—21no—
104C13×C22⋊Q8—21no—
105C13×C22⋊Q8—21no—
106C13×C22⋊Q8—21no—
107C13×C22⋊Q8—21no—
108C13×C22⋊Q8—21no—
109C13×C22⋊Q8—21no—
110C13×C22⋊Q8C2311yescharacteristic
111C13×#121—21no—
112C13×#121—21no—
113C13×#121—21no—
114C13×#121—21no—
115C13×#121—21no—
116C13×#121—21no—
117C13×#121—21no—
118C13×#121—21no—
119C13×#121—21no—
120C13×#121—21no—
121C13×#121—21no—
122C13×#121—21no—
123C13×#121C2311yescharacteristic
124C13×#121C2311yescharacteristic
125C13×#121C2311yescharacteristic
126C13×#120—21no—
127C13×#120—21no—
128C13×#120—21no—
129C13×#120—21no—
130C13×#120—21no—
131C4×Q8×C13D411yescharacteristic
132C4×D4×C13—21no—
133C4×D4×C13—21no—
134C4×D4×C13—21no—
135C4×D4×C13—21no—
136C4×D4×C13—21no—
137C4×D4×C13—21no—
138C4×D4×C13—21no—
139C4×D4×C13—21no—
140C4×D4×C13D411yescharacteristic
141C4×D4×C13D411yescharacteristic
142C4×D4×C13D411yescharacteristic
143C13×#117—21no—
144C13×#117—21no—
145C2×C13×C4⋊C4—21no—
146C2×C13×C4⋊C4—21no—
147C2×C13×C4⋊C4—21no—
148C2×C13×C4⋊C4—22no—
149C2×C13×C4⋊C4D411yescharacteristic
150C2×C13×C4⋊C4D411yescharacteristic
151C2×C13×C4⋊C4C2311yescharacteristic
152C2×C13×C22⋊C4—21no—
153C2×C13×C22⋊C4—21no—
154C2×C13×C22⋊C4—22no—
155C2×C13×C22⋊C4D411yescharacteristic
156C2×C13×C22⋊C4D411yescharacteristic
157C2×C13×C22⋊C4C2311yescharacteristic
158C2×C42×C13C2311yescharacteristic
159C13×C4⋊C8—21no—
160C13×C4⋊C8—21no—
161C13×#103—22no—
162C13×#103—22no—
163C13×#103—22no—
164C13×#103—22no—
165C13×C22⋊C8C2312yes—
166C13×C22⋊C8C2312yes—
167C13×#97—21no—
168C4×C8×C13—21no—
169C13×#95—21no—
170C13×#95—21no—
171C13×#95—22no—
172C13×#95—22no—
173C13×#95C2312yes—
174#18463C1311yesmaximal, characteristic, direct product factor, Sylow
175C24×C13—21no—
176C24×C13C2×D411yescharacteristic
177C13×#41—82no—
178C13×#41—82no—
179C2×Q8×C13—21no—
180C2×Q8×C13—21no—
181C2×Q8×C13—22no—
182C2×Q8×C13—22no—
183C2×Q8×C13—82no—
184C2×Q8×C13C2×D411yescharacteristic
185C2×D4×C13—21no—
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13—21no—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—21no—
194C2×D4×C13—21no—
195C2×D4×C13—21no—
196C2×D4×C13—21no—
197C2×D4×C13—82no—
198C2×D4×C13C2×D411yescharacteristic
199C2×D4×C13C2×D411yescharacteristic
200C2×D4×C13C2×D411yescharacteristic
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2411yescharacteristic
217C13×Q16—82no—
218C13×SD16—82no—
219C13×SD16—82no—
220C13×SD16—82no—
221C2×C8×C13—22no—
222C2×C8×C13—22no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—21no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4—21no—
238C13×C4⋊C4—21no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4—41no—
241C13×C4⋊C4—41no—
242C13×C4⋊C4—41no—
243C13×C4⋊C4—41no—
244C13×C4⋊C4—82no—
245C13×C4⋊C4C2×D411yescharacteristic
246C13×C4⋊C4C2×D411yescharacteristic
247C13×C4⋊C4C2×D411yescharacteristic
248C13×C4⋊C4C2×D411yescharacteristic
249C13×C22⋊C4—21no—
250C13×C22⋊C4—21no—
251C13×C22⋊C4—21no—
252C13×C22⋊C4—21no—
253C13×C22⋊C4—21no—
254C13×C22⋊C4—21no—
255C13×C22⋊C4—21no—
256C13×C22⋊C4—21no—
257C13×C22⋊C4—21no—
