Finite Group Databasebeta

← C13×#18448 #15704787

Subgroups — C13×#18448 #15704787

Order 3328.

968 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3535C211yesmaximal, characteristic, complemented
2C13×#3193C211yesmaximal, characteristic, complemented
3C13×#3188C211yesmaximal, characteristic, complemented
4C13×#2813C211yesmaximal, characteristic, complemented
5C13×#1618C211yesmaximal, characteristic, complemented
6C13×#1617C211yesmaximal, characteristic, complemented
7C13×#1615C211yesmaximal, characteristic, complemented
8C13×#1614C211yesmaximal, characteristic, complemented
9C13×#1600C211yesmaximal, characteristic, complemented
10C13×#1599C211yesmaximal, characteristic, complemented
11C13×#1597C211yesmaximal, characteristic, complemented
12C13×#1596C211yesmaximal, characteristic, complemented
13C13×#1520C211yesmaximal, characteristic, complemented
14C13×#1513C211yesmaximal, characteristic, complemented
15C13×#1468C211yesmaximal, characteristic, complemented
16C13×#563—21no—
17C13×#562—21no—
18C13×#554—21no—
19C13×#552—21no—
20C13×#551—21no—
21C13×#551—21no—
22C13×#547—21no—
23C13×#546—21no—
24C13×#544C2211yescharacteristic
25C13×#543C2211yescharacteristic
26C13×#542—21no—
27C13×#539—21no—
28C13×#539—21no—
29C13×#539C2211yescharacteristic
30C13×#538C2211yescharacteristic
31C13×#536—21no—
32C13×#525C2211yescharacteristic
33C2×C13×#123C2211yescharacteristic
34C2×C13×C22⋊Q8C2211yescharacteristic
35C2×C13×#121C2211yescharacteristic
36C13×#484C2211yescharacteristic
37C13×#484C2211yescharacteristic
38C13×#484C2211yescharacteristic
39C13×#482—21no—
40C13×#481C2211yescharacteristic
41C13×#480—21no—
42C13×#468—21no—
43C13×#468—21no—
44C13×#466—21no—
45C13×#465—21no—
46C13×#450C2211yescharacteristic
47C13×#450C2211yescharacteristic
48C13×#450C2211yescharacteristic
49C13×#449—21no—
50C13×#448—21no—
51C13×#447C2211yescharacteristic
52C13×#407C2211yescharacteristic
53C2×C13×C22⋊C8C2211yescharacteristic
54C13×#400C2211yescharacteristic
55C13×#399C2211yescharacteristic
56C13×#396—21no—
57C13×#394—21no—
58C13×#394—21no—
59C13×#394C2211yescharacteristic
60C13×#392—21no—
61C13×#392C2211yescharacteristic
62C13×#380C2211yescharacteristic
63C13×#328C2211yescharacteristic
64C13×#328C2211yescharacteristic
65C13×#328C2211yescharacteristic
66C13×#328C2211yescharacteristic
67C13×#328C2211yescharacteristic
68C13×#328C2211yescharacteristic
69C13×#327C2211yescharacteristic
70C13×#327C2211yescharacteristic
71C13×#324C2211yescharacteristic
72C13×#324C2211yescharacteristic
73C13×#323C2211yescharacteristic
74C13×#323C2211yescharacteristic
75C2×C13×#41—21no—
76C2×C13×#41D411yescharacteristic, complemented
77C22×Q8×C13D411yescharacteristic, complemented
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13D411yescharacteristic
81C22×D4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C2×C13×SD16—21no—
84C2×C13×SD16—21no—
85C2×C13×SD16—21no—
86C2×C13×D8—21no—
87C2×C13×M16—21no—
88C22×C8×C13—21no—
89C13×C4⋊Q8—21no—
90C13×C4⋊Q8—21no—
91C13×C4⋊Q8—21no—
