Finite Group Databasebeta

← C13×#18280 #15704619

Subgroups — C13×#18280 #15704619

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3560C211yesmaximal, characteristic, complemented
2C13×#3114C211yesmaximal, characteristic, complemented
3C13×#3100C211yesmaximal, characteristic, complemented
4C13×#2603C211yesmaximal, characteristic, complemented
5C13×#1612C211yesmaximal, characteristic, complemented
6C13×#1610C211yesmaximal, characteristic, complemented
7C13×#1609C211yesmaximal, characteristic, complemented
8C13×#1607C211yesmaximal, characteristic, complemented
9C13×#1600C211yesmaximal, characteristic, complemented
10C13×#1598C211yesmaximal, characteristic, complemented
11C13×#1597C211yesmaximal, characteristic, complemented
12C13×#1595C211yesmaximal, characteristic, complemented
13C13×#1505C211yesmaximal, characteristic, complemented
14C13×#1500C211yesmaximal, characteristic, complemented
15C13×#1473C211yesmaximal, characteristic, complemented
16C13×#563—21no—
17C13×#560—21no—
18C13×#553—21no—
19C13×#553—21no—
20C13×#551—21no—
21C13×#547—21no—
22C13×#546—21no—
23C13×#546—21no—
24C13×#542—21no—
25C13×#539—21no—
26C13×#539C2211yescharacteristic
27C13×#538—21no—
28C13×#538—21no—
29C13×#538C2211yescharacteristic
30C13×#537C2211yescharacteristic
31C13×#534C2211yescharacteristic
32C13×#532C2211yescharacteristic
33C13×#529C2211yescharacteristic
34C2×C13×#126C2211yescharacteristic
35C2×C4×D4×C13C2211yescharacteristic, complemented
36C13×#483C2211yescharacteristic, complemented
37C13×#480C2211yescharacteristic
38C13×#480C2211yescharacteristic
39C13×#480C2211yescharacteristic, complemented
40C13×#478—21no—
41C13×#474—21no—
42C13×#463—21no—
43C13×#459—21no—
44C13×#450C2211yescharacteristic, complemented
45C13×#447C2211yescharacteristic
46C13×#447C2211yescharacteristic
47C13×#447C2211yescharacteristic, complemented
48C13×#442—21no—
49C13×#440—21no—
50C4×C13×D8—21no—
51C4×C13×D8—21no—
52C13×#432C2211yescharacteristic, complemented
53C13×#431C2211yescharacteristic, complemented
54C13×#398C2211yescharacteristic, complemented
55C13×#397C2211yescharacteristic
56C13×#394C2211yescharacteristic, complemented
57C13×#392C2211yescharacteristic
58C13×#390—21no—
59C13×#388—21no—
60C13×#386—21no—
61C13×#385—21no—
62C13×#376C2211yescharacteristic, complemented
63C13×#328C2211yescharacteristic, complemented
64C13×#328C2211yescharacteristic, complemented
65C13×#327C2211yescharacteristic
66C13×#327C2211yescharacteristic
67C13×#327C2211yescharacteristic
68C13×#327C2211yescharacteristic
69C13×#327C2211yescharacteristic, complemented
70C13×#327C2211yescharacteristic, complemented
71C13×#324C2211yescharacteristic, complemented
72C13×#324C2211yescharacteristic, complemented
73C13×#323C2211yescharacteristic
74C13×#323C2211yescharacteristic
75C2×C13×#41—21no—
76C2×C13×#41—21no—
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C2×C13×SD16—21no—
82C2×C13×D8—21no—
83C2×C13×D8—21no—
84C2×C13×D8—21no—
85C13×C4⋊Q8—21no—
