Finite Group Databasebeta

← C13×#18464 #15704803

Subgroups — C13×#18464 #15704803

Order 3328.

970 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3564C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic, complemented
3C13×#3208C211yesmaximal, characteristic, complemented
4C13×#2818C211yesmaximal, characteristic, complemented
5C13×#1600C212yesmaximal, complemented
6C13×#1599C212yesmaximal, complemented
7C13×#1597C212yesmaximal, complemented
8C13×#1596C212yesmaximal, complemented
9C13×#1521C211yesmaximal, characteristic, complemented
10C13×#1515C211yesmaximal, characteristic, complemented
11C13×#1473C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#563—21no—
14C13×#556—21no—
15C13×#554—21no—
16C13×#552—21no—
17C13×#552—21no—
18C13×#551—21no—
19C13×#551—21no—
20C13×#544C2211yescharacteristic
21C13×#543C2211yescharacteristic
22C13×#542—21no—
23C13×#541—21no—
24C13×#541—21no—
25C13×#539—21no—
26C13×#539C2211yescharacteristic
27C13×#538C2211yescharacteristic
28C13×#533C2211yescharacteristic
29C2×C13×#127C2211yescharacteristic
30C13×#529C2211yescharacteristic
31C2×C13×#126C2211yescharacteristic
32C13×#496—21no—
33C13×#492—21no—
34C13×#490—21no—
35C13×#486—21no—
36C13×#460—21no—
37C13×#460—21no—
38C13×#460—21no—
39C13×#459—21no—
40C13×#450C2212yes—
41C13×#450C2212yes—
42C13×#450C2212yes—
43C13×#447C2212yes—
44C13×#432C2211yescharacteristic
45C13×#431C2211yescharacteristic
46C13×#394—21no—
47C13×#394—21no—
48C13×#394C2212yes—
49C13×#392—21no—
50C13×#392—21no—
51C13×#392C2212yes—
52C13×#383C2211yescharacteristic
53C13×#328C2212yes—
54C13×#328C2212yes—
55C13×#328C2212yes—
56C13×#327C2212yes—
57C13×#324C2212yes—
58C13×#323C2212yes—
59C22×D4×C13—22no—
60C22×D4×C13—21no—
61C22×D4×C13—21no—
62C22×D4×C13C2312yes—
63C2×C13×SD16—22no—
64C2×C13×SD16—22no—
65C2×C13×SD16—22no—
66C2×C13×D8—22no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—21no—
69C13×C4⋊Q8—21no—
70C13×C4⋊Q8D411yescharacteristic, complemented
71C13×C4⋊Q8D411yescharacteristic, complemented
72C13×#127—21no—
73C13×#127—21no—
74C13×#127—21no—
75C13×#127—21no—
76C13×#126—21no—
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×#126—21no—
87C13×#126—21no—
88C13×#126—21no—
89C13×#125—21no—
90C13×#125—21no—
91C13×#125—21no—
92C13×#125—21no—
93C13×#125—21no—
94C13×#125—21no—
95C13×#125—21no—
96C13×#125—21no—
97C13×#125—21no—
98C13×#125D411yescharacteristic, complemented
99C13×#124—21no—
100C13×#124—21no—
101C13×#124—21no—
102C13×#124D411yescharacteristic, complemented
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×C22⋊Q8—21no—
112C13×C22⋊Q8—21no—
113C13×C22⋊Q8—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⋊Q8—21no—
122C13×C22⋊Q8—21no—
123C13×C22⋊Q8—21no—
124C13×C22⋊Q8—21no—
125C13×C22⋊Q8C2311yescharacteristic
126C13×C22⋊Q8C2311yescharacteristic
127C13×C22⋊Q8C2311yescharacteristic
128C13×#121—21no—
129C13×#121C2311yescharacteristic
130C13×#120—21no—
131C4×Q8×C13—21no—
132C4×Q8×C13—21no—
133C4×Q8×C13—21no—
134C4×Q8×C13D411yescharacteristic, complemented
135C4×Q8×C13D411yescharacteristic, complemented
136C4×Q8×C13D411yescharacteristic, complemented
137C4×D4×C13—21no—
138C4×D4×C13—21no—
139C4×D4×C13—21no—
140C4×D4×C13—21no—
141C4×D4×C13—21no—
142C4×D4×C13D411yescharacteristic, complemented
143C13×#117—21no—
144C13×#117—21no—
145C13×#117—21no—
146C13×#117—21no—
147C13×#117—21no—
148C13×#117—21no—
149C2×C13×C4⋊C4—21no—
150C2×C13×C4⋊C4D411yescharacteristic
151C2×C13×C4⋊C4D411yescharacteristic