92C13×#126—21no—
93C13×#126—21no—
94C13×#126—21no—
95C13×#126—21no—
96C13×#126—21no—
97C13×#126—21no—
98C13×#125—21no—
99C13×#125—21no—
100C13×#125—21no—
101C13×#125—21no—
102C13×#125—21no—
103C13×#124—21no—
104C13×#124—21no—
105C13×#124—21no—
106C13×#124—21no—
107C13×#123—21no—
108C13×#123—21no—
109C13×#123—21no—
110C13×#123—21no—
111C13×#123—21no—
112C13×#123—21no—
113C13×#123—21no—
114C13×#123—21no—
115C13×#123—21no—
116C13×#123—21no—
117C13×#123—21no—
118C13×#123—21no—
119C13×#123—21no—
120C13×#123—21no—
121C13×C22⋊Q8—21no—
122C13×C22⋊Q8—21no—
123C13×C22⋊Q8—21no—
124C13×C22⋊Q8—21no—
125C13×C22⋊Q8—21no—
126C13×C22⋊Q8—21no—
127C13×C22⋊Q8—21no—
128C13×C22⋊Q8—21no—
129C13×C22⋊Q8—21no—
130C13×C22⋊Q8—21no—
131C13×C22⋊Q8—21no—
132C13×C22⋊Q8—21no—
133C13×C22⋊Q8—21no—
134C13×C22⋊Q8—21no—
135C13×C22⋊Q8D411yescharacteristic, complemented
136C13×C22⋊Q8D411yescharacteristic, complemented
137C13×C22⋊Q8D411yescharacteristic, complemented
138C13×C22⋊Q8C2311yescharacteristic
139C13×C22⋊Q8C2311yescharacteristic
140C13×C22⋊Q8C2311yescharacteristic
141C13×#121—21no—
142C13×#121—21no—
143C13×#121—21no—
144C13×#121—21no—
145C13×#121—21no—
146C13×#121—21no—
147C13×#121—21no—
148C13×#121—21no—
149C13×#121D411yescharacteristic, complemented
150C13×#121C2311yescharacteristic
151C13×#120—21no—
152C13×#120—21no—
153C4×Q8×C13—21no—
154C4×D4×C13—21no—
155C4×D4×C13—21no—
156C4×D4×C13—21no—
157C4×D4×C13—21no—
158C4×D4×C13—21no—
159C4×D4×C13—21no—
160C4×D4×C13—21no—
161C13×#117—21no—
162C13×#117—21no—
163C13×#117—21no—
164C13×#117D411yescharacteristic, complemented
165C2×C13×C4⋊C4—21no—
166C2×C13×C4⋊C4—21no—
167C2×C13×C4⋊C4—21no—
168C2×C13×C4⋊C4—21no—
169C2×C13×C4⋊C4D411yescharacteristic
170C2×C13×C4⋊C4D411yescharacteristic, complemented
171C2×C13×C4⋊C4C2311yescharacteristic
172C2×C13×C4⋊C4C2311yescharacteristic
173C2×C13×C22⋊C4—21no—
174C2×C13×C22⋊C4—21no—
175C2×C13×C22⋊C4—21no—
176C2×C13×C22⋊C4—21no—
177C2×C13×C22⋊C4—21no—
178C2×C13×C22⋊C4—21no—
179C2×C13×C22⋊C4—21no—
180C2×C13×C22⋊C4—21no—
181C2×C13×C22⋊C4D411yescharacteristic
182C2×C13×C22⋊C4D411yescharacteristic
183C2×C13×C22⋊C4C2311yescharacteristic
184C13×#107—21no—
185C13×#107—21no—
186C13×#107—21no—
187C13×#106—21no—
188C13×#103—21no—
189C13×#103—21no—
190C13×#103—21no—
191C13×#102—21no—
192C13×#102—21no—
193C13×#102—21no—
194C13×#102—21no—
195C13×#102—21no—
196C13×C22⋊C8—21no—
197C13×C22⋊C8—21no—
198C13×C22⋊C8C2311yescharacteristic
199C13×C22⋊C8C2311yescharacteristic
200C13×C22⋊C8C2311yescharacteristic
201C13×C22⋊C8C2311yescharacteristic
202C13×#95—21no—
203C13×#95—21no—
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#18448C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13C2×D411yescharacteristic
209C24×C13C2×D411yescharacteristic
210C13×#41—82no—
211C13×#41—81no—
212C2×Q8×C13—21no—
213C2×Q8×C13—21no—
214C2×Q8×C13—21no—
215C2×Q8×C13—81no—
216C2×Q8×C13C2×D411yescharacteristic
217C2×Q8×C13C2×D411yescharacteristic
218C2×Q8×C13C2×D411yescharacteristic
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—41no—