86C13×C4⋊Q8D411yescharacteristic, complemented
87C13×#127D411yescharacteristic, complemented
88C13×#126—21no—
89C13×#126—21no—
90C13×#126—21no—
91C13×#126—21no—
92C13×#126—21no—
93C13×#126—21no—
94C13×#126—21no—
95C13×#126—21no—
96C13×#126—21no—
97C13×#125—21no—
98C13×#125—21no—
99C13×#125D411yescharacteristic, complemented
100C13×#124—21no—
101C13×#124—21no—
102C13×#124—21no—
103C13×#124—21no—
104C13×#124D411yescharacteristic, complemented
105C13×#123—21no—
106C13×#123—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×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⋊Q8C2311yescharacteristic
125C13×#121—21no—
126C13×#121—21no—
127C13×#121—21no—
128C13×#121—21no—
129C13×#121—21no—
130C13×#121—21no—
131C13×#121—21no—
132C13×#121—21no—
133C13×#121—21no—
134C13×#121—21no—
135C13×#121—21no—
136C13×#121—21no—
137C13×#121C2311yescharacteristic
138C13×#121C2311yescharacteristic
139C13×#121C2311yescharacteristic
140C13×#120—21no—
141C13×#120—21no—
142C13×#120—21no—
143C13×#120—21no—
144C13×#120—21no—
145C4×Q8×C13D411yescharacteristic, complemented
146C4×D4×C13—21no—
147C4×D4×C13—21no—
148C4×D4×C13—21no—
149C4×D4×C13—21no—
150C4×D4×C13—21no—
151C4×D4×C13—21no—
152C4×D4×C13—21no—
153C4×D4×C13—21no—
154C4×D4×C13—21no—
155C4×D4×C13—21no—
156C4×D4×C13—21no—
157C4×D4×C13—21no—
158C4×D4×C13D411yescharacteristic, complemented
159C4×D4×C13D411yescharacteristic, complemented
160C4×D4×C13D411yescharacteristic, complemented
161C13×#117—21no—
162C13×#117—21no—
163C2×C13×C4⋊C4—21no—
164C2×C13×C4⋊C4—21no—
165C2×C13×C4⋊C4D411yescharacteristic
166C2×C13×C4⋊C4D411yescharacteristic
167C2×C13×C4⋊C4C2311yescharacteristic
168C2×C13×C4⋊C4C2311yescharacteristic
169C2×C13×C22⋊C4—21no—
170C2×C13×C22⋊C4—21no—
171C2×C13×C22⋊C4—21no—
172C2×C13×C22⋊C4—21no—
173C2×C13×C22⋊C4—21no—
174C2×C13×C22⋊C4—21no—
175C2×C13×C22⋊C4—21no—
176C2×C13×C22⋊C4D411yescharacteristic
177C2×C13×C22⋊C4D411yescharacteristic
178C2×C13×C22⋊C4C2311yescharacteristic
179C2×C42×C13—21no—
180C2×C42×C13C2311yescharacteristic
181C13×#107—21no—
182C13×#107—21no—
183C13×#107—21no—
184C13×#106—21no—
185C13×C4⋊C8—21no—
186C13×C4⋊C8—21no—
187C13×#103—21no—
188C13×#102—21no—
189C13×#102—21no—
190C13×#102—21no—
191C13×#102—21no—
192C13×#102—21no—
193C13×#102—21no—
194C13×#102—21no—
195C13×C22⋊C8C2311yescharacteristic
196C13×C22⋊C8C2311yescharacteristic
197C13×C22⋊C8C2311yescharacteristic
198C13×C22⋊C8C2311yescharacteristic
199C13×#97—21no—
200C4×C8×C13—21no—
201C13×#95—21no—
202C13×#95—21no—
203C13×#95—21no—
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#18280C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C24×C13C2×D411yescharacteristic
210C13×#41—81no—
211C13×#41—81no—
212C13×#41—81no—
213C13×#41—81no—
214C2×Q8×C13—21no—
215C2×Q8×C13—21no—
216C2×Q8×C13C2×D411yescharacteristic
217C2×D4×C13—21no—
218C2×D4×C13—21no—
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—21no—
229C2×D4×C13—21no—
230C2×D4×C13—21no—
231C2×D4×C13—42no—
232C2×D4×C13—42no—
233C2×D4×C13—42no—
234C2×D4×C13—81no—