258C13×C22⋊C4—21no—
259C13×C22⋊C4—21no—
260C13×C22⋊C4—21no—
261C13×C22⋊C4—21no—
262C13×C22⋊C4—21no—
263C13×C22⋊C4—21no—
264C13×C22⋊C4—21no—
265C13×C22⋊C4—21no—
266C13×C22⋊C4—21no—
267C13×C22⋊C4—21no—
268C13×C22⋊C4—21no—
269C13×C22⋊C4—21no—
270C13×C22⋊C4—21no—
271C13×C22⋊C4—21no—
272C13×C22⋊C4—21no—
273C13×C22⋊C4—21no—
274C13×C22⋊C4—82no—
275C42×C13—21no—
276C42×C13—21no—
277C42×C13—21no—
278C42×C13C2×D411yescharacteristic
279C42×C13C2×D411yescharacteristic
280C42×C13C2×D411yescharacteristic
281C42×C13C2×D411yescharacteristic
282#3560C2×C1311yescharacteristic
283#3218C2×C1311yescharacteristic, complemented
284#3206C2×C1311yescharacteristic, complemented
285#2821C2×C1311yescharacteristic, complemented
286#1606C2×C1312yescomplemented
287#1604C2×C1312yescomplemented
288#1603C2×C1312yescomplemented
289#1601C2×C1312yescomplemented
290#1521C2×C1311yescharacteristic, complemented
291#1514C2×C1311yescharacteristic, complemented
292#1473C2×C1311yescharacteristic, complemented
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—22no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—81no—
301C23×C13—81no—
302C23×C13—81no—
303C23×C13C22×D411yescharacteristic
304Q8×C13—41no—
305Q8×C13—42no—
306Q8×C13—42no—
307Q8×C13—42no—
308Q8×C13—42no—
309Q8×C13—81no—
310Q8×C13—81no—
311D4×C13—41no—
312D4×C13—41no—
313D4×C13—41no—
314D4×C13—42no—
315D4×C13—42no—
316D4×C13—42no—
317D4×C13—81no—
318D4×C13—81no—
319D4×C13—81no—
320D4×C13—81no—
321D4×C13—81no—
322D4×C13—81no—
323D4×C13—81no—
324D4×C13—81no—
325D4×C13—81no—
326C2×C4×C13—22no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—22no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—42no—
341C2×C4×C13—42no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—81no—
347C2×C4×C13—81no—
348C2×C4×C13—81no—
349C2×C4×C13—81no—
350C2×C4×C13—81no—
351C2×C4×C13—81no—
352C2×C4×C13—81no—
353C2×C4×C13—81no—
354C2×C4×C13#12011yescharacteristic
355C2×C4×C13#12011yescharacteristic
356C2×C4×C13#12011yescharacteristic
357C2×C4×C13#12011yescharacteristic
358C2×C4×C13C22×D411yescharacteristic
359C2×C4×C13C22×D411yescharacteristic
360C8×C13—42no—
361C8×C13—42no—
362#563—21no—
363#560—21no—
364#553—21no—
365#553—21no—
366#551—21no—
367#547—21no—
368#546—21no—
369#546—21no—
370#542—21no—
371#539—21no—
372#539C22×C1311yescharacteristic
373#538—21no—
374#538—21no—
375#538C22×C1311yescharacteristic
376#537C22×C1311yescharacteristic
377#534C22×C1311yescharacteristic
378#532C22×C1311yescharacteristic
379C2×C4⋊Q8C22×C1311yescharacteristic, complemented
380#529C22×C1311yescharacteristic
381C2×#126C22×C1311yescharacteristic
382#497—21no—
383#492—21no—
384#491—21no—
385#487—21no—
386#462—21no—
387#461—21no—
388#461—21no—
389#461—21no—
390#451C22×C1312yescomplemented
391#448C22×C1312yes—
392#448C22×C1312yes—
393#448C22×C1312yescomplemented
394#432C22×C1311yescharacteristic, complemented
395#431C22×C1311yescharacteristic, complemented
396#400—21no—
397#399—21no—
398#398—21no—
399#397—21no—
400#395C22×C1312yescomplemented
401#393C22×C1312yes—
