Finite Group Databasebeta

← C13×#18462 #15704801

Subgroups — C13×#18462 #15704801

Order 3328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3560C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic, complemented
3C13×#3205C211yesmaximal, characteristic, complemented
4C13×#2818C211yesmaximal, characteristic, complemented
5C13×#1600C212yesmaximal, complemented
6C13×#1598C212yesmaximal, complemented
7C13×#1597C212yesmaximal, complemented
8C13×#1595C212yesmaximal, 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×#127C2211yescharacteristic, complemented
30C13×#529C2211yescharacteristic
31C2×C13×#126C2211yescharacteristic
32C13×#496—21no—
33C13×#493—21no—
34C13×#490—21no—
35C13×#486—21no—
36C13×#460—21no—
37C13×#459—21no—
38C13×#459—21no—
39C13×#459—21no—
40C13×#450C2212yescomplemented
41C13×#447C2212yes—
42C13×#447C2212yes—
43C13×#447C2212yescomplemented
44C13×#432C2211yescharacteristic, complemented
45C13×#431C2211yescharacteristic, complemented
46C13×#394—21no—
47C13×#394—21no—
48C13×#394C2212yescomplemented
49C13×#392—21no—
50C13×#392—21no—
51C13×#392C2212yes—
52C13×#383C2211yescharacteristic, complemented
53C13×#328C2212yescomplemented
54C13×#327C2212yes—
55C13×#327C2212yes—
56C13×#327C2212yescomplemented
57C13×#324C2212yescomplemented
58C13×#323C2212yes—
59C2×C13×#41—21no—
60C2×C13×#41—21no—
61C22×D4×C13—21no—
62C22×D4×C13—22no—
63C22×D4×C13—21no—
64C22×D4×C13—21no—
65C22×D4×C13C2312yes—
66C2×C13×SD16—22no—
67C2×C13×D8—22no—
68C2×C13×D8—22no—
69C2×C13×D8—22no—
70C13×C4⋊Q8—21no—
71C13×C4⋊Q8D411yescharacteristic, complemented
72C13×#127—21no—
73C13×#127—21no—
74C13×#127—21no—
75C13×#127—21no—
76C13×#127D411yescharacteristic, complemented
77C13×#126—21no—
78C13×#126—21no—
79C13×#126—21no—
80C13×#126—21no—
81C13×#126—21no—
82C13×#126—21no—
83C13×#126—21no—
84C13×#126—21no—
85C13×#126—21no—
86C13×#125—21no—
87C13×#125—21no—
88C13×#125D411yescharacteristic, complemented
89C13×#124—21no—
90C13×#124—21no—
91C13×#124—21no—
92C13×#124—21no—
93C13×#124D411yescharacteristic, complemented
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×#123—21no—
104C13×#123—21no—
105C13×#123—21no—
106C13×C22⋊Q8—21no—
107C13×C22⋊Q8—21no—
108C13×C22⋊Q8—21no—
109C13×C22⋊Q8—21no—
110C13×C22⋊Q8—21no—
111C13×C22⋊Q8—21no—
112C13×C22⋊Q8—21no—
113C13×C22⋊Q8C2311yescharacteristic
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×#121—21no—
124C13×#121—21no—
125C13×#121—21no—
126C13×#121C2311yescharacteristic
127C13×#121C2311yescharacteristic
128C13×#121C2311yescharacteristic
129C13×#120—21no—
130C13×#120—21no—
131C13×#120—21no—
132C13×#120—21no—
133C13×#120—21no—
134C4×Q8×C13D411yescharacteristic, complemented
135C4×D4×C13—21no—
136C4×D4×C13—21no—
137C4×D4×C13—21no—
138C4×D4×C13—21no—
139C4×D4×C13—21no—
140C4×D4×C13—21no—
141C4×D4×C13—21no—
142C4×D4×C13—21no—
143C4×D4×C13D411yescharacteristic, complemented
144C4×D4×C13D411yescharacteristic, complemented
145C4×D4×C13D411yescharacteristic, complemented
146C13×#117—21no—
147C13×#117—21no—
148C2×C13×C4⋊C4—21no—
