Finite Group Databasebeta

← C13×#18470 #15704809

Subgroups — C13×#18470 #15704809

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3560C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic, complemented
3C13×#3226C211yesmaximal, characteristic, complemented
4C13×#2821C211yesmaximal, characteristic, complemented
5C13×#1612C212yesmaximal, complemented
6C13×#1610C212yesmaximal, complemented
7C13×#1609C212yesmaximal, complemented
8C13×#1607C212yesmaximal, 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×#501—21no—
33C13×#500—21no—
34C13×#489—21no—
35C13×#486—21no—
36C13×#483C2212yescomplemented
37C13×#480C2212yes—
38C13×#480C2212yes—
39C13×#480C2212yescomplemented
40C13×#477—21no—
41C13×#476—21no—
42C13×#474—21no—
43C13×#474—21no—
44C13×#432C2211yescharacteristic, complemented
45C13×#431C2211yescharacteristic, complemented
46C13×#400—21no—
47C13×#399—21no—
48C13×#398C2212yescomplemented
49C13×#397C2212yes—
50C13×#395—21no—
51C13×#393—21no—
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×C13—21no—
62C22×D4×C13—21no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8D411yescharacteristic
69C13×#127D411yescharacteristic
70C13×#126—21no—
71C13×#126—21no—
72C13×#126—21no—
73C13×#126—21no—
74C13×#126—21no—
75C13×#126—21no—
76C13×#126—21no—
77C13×#126—21no—
78C13×#126—21no—
79C13×#125—21no—
80C13×#125—21no—
81C13×#125D411yescharacteristic
82C13×#124—21no—
83C13×#124—21no—
84C13×#124—21no—
85C13×#124—21no—
86C13×#124D411yescharacteristic
87C13×#123—21no—
88C13×#123—21no—
89C13×#123—21no—
90C13×#123—21no—
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×C22⋊Q8—21no—
100C13×C22⋊Q8—21no—
101C13×C22⋊Q8—21no—
102C13×C22⋊Q8—21no—
103C13×C22⋊Q8—21no—
104C13×C22⋊Q8—21no—
105C13×C22⋊Q8—21no—
106C13×C22⋊Q8C2311yescharacteristic
107C13×#121—21no—
108C13×#121—21no—
109C13×#121—21no—
110C13×#121—21no—
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×#121C2311yescharacteristic
120C13×#121C2311yescharacteristic
121C13×#121C2311yescharacteristic
122C13×#120—21no—
123C13×#120—21no—
124C13×#120—21no—
125C13×#120—21no—
126C13×#120—21no—
127C4×Q8×C13D411yescharacteristic
128C4×D4×C13—21no—
129C4×D4×C13—21no—
130C4×D4×C13—21no—
131C4×D4×C13—21no—
132C4×D4×C13—21no—
133C4×D4×C13—21no—
134C4×D4×C13—21no—
135C4×D4×C13—21no—
136C4×D4×C13D411yescharacteristic
137C4×D4×C13D411yescharacteristic
138C4×D4×C13D411yescharacteristic
139C13×#117—21no—
140C13×#117—21no—
141C2×C13×C4⋊C4—21no—
142C2×C13×C4⋊C4—21no—
143C2×C13×C4⋊C4—22no—
144C2×C13×C4⋊C4D411yescharacteristic
145C2×C13×C4⋊C4D411yescharacteristic
146C2×C13×C4⋊C4C2312yes—
147C2×C13×C4⋊C4C2311yescharacteristic
148C2×C13×C22⋊C4—21no—
149C2×C13×C22⋊C4—21no—
150C2×C13×C22⋊C4—22no—
151C2×C13×C22⋊C4D411yescharacteristic
152C2×C13×C22⋊C4D411yescharacteristic
153C2×C13×C22⋊C4C2311yescharacteristic
154C2×C42×C13C2311yescharacteristic
155C13×#107—22no—
156C13×#107—22no—
157C13×#107—22no—
158C13×#106—22no—
159C13×C4⋊C8—21no—
160C13×C4⋊C8—21no—
161C13×#103—22no—
162C13×#102—22no—
163C13×#102—22no—
164C13×#102—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#18470C1311yesmaximal, 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—41no—
182C2×Q8×C13—41no—