152C2×C13×C4⋊C4C2311yescharacteristic
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#18464C1311yesmaximal, characteristic, direct product factor, Sylow
175C24×C13—22no—
176C24×C13C2×D411yescharacteristic
177C2×Q8×C13—21no—
178C2×Q8×C13—21no—
179C2×Q8×C13—21no—
180C2×Q8×C13C2×D411yescharacteristic
181C2×Q8×C13C2×D411yescharacteristic
182C2×Q8×C13C2×D411yescharacteristic
183C2×D4×C13—21no—
184C2×D4×C13—21no—
185C2×D4×C13—21no—
186C2×D4×C13—22no—
187C2×D4×C13—22no—
188C2×D4×C13—41no—
189C2×D4×C13—41no—
190C2×D4×C13—41no—
191C2×D4×C13—41no—
192C2×D4×C13—82no—
193C2×D4×C13—82no—
194C2×D4×C13—82no—
195C2×D4×C13—82no—
196C2×D4×C13—82no—
197C2×D4×C13—82no—
198C2×D4×C13C2×D411yescharacteristic
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—22no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2411yescharacteristic
211C13×SD16—82no—
212C13×SD16—82no—
213C13×SD16—82no—
214C13×D8—82no—
215C2×C8×C13—22no—
216C2×C8×C13—22no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—21no—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—21no—
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—21no—
241C13×C4⋊C4—21no—
242C13×C4⋊C4—21no—
243C13×C4⋊C4—21no—
244C13×C4⋊C4—21no—
245C13×C4⋊C4—21no—
246C13×C4⋊C4C2×D411yescharacteristic
247C13×C4⋊C4C2×D411yescharacteristic
248C13×C4⋊C4C2×D411yescharacteristic
249C13×C4⋊C4C2×D411yescharacteristic
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—82no—
272C13×C22⋊C4—82no—
273C13×C22⋊C4—82no—
274C42×C13—21no—
275C42×C13—21no—
276C42×C13—21no—
277C42×C13—21no—
278C42×C13—21no—
279C42×C13—21no—
280C42×C13—21no—
281C42×C13C2×D411yescharacteristic
282C42×C13C2×D411yescharacteristic
283C42×C13C2×D411yescharacteristic
284C42×C13C2×D411yescharacteristic
285#3564C2×C1311yescharacteristic, complemented
286#3217C2×C1311yescharacteristic, complemented
287#3208C2×C1311yescharacteristic, complemented
288#2818C2×C1311yescharacteristic, complemented
289#1600C2×C1312yescomplemented
290#1599C2×C1312yescomplemented
291#1597C2×C1312yescomplemented
292#1596C2×C1312yescomplemented
293#1521C2×C1311yescharacteristic, complemented
294#1515C2×C1311yescharacteristic, complemented
295#1473C2×C1311yescharacteristic, complemented
296C23×C13—21no—
297C23×C13—21no—
298C23×C13—22no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—42no—
302C23×C13—42no—
303C23×C13—42no—
304C23×C13—42no—
305C23×C13—42no—
306C23×C13—42no—
307C23×C13—42no—
308C23×C13C22×D411yescharacteristic
309Q8×C13—41no—
310Q8×C13—41no—
311Q8×C13—41no—
312Q8×C13—81no—
313Q8×C13—81no—
314Q8×C13—81no—
315D4×C13—41no—
316D4×C13—42no—
317D4×C13—42no—
318D4×C13—42no—
319D4×C13—42no—
320D4×C13—42no—
321D4×C13—82no—
322D4×C13—82no—
323D4×C13—82no—
324D4×C13—82no—
325D4×C13—81no—
326D4×C13—81no—
327D4×C13—88no—
328C2×C4×C13—22no—
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—21no—
336C2×C4×C13—21no—
337C2×C4×C13—21no—
338C2×C4×C13—21no—
339C2×C4×C13—22no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—81no—
348C2×C4×C13—81no—
349C2×C4×C13—81no—
350C2×C4×C13—81no—
351C2×C4×C13—81no—
352C2×C4×C13#12011yescharacteristic
353C2×C4×C13#12011yescharacteristic
354C2×C4×C13#12011yescharacteristic
355C2×C4×C13#12011yescharacteristic
356C2×C4×C13C22×D411yescharacteristic
357C2×C4×C13C22×D411yescharacteristic
358C8×C13—42no—
359C8×C13—42no—
360#563—21no—
361#563—21no—
362#556—21no—
363#554—21no—
364#552—21no—
365#552—21no—
366#551—21no—
367#551—21no—
368#544C22×C1311yescharacteristic