229C2×D4×C13—41no—
230C2×D4×C13—81no—
231C2×D4×C13—81no—
232C2×D4×C13—81no—
233C2×D4×C13—81no—
234C2×D4×C13—81no—
235C2×D4×C13—81no—
236C2×D4×C13—81no—
237C2×D4×C13C2×D411yescharacteristic
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×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—81no—
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2×D411yescharacteristic
251C22×C4×C13C2×D411yescharacteristic
252C22×C4×C13C2×D411yescharacteristic
253C22×C4×C13C2×D411yescharacteristic
254C22×C4×C13C2×D411yescharacteristic
255C22×C4×C13C2×D411yescharacteristic
256C22×C4×C13C2×D411yescharacteristic
257C22×C4×C13C2411yescharacteristic
258C13×SD16—81no—
259C13×SD16—81no—
260C13×SD16—81no—
261C13×D8—81no—
262C13×M16—81no—
263C2×C8×C13—21no—
264C2×C8×C13—21no—
265C2×C8×C13—21no—
266C2×C8×C13—21no—
267C2×C8×C13—81no—
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—21no—
277C13×C4⋊C4—21no—
278C13×C4⋊C4—21no—
279C13×C4⋊C4—21no—
280C13×C4⋊C4—21no—
281C13×C4⋊C4—21no—
282C13×C4⋊C4—21no—
283C13×C4⋊C4—21no—
284C13×C4⋊C4—21no—
285C13×C4⋊C4—21no—
286C13×C4⋊C4—21no—
287C13×C4⋊C4—21no—
288C13×C4⋊C4—21no—
289C13×C4⋊C4—21no—
290C13×C4⋊C4—21no—
291C13×C4⋊C4—21no—
292C13×C4⋊C4—21no—
293C13×C4⋊C4—81no—
294C13×C4⋊C4—81no—
295C13×C4⋊C4C2×D411yescharacteristic
296C13×C4⋊C4C2×D411yescharacteristic
297C13×C4⋊C4C2×D411yescharacteristic
298C13×C4⋊C4C2×D411yescharacteristic
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—21no—
313C13×C22⋊C4—21no—
314C13×C22⋊C4—21no—
315C13×C22⋊C4—21no—
316C13×C22⋊C4—21no—
317C13×C22⋊C4—21no—
318C13×C22⋊C4—21no—
319C13×C22⋊C4—21no—
320C13×C22⋊C4—21no—
321C13×C22⋊C4—21no—
322C13×C22⋊C4—41no—
323C13×C22⋊C4—41no—
324C13×C22⋊C4—81no—
325C13×C22⋊C4—81no—
326C13×C22⋊C4—81no—
327C13×C22⋊C4—81no—
328C13×C22⋊C4—81no—
329C42×C13—21no—
330C42×C13—21no—
331C42×C13—21no—
332C42×C13—21no—
333C42×C13—21no—
334#3535C2×C1311yescharacteristic, complemented
335#3193C2×C1311yescharacteristic, complemented
336#3188C2×C1311yescharacteristic, complemented
337#2813C2×C1311yescharacteristic, complemented
338#1618C2×C1311yescharacteristic, complemented
339#1617C2×C1311yescharacteristic, complemented
340#1615C2×C1311yescharacteristic, complemented
341#1614C2×C1311yescharacteristic, complemented
342#1600C2×C1311yescharacteristic, complemented
343#1599C2×C1311yescharacteristic, complemented
344#1597C2×C1311yescharacteristic, complemented
345#1596C2×C1311yescharacteristic, complemented
346#1520C2×C1311yescharacteristic, complemented
347#1513C2×C1311yescharacteristic, complemented
348#1468C2×C1311yescharacteristic, complemented
349C23×C13—21no—
350C23×C13—21no—
351C23×C13—21no—
352C23×C13—21no—
353C23×C13—21no—
354C23×C13—21no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
366C23×C13#12011yescharacteristic
367C23×C13#12011yescharacteristic
368C23×C13C22×D411yescharacteristic
369Q8×C13—41no—
370Q8×C13—41no—
371Q8×C13—41no—
372Q8×C13—81no—
373Q8×C13—81no—
374Q8×C13—81no—
375D4×C13—41no—
376D4×C13—41no—