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⋊C4—22no—
156C2×C13×C22⋊C4—22no—
157C2×C13×C22⋊C4D411yescharacteristic
158C2×C13×C22⋊C4D411yescharacteristic
159C2×C13×C22⋊C4C2311yescharacteristic
160C2×C42×C13C2311yescharacteristic
161C13×C4⋊C8—21no—
162C13×C4⋊C8—21no—
163C13×#102—22no—
164C13×#102—22no—
165C13×#102—22no—
166C13×#102—22no—
167C13×C22⋊C8C2312yes—
168C13×C22⋊C8C2312yes—
169C13×#97—21no—
170C4×C8×C13—21no—
171C13×#95—21no—
172C13×#95—21no—
173C13×#95C2312yes—
174#18462C1311yesmaximal, characteristic, direct product factor, Sylow
175C24×C13—21no—
176C24×C13—22no—
177C24×C13C2×D411yescharacteristic
178C13×#41—82no—
179C13×#41—82no—
180C2×Q8×C13—21no—
181C2×Q8×C13—21no—
182C2×Q8×C13C2×D411yescharacteristic
183C2×D4×C13—21no—
184C2×D4×C13—21no—
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—22no—
196C2×D4×C13—22no—
197C2×D4×C13—41no—
198C2×D4×C13—41no—
199C2×D4×C13—41no—
200C2×D4×C13—41no—
201C2×D4×C13—82no—
202C2×D4×C13—82no—
203C2×D4×C13—82no—
204C2×D4×C13—82no—
205C2×D4×C13—82no—
206C2×D4×C13—82no—
207C2×D4×C13—82no—
208C2×D4×C13C2×D411yescharacteristic
209C2×D4×C13C2×D411yescharacteristic
210C2×D4×C13C2×D411yescharacteristic
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—22no—
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13C2×D411yescharacteristic
225C22×C4×C13C2411yescharacteristic
226C13×SD16—82no—
227C13×D8—82no—
228C13×D8—82no—
229C13×D8—82no—
230C2×C8×C13—22no—
231C2×C8×C13—22no—
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—21no—
241C13×C4⋊C4—21no—
242C13×C4⋊C4—21no—
243C13×C4⋊C4—21no—
244C13×C4⋊C4—21no—
245C13×C4⋊C4—21no—
246C13×C4⋊C4—21no—
247C13×C4⋊C4—21no—
248C13×C4⋊C4—21no—
249C13×C4⋊C4C2×D411yescharacteristic
250C13×C4⋊C4C2×D411yescharacteristic
251C13×C4⋊C4C2×D411yescharacteristic
252C13×C4⋊C4C2×D411yescharacteristic
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—21no—
275C13×C22⋊C4—21no—
276C13×C22⋊C4—21no—
277C13×C22⋊C4—21no—
278C13×C22⋊C4—82no—
279C13×C22⋊C4—82no—
280C13×C22⋊C4—82no—
281C42×C13—21no—
282C42×C13—21no—
283C42×C13—21no—
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2×D411yescharacteristic
287C42×C13C2×D411yescharacteristic
288#3560C2×C1311yescharacteristic, complemented
289#3217C2×C1311yescharacteristic, complemented
290#3205C2×C1311yescharacteristic, complemented
291#2818C2×C1311yescharacteristic, complemented
292#1600C2×C1312yescomplemented
293#1598C2×C1312yescomplemented
294#1597C2×C1312yescomplemented
295#1595C2×C1312yescomplemented
296#1521C2×C1311yescharacteristic, complemented
297#1514C2×C1311yescharacteristic, complemented
298#1473C2×C1311yescharacteristic, complemented
299C23×C13—21no—
300C23×C13—21no—
301C23×C13—21no—
302C23×C13—21no—
303C23×C13—22no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—42no—
307C23×C13—42no—
308C23×C13—42no—
309C23×C13—42no—
310C23×C13—42no—
311C23×C13—42no—
312C23×C13—42no—
313C23×C13—81no—
314C23×C13—81no—
315C23×C13—81no—
316C23×C13C22×D411yescharacteristic
317Q8×C13—41no—
318Q8×C13—81no—
319Q8×C13—81no—