402#383C22×C1311yescharacteristic, complemented
403#328C22×C1312yescomplemented
404#327C22×C1312yes—
405#327C22×C1312yes—
406#327C22×C1312yescomplemented
407#324C22×C1312yescomplemented
408#323C22×C1312yes—
409C22×C13—21no—
410C22×C13—21no—
411C22×C13—41no—
412C22×C13—41no—
413C22×C13—41no—
414C22×C13—41no—
415C22×C13—41no—
416C22×C13—41no—
417C22×C13—41no—
418C22×C13—41no—
419C22×C13—41no—
420C22×C13—41no—
421C22×C13—41no—
422C22×C13—41no—
423C22×C13—82no—
424C22×C13—162no—
425C22×C13C2×#12011yescharacteristic
426C22×C13#57712yes—
427C4×C13—21no—
428C4×C13—21no—
429C4×C13—21no—
430C4×C13—21no—
431C4×C13—21no—
432C4×C13—21no—
433C4×C13—41no—
434C4×C13—41no—
435C4×C13—41no—
436C4×C13—41no—
437C4×C13—41no—
438C4×C13—41no—
439C4×C13—41no—
440C4×C13—41no—
441C4×C13—82no—
442C4×C13—82no—
443C2×#41—21no—
444C2×#41—21no—
445C22×Q8C23×C1312yes—
446C22×D4—21no—
447C2×Q16—22no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—22no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8D4×C1311yescharacteristic
457#127D4×C1311yescharacteristic
458#126—21no—
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#126—21no—
465#126—21no—
466#126—21no—
467#125—21no—
468#125—21no—
469#125D4×C1311yescharacteristic
470#124—21no—
471#124—21no—
472#124—21no—
473#124—21no—
474#124D4×C1311yescharacteristic
475#123—21no—
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8C23×C1311yescharacteristic
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121C23×C1311yescharacteristic
508#121C23×C1311yescharacteristic
509#121C23×C1311yescharacteristic
510#120—21no—
511#120—21no—
512#120—21no—
513#120—21no—
514#120—21no—
515C4×Q8D4×C1311yescharacteristic
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4D4×C1311yescharacteristic
525C4×D4D4×C1311yescharacteristic
526C4×D4D4×C1311yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4D4×C1311yescharacteristic
534C2×C4⋊C4D4×C1311yescharacteristic
535C2×C4⋊C4C23×C1311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4D4×C1311yescharacteristic
540C2×C22⋊C4D4×C1311yescharacteristic
541C2×C22⋊C4C23×C1311yescharacteristic
542C2×C42C23×C1311yescharacteristic
543C4⋊C8—21no—
544C4⋊C8—21no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549C22⋊C8C23×C1312yes—
550C22⋊C8C23×C1312yes—
551#97—21no—
552C4×C8—21no—
553#95—21no—
554#95—21no—
555#95—22no—
556#95—22no—
557#95C23×C1312yes—
558C2×C13—22no—
559C2×C13—81no—
560C2×C13—81no—
561C2×C13—81no—
562C2×C13—81no—
563C2×C13#300911yescharacteristic
564C2×C13#302211yescharacteristic
565C2×C13#302711yescharacteristic
566C24—21no—
567C24C2×D4×C1311yescharacteristic
568#41—82no—
569#41—82no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—82no—
575C2×Q8C2×D4×C1311yescharacteristic
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—82no—
589C2×D4C2×D4×C1311yescharacteristic
590C2×D4C2×D4×C1311yescharacteristic
591C2×D4C2×D4×C1311yescharacteristic
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4C2×D4×C1311yescharacteristic
603C22×C4C2×D4×C1311yescharacteristic