235C2×D4×C13—81no—
236C2×D4×C13—81no—
237C2×D4×C13C2×D411yescharacteristic
238C2×D4×C13C2×D411yescharacteristic
239C2×D4×C13C2×D411yescharacteristic
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—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—41no—
252C22×C4×C13—41no—
253C22×C4×C13—81no—
254C22×C4×C13—81no—
255C22×C4×C13C2×D411yescharacteristic
256C22×C4×C13C2×D411yescharacteristic
257C22×C4×C13C2×D411yescharacteristic
258C22×C4×C13C2×D411yescharacteristic
259C22×C4×C13C2×D411yescharacteristic
260C22×C4×C13C2411yescharacteristic
261C13×SD16—42no—
262C13×D8—42no—
263C13×D8—42no—
264C13×D8—42no—
265C2×C8×C13—21no—
266C2×C8×C13—21no—
267C2×C8×C13—21no—
268C2×C8×C13—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—81no—
289C13×C4⋊C4C2×D411yescharacteristic
290C13×C4⋊C4C2×D411yescharacteristic
291C13×C4⋊C4C2×D411yescharacteristic
292C13×C4⋊C4C2×D411yescharacteristic
293C13×C22⋊C4—21no—
294C13×C22⋊C4—21no—
295C13×C22⋊C4—21no—
296C13×C22⋊C4—21no—
297C13×C22⋊C4—21no—
298C13×C22⋊C4—21no—
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—42no—
319C13×C22⋊C4—42no—
320C13×C22⋊C4—41no—
321C13×C22⋊C4—41no—
322C13×C22⋊C4—81no—
323C13×C22⋊C4—81no—
324C42×C13—21no—
325C42×C13—21no—
326C42×C13—21no—
327C42×C13—42no—
328C42×C13C2×D411yescharacteristic
329C42×C13C2×D411yescharacteristic
330C42×C13C2×D411yescharacteristic
331C42×C13C2×D411yescharacteristic
332#3560C2×C1311yescharacteristic, complemented
333#3114C2×C1311yescharacteristic, complemented
334#3100C2×C1311yescharacteristic, complemented
335#2603C2×C1311yescharacteristic, complemented
336#1612C2×C1311yescharacteristic, complemented
337#1610C2×C1311yescharacteristic, complemented
338#1609C2×C1311yescharacteristic, complemented
339#1607C2×C1311yescharacteristic, complemented
340#1600C2×C1311yescharacteristic, complemented
341#1598C2×C1311yescharacteristic, complemented
342#1597C2×C1311yescharacteristic, complemented
343#1595C2×C1311yescharacteristic, complemented
344#1505C2×C1311yescharacteristic, complemented
345#1500C2×C1311yescharacteristic, complemented
346#1473C2×C1311yescharacteristic, complemented
347C23×C13—22no—
348C23×C13—21no—
349C23×C13—21no—
350C23×C13—21no—
351C23×C13—21no—
352C23×C13—21no—
353C23×C13—21no—
354C23×C13—41no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—81no—
363C23×C13—81no—
364C23×C13—81no—
365C23×C13C22×D411yescharacteristic
366Q8×C13—41no—
367Q8×C13—81no—
368Q8×C13—81no—
369D4×C13—22no—
370D4×C13—22no—
371D4×C13—41no—
372D4×C13—41no—
373D4×C13—41no—
374D4×C13—41no—
375D4×C13—41no—
376D4×C13—41no—
377D4×C13—41no—
378D4×C13—41no—
379D4×C13—41no—
380D4×C13—41no—
381D4×C13—41no—
382D4×C13—81no—
383D4×C13—81no—
384D4×C13—81no—
385D4×C13—81no—
386D4×C13—81no—
387D4×C13—81no—
388D4×C13—81no—
389D4×C13—81no—
390D4×C13—81no—
391D4×C13—84no—
392C2×C4×C13—21no—
393C2×C4×C13—21no—
394C2×C4×C13—22no—
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—21no—
404C2×C4×C13—21no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