320D4×C13—41no—
321D4×C13—41no—
322D4×C13—41no—
323D4×C13—42no—
324D4×C13—42no—
325D4×C13—42no—
326D4×C13—42no—
327D4×C13—42no—
328D4×C13—42no—
329D4×C13—42no—
330D4×C13—81no—
331D4×C13—81no—
332D4×C13—82no—
333D4×C13—82no—
334D4×C13—82no—
335D4×C13—82no—
336D4×C13—81no—
337D4×C13—81no—
338D4×C13—81no—
339D4×C13—81no—
340D4×C13—81no—
341D4×C13—81no—
342D4×C13—81no—
343D4×C13—88no—
344C2×C4×C13—22no—
345C2×C4×C13—21no—
346C2×C4×C13—21no—
347C2×C4×C13—21no—
348C2×C4×C13—21no—
349C2×C4×C13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
352C2×C4×C13—21no—
353C2×C4×C13—22no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—42no—
359C2×C4×C13—42no—
360C2×C4×C13—42no—
361C2×C4×C13—81no—
362C2×C4×C13—81no—
363C2×C4×C13—81no—
364C2×C4×C13—81no—
365C2×C4×C13—81no—
366C2×C4×C13—81no—
367C2×C4×C13—81no—
368C2×C4×C13—81no—
369C2×C4×C13#12011yescharacteristic
370C2×C4×C13#12011yescharacteristic
371C2×C4×C13#12011yescharacteristic
372C2×C4×C13#12011yescharacteristic
373C2×C4×C13C22×D411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C8×C13—42no—
376C8×C13—42no—
377#563—21no—
378#560—21no—
379#553—21no—
380#553—21no—
381#551—21no—
382#547—21no—
383#546—21no—
384#546—21no—
385#542—21no—
386#539—21no—
387#539C22×C1311yescharacteristic
388#538—21no—
389#538—21no—
390#538C22×C1311yescharacteristic
391#537C22×C1311yescharacteristic
392#534C22×C1311yescharacteristic
393#532C22×C1311yescharacteristic
394C2×#127C22×C1311yescharacteristic, complemented
395#529C22×C1311yescharacteristic
396C2×#126C22×C1311yescharacteristic
397#496—21no—
398#493—21no—
399#490—21no—
400#486—21no—
401#460—21no—
402#459—21no—
403#459—21no—
404#459—21no—
405#450C22×C1312yescomplemented
406#447C22×C1312yes—
407#447C22×C1312yes—
408#447C22×C1312yescomplemented
409#432C22×C1311yescharacteristic, complemented
410#431C22×C1311yescharacteristic, complemented
411#394—21no—
412#394—21no—
413#394C22×C1312yescomplemented
414#392—21no—
415#392—21no—
416#392C22×C1312yes—
417#383C22×C1311yescharacteristic, complemented
418#328C22×C1312yescomplemented
419#327C22×C1312yes—
420#327C22×C1312yes—
421#327C22×C1312yescomplemented
422#324C22×C1312yescomplemented
423#323C22×C1312yes—
424C22×C13—21no—
425C22×C13—21no—
426C22×C13—41no—
427C22×C13—41no—
428C22×C13—41no—
429C22×C13—41no—
430C22×C13—41no—
431C22×C13—41no—
432C22×C13—41no—
433C22×C13—41no—
434C22×C13—41no—
435C22×C13—41no—
436C22×C13—41no—
437C22×C13—41no—
438C22×C13—82no—
439C22×C13—82no—
440C22×C13—82no—
441C22×C13—82no—
442C22×C13—82no—
443C22×C13—82no—
444C22×C13—82no—
445C22×C13—82no—
446C22×C13—162no—
447C22×C13C2×#12011yescharacteristic
448C22×C13#57612yes—
449C4×C13—21no—
450C4×C13—21no—
451C4×C13—21no—
452C4×C13—21no—
453C4×C13—21no—
454C4×C13—21no—
455C4×C13—41no—
456C4×C13—41no—
457C4×C13—41no—
458C4×C13—41no—
459C4×C13—41no—
460C4×C13—41no—
461C4×C13—41no—
462C4×C13—41no—
463C4×C13—82no—
464C2×#41—21no—
465C2×#41—21no—
466C22×D4—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4C23×C1312yes—
471C2×SD16—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C4⋊Q8—21no—