369#543C22×C1311yescharacteristic
370#542—21no—
371#541—21no—
372#541—21no—
373#539—21no—
374#539C22×C1311yescharacteristic
375#538C22×C1311yescharacteristic
376#533C22×C1311yescharacteristic
377C2×#127C22×C1311yescharacteristic
378#529C22×C1311yescharacteristic
379C2×#126C22×C1311yescharacteristic
380#496—21no—
381#492—21no—
382#490—21no—
383#486—21no—
384#460—21no—
385#460—21no—
386#460—21no—
387#459—21no—
388#450C22×C1312yes—
389#450C22×C1312yes—
390#450C22×C1312yes—
391#447C22×C1312yes—
392#432C22×C1311yescharacteristic
393#431C22×C1311yescharacteristic
394#394—21no—
395#394—21no—
396#394C22×C1312yes—
397#392—21no—
398#392—21no—
399#392C22×C1312yes—
400#383C22×C1311yescharacteristic
401#328C22×C1312yes—
402#328C22×C1312yes—
403#328C22×C1312yes—
404#327C22×C1312yes—
405#324C22×C1312yes—
406#323C22×C1312yes—
407C22×C13—21no—
408C22×C13—21no—
409C22×C13—41no—
410C22×C13—41no—
411C22×C13—41no—
412C22×C13—41no—
413C22×C13—41no—
414C22×C13—41no—
415C22×C13—82no—
416C22×C13—82no—
417C22×C13—82no—
418C22×C13—82no—
419C22×C13—82no—
420C22×C13—82no—
421C22×C13—82no—
422C22×C13—82no—
423C22×C13C2×#12011yescharacteristic
424C22×C13#57712yes—
425C4×C13—21no—
426C4×C13—21no—
427C4×C13—21no—
428C4×C13—21no—
429C4×C13—21no—
430C4×C13—21no—
431C4×C13—41no—
432C4×C13—41no—
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—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C23×C1312yes—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—22no—
449C2×D8—22no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8D4×C1311yescharacteristic, complemented
454C4⋊Q8D4×C1311yescharacteristic, complemented
455#127—21no—
456#127—21no—
457#127—21no—
458#127—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#126—21no—
468#126—21no—
469#126—21no—
470#126—21no—
471#126—21no—
472#125—21no—
473#125—21no—
474#125—21no—
475#125—21no—
476#125—21no—
477#125—21no—
478#125—21no—
479#125—21no—
480#125—21no—
481#125D4×C1311yescharacteristic, complemented
482#124—21no—
483#124—21no—
484#124—21no—
485#124D4×C1311yescharacteristic, complemented
486#123—21no—
487#123—21no—
488#123—21no—
489#123—21no—
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8C23×C1311yescharacteristic
509C22⋊Q8C23×C1311yescharacteristic
510C22⋊Q8C23×C1311yescharacteristic
511#121—21no—
512#121C23×C1311yescharacteristic
513#120—21no—
514C4×Q8—21no—
515C4×Q8—21no—
516C4×Q8—21no—
517C4×Q8D4×C1311yescharacteristic, complemented
518C4×Q8D4×C1311yescharacteristic, complemented
519C4×Q8D4×C1311yescharacteristic, complemented
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C1311yescharacteristic, complemented
526#117—21no—
527#117—21no—
528#117—21no—
529#117—21no—
530#117—21no—
531#117—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4D4×C1311yescharacteristic
534C2×C4⋊C4D4×C1311yescharacteristic
535C2×C4⋊C4C23×C1311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4D4×C1311yescharacteristic
541C2×C22⋊C4D4×C1311yescharacteristic
542C2×C22⋊C4C23×C1311yescharacteristic
543C2×C42C23×C1311yescharacteristic
544C4⋊C8—21no—
545C4⋊C8—21no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550C22⋊C8C23×C1312yes—
551C22⋊C8C23×C1312yes—
552#97—21no—
553C4×C8—21no—
554#95—21no—
555#95—21no—
556#95C23×C1312yes—
557C2×C13—22no—
558C2×C13—81no—
559C2×C13—81no—
560C2×C13—162no—
561C2×C13#301011yescharacteristic
562C2×C13#302111yescharacteristic
563C2×C13#302711yescharacteristic
564C24—22no—
565C24C2×D4×C1311yescharacteristic