604C22×C4C2×D4×C1311yescharacteristic
605C22×C4C2×D4×C1311yescharacteristic
606C22×C4C2×D4×C1311yescharacteristic
607C22×C4C24×C1311yescharacteristic
608Q16—82no—
609SD16—82no—
610SD16—82no—
611SD16—82no—
612C2×C8—22no—
613C2×C8—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—82no—
636C4⋊C4C2×D4×C1311yescharacteristic
637C4⋊C4C2×D4×C1311yescharacteristic
638C4⋊C4C2×D4×C1311yescharacteristic
639C4⋊C4C2×D4×C1311yescharacteristic
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—82no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42C2×D4×C1311yescharacteristic
670C42C2×D4×C1311yescharacteristic
671C42C2×D4×C1311yescharacteristic
672C42C2×D4×C1311yescharacteristic
673C13#1846311yescharacteristic, direct product factor, Sylow
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23C22×D4×C1311yescharacteristic
685Q8—41no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—81no—
691Q8—81no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—81no—
705D4—81no—
706D4—81no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4C13×#12011yescharacteristic
736C2×C4C13×#12011yescharacteristic
737C2×C4C13×#12011yescharacteristic
738C2×C4C13×#12011yescharacteristic
739C2×C4C22×D4×C1311yescharacteristic
740C2×C4C22×D4×C1311yescharacteristic
741C8—42no—
742C8—42no—
743C22—21no—
744C22—21no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—82no—
758C22—162no—
759C22C2×C13×#12011yescharacteristic
760C22C13×#57712yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—82no—
776C4—82no—
777C2—22no—
778C2—81no—
779C2—81no—
780C2—81no—
781C2—81no—
782C2C13×#300911yescharacteristic
783C2C13×#302211yescharacteristic
784C2C13×#302711yescharacteristic
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×#3218C2semidirect
3. C13×#3206C2semidirect
4. C13×#2821C2semidirect
5. C13×#1606C2semidirect
6. C13×#1604C2semidirect
7. C13×#1603C2semidirect
8. C13×#1601C2semidirect
9. C13×#1521C2semidirect
10. C13×#1514C2semidirect
11. C13×#1473C2semidirect
29. C2×C13×C4⋊Q8C22semidirect
40. C13×#451C22semidirect
43. C13×#448C22semidirect
44. C13×#432C22semidirect
45. C13×#431C22semidirect
50. C13×#395C22semidirect
52. C13×#383C22semidirect
53. C13×#328C22semidirect
56. C13×#327C22semidirect
57. C13×#324C22semidirect
174. #18463C13direct (N × H)
283. #3218C2×C13semidirect
284. #3206C2×C13semidirect
285. #2821C2×C13semidirect
286. #1606C2×C13semidirect
287. #1604C2×C13semidirect
288. #1603C2×C13semidirect
289. #1601C2×C13semidirect
290. #1521C2×C13semidirect
291. #1514C2×C13semidirect
292. #1473C2×C13semidirect
379. C2×C4⋊Q8C22×C13semidirect
390. #451C22×C13semidirect
393. #448C22×C13semidirect
394. #432C22×C13semidirect
395. #431C22×C13semidirect
400. #395C22×C13semidirect
402. #383C22×C13semidirect
403. #328C22×C13semidirect
406. #327C22×C13semidirect
407. #324C22×C13semidirect
673. C13#18463direct (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×#32182
C13×#32062
C13×#28212
C13×#16062
C13×#16042
C13×#16032
C13×#16012
C13×#15212
C13×#15142
C13×#14732
#1846313