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
217C2×C8×C13—22no—
218C2×C8×C13—22no—
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—22no—
237C13×C4⋊C4—22no—
238C13×C4⋊C4—41no—
239C13×C4⋊C4—41no—
240C13×C4⋊C4—82no—
241C13×C4⋊C4C2×D411yescharacteristic
242C13×C4⋊C4C2×D411yescharacteristic
243C13×C4⋊C4C2×D411yescharacteristic
244C13×C4⋊C4C2×D411yescharacteristic
245C13×C22⋊C4—21no—
246C13×C22⋊C4—21no—
247C13×C22⋊C4—21no—
248C13×C22⋊C4—21no—
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—82no—
271C42×C13—21no—
272C42×C13—21no—
273C42×C13—21no—
274C42×C13C2×D411yescharacteristic
275C42×C13C2×D411yescharacteristic
276C42×C13C2×D411yescharacteristic
277C42×C13C2×D411yescharacteristic
278#3560C2×C1311yescharacteristic
279#3238C2×C1311yescharacteristic, complemented
280#3226C2×C1311yescharacteristic, complemented
281#2821C2×C1311yescharacteristic, complemented
282#1612C2×C1312yescomplemented
283#1610C2×C1312yescomplemented
284#1609C2×C1312yescomplemented
285#1607C2×C1312yescomplemented
286#1521C2×C1311yescharacteristic, complemented
287#1514C2×C1311yescharacteristic, complemented
288#1473C2×C1311yescharacteristic, complemented
289C23×C13—21no—
290C23×C13—21no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—22no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—81no—
297C23×C13—81no—
298C23×C13—81no—
299C23×C13C22×D411yescharacteristic
300Q8×C13—41no—
301Q8×C13—81no—
302Q8×C13—82no—
303Q8×C13—82no—
304Q8×C13—81no—
305D4×C13—41no—
306D4×C13—41no—
307D4×C13—41no—
308D4×C13—42no—
309D4×C13—42no—
310D4×C13—42no—
311D4×C13—81no—
312D4×C13—81no—
313D4×C13—81no—
314D4×C13—81no—
315D4×C13—81no—
316D4×C13—81no—
317D4×C13—81no—
318D4×C13—81no—
319D4×C13—81no—
320C2×C4×C13—22no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—21no—
324C2×C4×C13—21no—
325C2×C4×C13—21no—
326C2×C4×C13—21no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—22no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—42no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—42no—
340C2×C4×C13—81no—
341C2×C4×C13—81no—
342C2×C4×C13—81no—
343C2×C4×C13—81no—
344C2×C4×C13—81no—
345C2×C4×C13—81no—
346C2×C4×C13—81no—
347C2×C4×C13—81no—
348C2×C4×C13#12011yescharacteristic
349C2×C4×C13#12011yescharacteristic
350C2×C4×C13#12011yescharacteristic
351C2×C4×C13#12011yescharacteristic
352C2×C4×C13C22×D411yescharacteristic
353C2×C4×C13C22×D411yescharacteristic
354C8×C13—42no—
355C8×C13—42no—
356#563—21no—
357#560—21no—
358#553—21no—
359#553—21no—
360#551—21no—
361#547—21no—
362#546—21no—
363#546—21no—
364#542—21no—
365#539—21no—
366#539C22×C1311yescharacteristic
367#538—21no—
368#538—21no—
369#538C22×C1311yescharacteristic
370#537C22×C1311yescharacteristic
371#534C22×C1311yescharacteristic
372#532C22×C1311yescharacteristic
373C2×C4⋊Q8C22×C1311yescharacteristic, complemented
374#529C22×C1311yescharacteristic
375C2×#126C22×C1311yescharacteristic
376#501—21no—
377#500—21no—
378#489—21no—
379#486—21no—
380#483C22×C1312yescomplemented
381#480C22×C1312yes—
382#480C22×C1312yes—
383#480C22×C1312yescomplemented
384#477—21no—
385#476—21no—
386#474—21no—
387#474—21no—
388#432C22×C1311yescharacteristic, complemented
389#431C22×C1311yescharacteristic, complemented