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8C2×D4×C1311yescharacteristic
570C2×Q8C2×D4×C1311yescharacteristic
571C2×Q8C2×D4×C1311yescharacteristic
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—82no—
582C2×D4—82no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4C2×D4×C1311yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4C2×D4×C1311yescharacteristic
595C22×C4C2×D4×C1311yescharacteristic
596C22×C4C2×D4×C1311yescharacteristic
597C22×C4C2×D4×C1311yescharacteristic
598C22×C4C2×D4×C1311yescharacteristic
599C22×C4C24×C1311yescharacteristic
600SD16—82no—
601SD16—82no—
602SD16—82no—
603D8—82no—
604C2×C8—22no—
605C2×C8—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
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—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4C2×D4×C1311yescharacteristic
636C4⋊C4C2×D4×C1311yescharacteristic
637C4⋊C4C2×D4×C1311yescharacteristic
638C4⋊C4C2×D4×C1311yescharacteristic
639C22⋊C4—21no—
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—82no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42C2×D4×C1311yescharacteristic
671C42C2×D4×C1311yescharacteristic
672C42C2×D4×C1311yescharacteristic
673C42C2×D4×C1311yescharacteristic
674C13#1846411yescharacteristic, direct product factor, Sylow
675C23—21no—
676C23—21no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23C22×D4×C1311yescharacteristic
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694D4—41no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—81no—
705D4—81no—
706D4—88no—
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—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4C13×#12011yescharacteristic
732C2×C4C13×#12011yescharacteristic
733C2×C4C13×#12011yescharacteristic
734C2×C4C13×#12011yescharacteristic
735C2×C4C22×D4×C1311yescharacteristic
736C2×C4C22×D4×C1311yescharacteristic
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22C2×C13×#12011yescharacteristic
756C22C13×#57712yes—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—82no—
774C2—22no—
775C2—81no—
776C2—81no—
777C2—162no—
778C2C13×#301011yescharacteristic
779C2C13×#302111yescharacteristic
780C2C13×#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×#3564C2semidirect
2. C13×#3217C2semidirect
3. C13×#3208C2semidirect
4. C13×#2818C2semidirect
5. C13×#1600C2semidirect
6. C13×#1599C2semidirect
7. C13×#1597C2semidirect
8. C13×#1596C2semidirect
9. C13×#1521C2semidirect
10. C13×#1515C2semidirect
11. C13×#1473C2semidirect
70. C13×C4⋊Q8D4semidirect
71. C13×C4⋊Q8D4semidirect
98. C13×#125D4semidirect
102. C13×#124D4semidirect
134. C4×Q8×C13D4semidirect
135. C4×Q8×C13D4semidirect
136. C4×Q8×C13D4semidirect
142. C4×D4×C13D4semidirect
174. #18464C13direct (N × H)
285. #3564C2×C13semidirect
286. #3217C2×C13semidirect
287. #3208C2×C13semidirect
288. #2818C2×C13semidirect
289. #1600C2×C13semidirect
290. #1599C2×C13semidirect
291. #1597C2×C13semidirect
292. #1596C2×C13semidirect
293. #1521C2×C13semidirect
294. #1515C2×C13semidirect
295. #1473C2×C13semidirect
453. C4⋊Q8D4×C13semidirect
454. C4⋊Q8D4×C13semidirect
481. #125D4×C13semidirect
485. #124D4×C13semidirect
517. C4×Q8D4×C13semidirect
518. C4×Q8D4×C13semidirect
519. C4×Q8D4×C13semidirect
525. C4×D4D4×C13semidirect
674. C13#18464direct (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×#32172
C13×#32082
C13×#28182
C13×#16002
C13×#15992
C13×#15972
C13×#15962
C13×#15212
C13×#15152
C13×#14732
#1846413