476C4⋊Q8D4×C1311yescharacteristic, complemented
477#127—21no—
478#127—21no—
479#127—21no—
480#127—21no—
481#127D4×C1311yescharacteristic, complemented
482#126—21no—
483#126—21no—
484#126—21no—
485#126—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#126—21no—
490#126—21no—
491#125—21no—
492#125—21no—
493#125D4×C1311yescharacteristic, complemented
494#124—21no—
495#124—21no—
496#124—21no—
497#124—21no—
498#124D4×C1311yescharacteristic, complemented
499#123—21no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—21no—
505#123—21no—
506#123—21no—
507#123—21no—
508#123—21no—
509#123—21no—
510#123—21no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8C23×C1311yescharacteristic
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121C23×C1311yescharacteristic
532#121C23×C1311yescharacteristic
533#121C23×C1311yescharacteristic
534#120—21no—
535#120—21no—
536#120—21no—
537#120—21no—
538#120—21no—
539C4×Q8D4×C1311yescharacteristic, complemented
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C1311yescharacteristic, complemented
549C4×D4D4×C1311yescharacteristic, complemented
550C4×D4D4×C1311yescharacteristic, complemented
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4D4×C1311yescharacteristic
555C2×C4⋊C4D4×C1311yescharacteristic
556C2×C4⋊C4C23×C1311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4D4×C1311yescharacteristic
563C2×C22⋊C4D4×C1311yescharacteristic
564C2×C22⋊C4C23×C1311yescharacteristic
565C2×C42C23×C1311yescharacteristic
566C4⋊C8—21no—
567C4⋊C8—21no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572C22⋊C8C23×C1312yes—
573C22⋊C8C23×C1312yes—
574#97—21no—
575C4×C8—21no—
576#95—21no—
577#95—21no—
578#95C23×C1312yes—
579C2×C13—22no—
580C2×C13—81no—
581C2×C13—81no—
582C2×C13—81no—
583C2×C13—81no—
584C2×C13—162no—
585C2×C13#300811yescharacteristic
586C2×C13#302111yescharacteristic
587C2×C13#302711yescharacteristic
588C24—21no—
589C24—22no—
590C24C2×D4×C1311yescharacteristic
591#41—82no—
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C1311yescharacteristic
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—82no—
615C2×D4—82no—
616C2×D4—82no—
617C2×D4—82no—
618C2×D4—82no—
619C2×D4—82no—
620C2×D4—82no—
621C2×D4C2×D4×C1311yescharacteristic
622C2×D4C2×D4×C1311yescharacteristic
623C2×D4C2×D4×C1311yescharacteristic
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4C2×D4×C1311yescharacteristic
634C22×C4C2×D4×C1311yescharacteristic
635C22×C4C2×D4×C1311yescharacteristic
636C22×C4C2×D4×C1311yescharacteristic
637C22×C4C2×D4×C1311yescharacteristic
638C22×C4C24×C1311yescharacteristic
639SD16—82no—
640D8—82no—
641D8—82no—
642D8—82no—
643C2×C8—22no—
644C2×C8—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4C2×D4×C1311yescharacteristic
663C4⋊C4C2×D4×C1311yescharacteristic
664C4⋊C4C2×D4×C1311yescharacteristic
665C4⋊C4C2×D4×C1311yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
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—21no—