377D4×C13—41no—
378D4×C13—41no—
379D4×C13—41no—
380D4×C13—42no—
381D4×C13—42no—
382D4×C13—41no—
383D4×C13—41no—
384D4×C13—81no—
385D4×C13—81no—
386D4×C13—81no—
387D4×C13—81no—
388D4×C13—82no—
389D4×C13—82no—
390D4×C13—84no—
391C2×C4×C13—21no—
392C2×C4×C13—21no—
393C2×C4×C13—21no—
394C2×C4×C13—21no—
395C2×C4×C13—21no—
396C2×C4×C13—21no—
397C2×C4×C13—21no—
398C2×C4×C13—21no—
399C2×C4×C13—21no—
400C2×C4×C13—21no—
401C2×C4×C13—21no—
402C2×C4×C13—21no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—42no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—81no—
422C2×C4×C13—81no—
423C2×C4×C13—81no—
424C2×C4×C13—81no—
425C2×C4×C13—81no—
426C2×C4×C13—81no—
427C2×C4×C13#12011yescharacteristic
428C2×C4×C13#12011yescharacteristic
429C2×C4×C13C22×D411yescharacteristic
430C2×C4×C13C22×D411yescharacteristic
431C8×C13—41no—
432C8×C13—41no—
433C8×C13—41no—
434C8×C13—41no—
435#563—21no—
436#562—21no—
437#554—21no—
438#552—21no—
439#551—21no—
440#551—21no—
441#547—21no—
442#546—21no—
443#544C22×C1311yescharacteristic
444#543C22×C1311yescharacteristic
445#542—21no—
446#539—21no—
447#539—21no—
448#539C22×C1311yescharacteristic
449#538C22×C1311yescharacteristic
450#536—21no—
451#525C22×C1311yescharacteristic
452C2×#123C22×C1311yescharacteristic
453C2×C22⋊Q8C22×C1311yescharacteristic
454C2×#121C22×C1311yescharacteristic
455#484C22×C1311yescharacteristic
456#484C22×C1311yescharacteristic
457#484C22×C1311yescharacteristic
458#482—21no—
459#481C22×C1311yescharacteristic
460#480—21no—
461#468—21no—
462#468—21no—
463#466—21no—
464#465—21no—
465#450C22×C1311yescharacteristic
466#450C22×C1311yescharacteristic
467#450C22×C1311yescharacteristic
468#449—21no—
469#448—21no—
470#447C22×C1311yescharacteristic
471#407C22×C1311yescharacteristic
472C2×C22⋊C8C22×C1311yescharacteristic
473#400C22×C1311yescharacteristic
474#399C22×C1311yescharacteristic
475#396—21no—
476#394—21no—
477#394—21no—
478#394C22×C1311yescharacteristic
479#392—21no—
480#392C22×C1311yescharacteristic
481#380C22×C1311yescharacteristic
482#328C22×C1311yescharacteristic
483#328C22×C1311yescharacteristic
484#328C22×C1311yescharacteristic
485#328C22×C1311yescharacteristic
486#328C22×C1311yescharacteristic
487#328C22×C1311yescharacteristic
488#327C22×C1311yescharacteristic
489#327C22×C1311yescharacteristic
490#324C22×C1311yescharacteristic
491#324C22×C1311yescharacteristic
492#323C22×C1311yescharacteristic
493#323C22×C1311yescharacteristic
494C22×C13—21no—
495C22×C13—21no—
496C22×C13—21no—
497C22×C13—21no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—21no—
501C22×C13—21no—
502C22×C13—41no—
503C22×C13—41no—
504C22×C13—41no—
505C22×C13—41no—
506C22×C13—41no—
507C22×C13—41no—
508C22×C13—81no—
509C22×C13—81no—
510C22×C13—81no—
511C22×C13—81no—
512C22×C13—81no—
513C22×C13—81no—
514C22×C13—81no—
515C22×C13—81no—
516C22×C13—81no—
517C22×C13—81no—
518C22×C13—81no—
519C22×C13C2×#12011yescharacteristic
520C22×C13#57711yescharacteristic
521C22×C13#57811yescharacteristic
522C4×C13—21no—
523C4×C13—21no—