390#400—21no—
391#399—21no—
392#398C22×C1312yescomplemented
393#397C22×C1312yes—
394#395—21no—
395#393—21no—
396#383C22×C1311yescharacteristic, complemented
397#328C22×C1312yescomplemented
398#327C22×C1312yes—
399#327C22×C1312yes—
400#327C22×C1312yescomplemented
401#324C22×C1312yescomplemented
402#323C22×C1312yes—
403C22×C13—21no—
404C22×C13—21no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13—41no—
410C22×C13—41no—
411C22×C13—41no—
412C22×C13—41no—
413C22×C13—41no—
414C22×C13—41no—
415C22×C13—41no—
416C22×C13—41no—
417C22×C13—82no—
418C22×C13—162no—
419C22×C13C2×#12011yescharacteristic
420C22×C13#57612yes—
421C4×C13—21no—
422C4×C13—21no—
423C4×C13—21no—
424C4×C13—21no—
425C4×C13—21no—
426C4×C13—21no—
427C4×C13—41no—
428C4×C13—41no—
429C4×C13—41no—
430C4×C13—41no—
431C4×C13—41no—
432C4×C13—41no—
433C4×C13—41no—
434C4×C13—41no—
435C4×C13—82no—
436C4×C13—82no—
437C2×#41—21no—
438C2×#41—21no—
439C22×Q8—21no—
440C22×D4—21no—
441C4⋊Q8—21no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8D4×C1311yescharacteristic
447#127D4×C1311yescharacteristic
448#126—21no—
449#126—21no—
450#126—21no—
451#126—21no—
452#126—21no—
453#126—21no—
454#126—21no—
455#126—21no—
456#126—21no—
457#125—21no—
458#125—21no—
459#125D4×C1311yescharacteristic
460#124—21no—
461#124—21no—
462#124—21no—
463#124—21no—
464#124D4×C1311yescharacteristic
465#123—21no—
466#123—21no—
467#123—21no—
468#123—21no—
469#123—21no—
470#123—21no—
471#123—21no—
472#123—21no—
473#123—21no—
474#123—21no—
475#123—21no—
476#123—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8C23×C1311yescharacteristic
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121C23×C1311yescharacteristic
498#121C23×C1311yescharacteristic
499#121C23×C1311yescharacteristic
500#120—21no—
501#120—21no—
502#120—21no—
503#120—21no—
504#120—21no—
505C4×Q8D4×C1311yescharacteristic
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4D4×C1311yescharacteristic
515C4×D4D4×C1311yescharacteristic
516C4×D4D4×C1311yescharacteristic
517#117—21no—
518#117—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4D4×C1311yescharacteristic
523C2×C4⋊C4D4×C1311yescharacteristic
524C2×C4⋊C4C23×C1312yes—
525C2×C4⋊C4C23×C1311yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4D4×C1311yescharacteristic
530C2×C22⋊C4D4×C1311yescharacteristic
531C2×C22⋊C4C23×C1311yescharacteristic
532C2×C42C23×C1311yescharacteristic
533#107—22no—
534#107—22no—
535#107—22no—
536#106—22no—
537C4⋊C8—21no—
538C4⋊C8—21no—
539#103—22no—
540#102—22no—
541#102—22no—
542#102—22no—
543C22⋊C8C23×C1312yes—
544C22⋊C8C23×C1312yes—
545#97—21no—
546C4×C8—21no—
547#95—21no—
548#95—21no—
549#95—22no—
550#95—22no—
551#95C23×C1312yes—
552C2×C13—22no—
553C2×C13—81no—
554C2×C13—81no—
555C2×C13—81no—
556C2×C13—81no—
557C2×C13#300811yescharacteristic
558C2×C13#302211yescharacteristic
559C2×C13#302811yescharacteristic
560C24—21no—
561C24C2×D4×C1311yescharacteristic
562#41—82no—
563#41—82no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×Q8—82no—
569C2×Q8C2×D4×C1311yescharacteristic
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—82no—
583C2×D4C2×D4×C1311yescharacteristic
584C2×D4C2×D4×C1311yescharacteristic