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⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42C2×D4×C1311yescharacteristic
698C42C2×D4×C1311yescharacteristic
699C42C2×D4×C1311yescharacteristic
700C42C2×D4×C1311yescharacteristic
701C13#1846211yescharacteristic, direct product factor, Sylow
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23C22×D4×C1311yescharacteristic
720Q8—41no—
721Q8—81no—
722Q8—81no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—81no—
734D4—81no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—88no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4C13×#12011yescharacteristic
773C2×C4C13×#12011yescharacteristic
774C2×C4C13×#12011yescharacteristic
775C2×C4C13×#12011yescharacteristic
776C2×C4C22×D4×C1311yescharacteristic
777C2×C4C22×D4×C1311yescharacteristic
778C8—42no—
779C8—42no—
780C22—21no—
781C22—21no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—162no—
803C22C2×C13×#12011yescharacteristic
804C22C13×#57612yes—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—82no—
820C2—22no—
821C2—81no—
822C2—81no—
823C2—81no—
824C2—81no—
825C2—162no—
826C2C13×#300811yescharacteristic
827C2C13×#302111yescharacteristic
828C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
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×#3560C2semidirect
2. C13×#3217C2semidirect
3. C13×#3205C2semidirect
4. C13×#2818C2semidirect
5. C13×#1600C2semidirect
6. C13×#1598C2semidirect
7. C13×#1597C2semidirect
8. C13×#1595C2semidirect
9. C13×#1521C2semidirect
10. C13×#1514C2semidirect
11. C13×#1473C2semidirect
29. C2×C13×#127C22semidirect
40. C13×#450C22semidirect
43. C13×#447C22semidirect
44. C13×#432C22semidirect
45. C13×#431C22semidirect
48. C13×#394C22semidirect
52. C13×#383C22semidirect
53. C13×#328C22semidirect
56. C13×#327C22semidirect
57. C13×#324C22semidirect
71. C13×C4⋊Q8D4semidirect
76. C13×#127D4semidirect
88. C13×#125D4semidirect
93. C13×#124D4semidirect
134. C4×Q8×C13D4semidirect
143. C4×D4×C13D4semidirect
144. C4×D4×C13D4semidirect
145. C4×D4×C13D4semidirect
174. #18462C13direct (N × H)
288. #3560C2×C13semidirect
289. #3217C2×C13semidirect
290. #3205C2×C13semidirect
291. #2818C2×C13semidirect
292. #1600C2×C13semidirect
293. #1598C2×C13semidirect
294. #1597C2×C13semidirect
295. #1595C2×C13semidirect
296. #1521C2×C13semidirect
297. #1514C2×C13semidirect
298. #1473C2×C13semidirect
394. C2×#127C22×C13semidirect
405. #450C22×C13semidirect
408. #447C22×C13semidirect
409. #432C22×C13semidirect
410. #431C22×C13semidirect
413. #394C22×C13semidirect
417. #383C22×C13semidirect
418. #328C22×C13semidirect
421. #327C22×C13semidirect
422. #324C22×C13semidirect
476. C4⋊Q8D4×C13semidirect
481. #127D4×C13semidirect
493. #125D4×C13semidirect
498. #124D4×C13semidirect
539. C4×Q8D4×C13semidirect
548. C4×D4D4×C13semidirect
549. C4×D4D4×C13semidirect
550. C4×D4D4×C13semidirect
701. C13#18462direct (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×#32172
C13×#32052
C13×#28182
C13×#16002
C13×#15982
C13×#15972
C13×#15952
C13×#15212
C13×#15142
C13×#14732
#1846213