524C4×C13—21no—
525C4×C13—21no—
526C4×C13—41no—
527C4×C13—41no—
528C4×C13—41no—
529C4×C13—41no—
530C4×C13—41no—
531C4×C13—41no—
532C4×C13—41no—
533C4×C13—41no—
534C4×C13—41no—
535C4×C13—41no—
536C4×C13—81no—
537C4×C13—81no—
538C4×C13—81no—
539C2×#41—21no—
540C2×#41D4×C1311yescharacteristic, complemented
541C22×Q8D4×C1311yescharacteristic, complemented
542C22×D4—21no—
543C22×D4—21no—
544C22×D4D4×C1311yescharacteristic
545C22×D4C23×C1311yescharacteristic
546C23×C4C23×C1311yescharacteristic
547C2×SD16—21no—
548C2×SD16—21no—
549C2×SD16—21no—
550C2×D8—21no—
551C2×M16—21no—
552C22×C8—21no—
553C4⋊Q8—21no—
554C4⋊Q8—21no—
555C4⋊Q8—21no—
556#126—21no—
557#126—21no—
558#126—21no—
559#126—21no—
560#126—21no—
561#126—21no—
562#125—21no—
563#125—21no—
564#125—21no—
565#125—21no—
566#125—21no—
567#124—21no—
568#124—21no—
569#124—21no—
570#124—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8D4×C1311yescharacteristic, complemented
600C22⋊Q8D4×C1311yescharacteristic, complemented
601C22⋊Q8D4×C1311yescharacteristic, complemented
602C22⋊Q8C23×C1311yescharacteristic
603C22⋊Q8C23×C1311yescharacteristic
604C22⋊Q8C23×C1311yescharacteristic
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121D4×C1311yescharacteristic, complemented
614#121C23×C1311yescharacteristic
615#120—21no—
616#120—21no—
617C4×Q8—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—21no—
625#117—21no—
626#117—21no—
627#117—21no—
628#117D4×C1311yescharacteristic, complemented
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C1311yescharacteristic
634C2×C4⋊C4D4×C1311yescharacteristic, complemented
635C2×C4⋊C4C23×C1311yescharacteristic
636C2×C4⋊C4C23×C1311yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C1311yescharacteristic
646C2×C22⋊C4D4×C1311yescharacteristic
647C2×C22⋊C4C23×C1311yescharacteristic
648#107—21no—
649#107—21no—
650#107—21no—
651#106—21no—
652#103—21no—
653#103—21no—
654#103—21no—
655#102—21no—
656#102—21no—
657#102—21no—
658#102—21no—
659#102—21no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8C23×C1311yescharacteristic
663C22⋊C8C23×C1311yescharacteristic
664C22⋊C8C23×C1311yescharacteristic
665C22⋊C8C23×C1311yescharacteristic
666#95—21no—
667#95—21no—
668#95C23×C1311yescharacteristic
669#95C23×C1311yescharacteristic
670C2×C13—21no—
671C2×C13—21no—
672C2×C13—41no—
673C2×C13—41no—
674C2×C13—81no—
675C2×C13—81no—
676C2×C13—161no—
677C2×C13#301311yescharacteristic
678C2×C13#302111yescharacteristic
679C2×C13#302611yescharacteristic
680C24—21no—
681C24C2×D4×C1311yescharacteristic
682C24C2×D4×C1311yescharacteristic
683#41—82no—
684#41—81no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—81no—
689C2×Q8C2×D4×C1311yescharacteristic
690C2×Q8C2×D4×C1311yescharacteristic
691C2×Q8C2×D4×C1311yescharacteristic
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4C2×D4×C1311yescharacteristic
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—81no—
722C22×C4C2×D4×C1311yescharacteristic
723C22×C4C2×D4×C1311yescharacteristic