585C2×D4C2×D4×C1311yescharacteristic
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4C2×D4×C1311yescharacteristic
597C22×C4C2×D4×C1311yescharacteristic
598C22×C4C2×D4×C1311yescharacteristic
599C22×C4C2×D4×C1311yescharacteristic
600C22×C4C2×D4×C1311yescharacteristic
601C22×C4C24×C1311yescharacteristic
602C2×C8—22no—
603C2×C8—22no—
604C4⋊C4—21no—
605C4⋊C4—21no—
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—22no—
622C4⋊C4—22no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—82no—
626C4⋊C4C2×D4×C1311yescharacteristic
627C4⋊C4C2×D4×C1311yescharacteristic
628C4⋊C4C2×D4×C1311yescharacteristic
629C4⋊C4C2×D4×C1311yescharacteristic
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
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—82no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42C2×D4×C1311yescharacteristic
660C42C2×D4×C1311yescharacteristic
661C42C2×D4×C1311yescharacteristic
662C42C2×D4×C1311yescharacteristic
663C13#1847011yescharacteristic, direct product factor, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23C22×D4×C1311yescharacteristic
675Q8—41no—
676Q8—81no—
677Q8—82no—
678Q8—82no—
679Q8—81no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—81no—
687D4—81no—
688D4—81no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4C13×#12011yescharacteristic
724C2×C4C13×#12011yescharacteristic
725C2×C4C13×#12011yescharacteristic
726C2×C4C13×#12011yescharacteristic
727C2×C4C22×D4×C1311yescharacteristic
728C2×C4C22×D4×C1311yescharacteristic
729C8—42no—
730C8—42no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—82no—
746C22—162no—
747C22C2×C13×#12011yescharacteristic
748C22C13×#57612yes—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—82no—
764C4—82no—
765C2—22no—
766C2—81no—
767C2—81no—
768C2—81no—
769C2—81no—
770C2C13×#300811yescharacteristic
771C2C13×#302211yescharacteristic
772C2C13×#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×#3238C2semidirect
3. C13×#3226C2semidirect
4. C13×#2821C2semidirect
5. C13×#1612C2semidirect
6. C13×#1610C2semidirect
7. C13×#1609C2semidirect
8. C13×#1607C2semidirect
9. C13×#1521C2semidirect
10. C13×#1514C2semidirect
11. C13×#1473C2semidirect
29. C2×C13×C4⋊Q8C22semidirect
36. C13×#483C22semidirect
39. C13×#480C22semidirect
44. C13×#432C22semidirect
45. C13×#431C22semidirect
48. C13×#398C22semidirect
52. C13×#383C22semidirect
53. C13×#328C22semidirect
56. C13×#327C22semidirect
57. C13×#324C22semidirect
174. #18470C13direct (N × H)
279. #3238C2×C13semidirect
280. #3226C2×C13semidirect
281. #2821C2×C13semidirect
282. #1612C2×C13semidirect
283. #1610C2×C13semidirect
284. #1609C2×C13semidirect
285. #1607C2×C13semidirect
286. #1521C2×C13semidirect
287. #1514C2×C13semidirect
288. #1473C2×C13semidirect
373. C2×C4⋊Q8C22×C13semidirect
380. #483C22×C13semidirect
383. #480C22×C13semidirect
388. #432C22×C13semidirect
389. #431C22×C13semidirect
392. #398C22×C13semidirect
396. #383C22×C13semidirect
397. #328C22×C13semidirect
400. #327C22×C13semidirect
401. #324C22×C13semidirect
663. C13#18470direct (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×#32382
C13×#32262
C13×#28212
C13×#16122
C13×#16102
C13×#16092
C13×#16072
C13×#15212
C13×#15142
C13×#14732
#1847013