724C22×C4C2×D4×C1311yescharacteristic
725C22×C4C2×D4×C1311yescharacteristic
726C22×C4C2×D4×C1311yescharacteristic
727C22×C4C2×D4×C1311yescharacteristic
728C22×C4C2×D4×C1311yescharacteristic
729C22×C4C2×D4×C1311yescharacteristic
730C22×C4C24×C1311yescharacteristic
731SD16—81no—
732SD16—81no—
733SD16—81no—
734D8—81no—
735M16—81no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—81no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—81no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C1311yescharacteristic
769C4⋊C4C2×D4×C1311yescharacteristic
770C4⋊C4C2×D4×C1311yescharacteristic
771C4⋊C4C2×D4×C1311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—41no—
796C22⋊C4—41no—
797C22⋊C4—81no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C13#1844811yescharacteristic, direct product factor, Sylow
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C13×#12011yescharacteristic
826C23C13×#12011yescharacteristic
827C23C22×D4×C1311yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—82no—
848D4—82no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4C13×#12011yescharacteristic
887C2×C4C13×#12011yescharacteristic
888C2×C4C22×D4×C1311yescharacteristic
889C2×C4C22×D4×C1311yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×C13×#12011yescharacteristic
920C22C13×#57711yescharacteristic
921C22C13×#57811yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C13×#301311yescharacteristic
947C2C13×#302111yescharacteristic
948C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C13×#3535C2semidirect
2. C13×#3193C2semidirect
3. C13×#3188C2semidirect
4. C13×#2813C2semidirect
5. C13×#1618C2semidirect
6. C13×#1617C2semidirect
7. C13×#1615C2semidirect
8. C13×#1614C2semidirect
9. C13×#1600C2semidirect
10. C13×#1599C2semidirect
11. C13×#1597C2semidirect
12. C13×#1596C2semidirect
13. C13×#1520C2semidirect
14. C13×#1513C2semidirect
15. C13×#1468C2semidirect
76. C2×C13×#41D4semidirect
77. C22×Q8×C13D4semidirect
135. C13×C22⋊Q8D4semidirect
136. C13×C22⋊Q8D4semidirect
137. C13×C22⋊Q8D4semidirect
149. C13×#121D4semidirect
164. C13×#117D4semidirect
170. C2×C13×C4⋊C4D4semidirect
206. #18448C13direct (N × H)
334. #3535C2×C13semidirect
335. #3193C2×C13semidirect
336. #3188C2×C13semidirect
337. #2813C2×C13semidirect
338. #1618C2×C13semidirect
339. #1617C2×C13semidirect
340. #1615C2×C13semidirect
341. #1614C2×C13semidirect
342. #1600C2×C13semidirect
343. #1599C2×C13semidirect
344. #1597C2×C13semidirect
345. #1596C2×C13semidirect
346. #1520C2×C13semidirect
347. #1513C2×C13semidirect
348. #1468C2×C13semidirect
540. C2×#41D4×C13semidirect
541. C22×Q8D4×C13semidirect
599. C22⋊Q8D4×C13semidirect
600. C22⋊Q8D4×C13semidirect
601. C22⋊Q8D4×C13semidirect
613. #121D4×C13semidirect
628. #117D4×C13semidirect
634. C2×C4⋊C4D4×C13semidirect
807. C13#18448direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35352
C13×#31932
C13×#31882
C13×#28132
C13×#16182
C13×#16172
C13×#16152
C13×#16142
C13×#16002
C13×#15992
C13×#15972
C13×#15962
C13×#15202
C13×#15132
C13×#14682
#1844813