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—81no—
418C2×C4×C13—81no—
419C2×C4×C13—81no—
420C2×C4×C13—82no—
421C2×C4×C13—82no—
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×C13#12011yescharacteristic
430C2×C4×C13#12011yescharacteristic
431C2×C4×C13C22×D411yescharacteristic
432C2×C4×C13C22×D411yescharacteristic
433C8×C13—41no—
434C8×C13—41no—
435C8×C13—41no—
436C8×C13—41no—
437#563—21no—
438#560—21no—
439#553—21no—
440#553—21no—
441#551—21no—
442#547—21no—
443#546—21no—
444#546—21no—
445#542—21no—
446#539—21no—
447#539C22×C1311yescharacteristic
448#538—21no—
449#538—21no—
450#538C22×C1311yescharacteristic
451#537C22×C1311yescharacteristic
452#534C22×C1311yescharacteristic
453#532C22×C1311yescharacteristic
454#529C22×C1311yescharacteristic
455C2×#126C22×C1311yescharacteristic
456C2×C4×D4C22×C1311yescharacteristic, complemented
457#483C22×C1311yescharacteristic, complemented
458#480C22×C1311yescharacteristic
459#480C22×C1311yescharacteristic
460#480C22×C1311yescharacteristic, complemented
461#478—21no—
462#474—21no—
463#463—21no—
464#459—21no—
465#450C22×C1311yescharacteristic, complemented
466#447C22×C1311yescharacteristic
467#447C22×C1311yescharacteristic
468#447C22×C1311yescharacteristic, complemented
469#442—21no—
470#440—21no—
471C4×D8—21no—
472C4×D8—21no—
473#432C22×C1311yescharacteristic, complemented
474#431C22×C1311yescharacteristic, complemented
475#398C22×C1311yescharacteristic, complemented
476#397C22×C1311yescharacteristic
477#394C22×C1311yescharacteristic, complemented
478#392C22×C1311yescharacteristic
479#390—21no—
480#388—21no—
481#386—21no—
482#385—21no—
483#376C22×C1311yescharacteristic, complemented
484#328C22×C1311yescharacteristic, complemented
485#328C22×C1311yescharacteristic, complemented
486#327C22×C1311yescharacteristic
487#327C22×C1311yescharacteristic
488#327C22×C1311yescharacteristic
489#327C22×C1311yescharacteristic
490#327C22×C1311yescharacteristic, complemented
491#327C22×C1311yescharacteristic, complemented
492#324C22×C1311yescharacteristic, complemented
493#324C22×C1311yescharacteristic, complemented
494#323C22×C1311yescharacteristic
495#323C22×C1311yescharacteristic
496C22×C13—21no—
497C22×C13—21no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—41no—
501C22×C13—41no—
502C22×C13—41no—
503C22×C13—41no—
504C22×C13—41no—
505C22×C13—41no—
506C22×C13—41no—
507C22×C13—41no—
508C22×C13—41no—
509C22×C13—42no—
510C22×C13—41no—
511C22×C13—41no—
512C22×C13—41no—
513C22×C13—81no—
514C22×C13—81no—
515C22×C13—81no—
516C22×C13—81no—
517C22×C13—81no—
518C22×C13—81no—
519C22×C13—162no—
520C22×C13C2×#12011yescharacteristic
521C22×C13#57611yescharacteristic
522C22×C13#57611yescharacteristic
523C4×C13—21no—
524C4×C13—21no—
525C4×C13—21no—
526C4×C13—21no—
527C4×C13—21no—
528C4×C13—21no—
529C4×C13—42no—
530C4×C13—41no—
531C4×C13—41no—
532C4×C13—41no—
533C4×C13—41no—
534C4×C13—41no—
535C4×C13—41no—
536C4×C13—41no—
537C4×C13—41no—
538C4×C13—81no—
539C4×C13—81no—
540C2×#41—21no—
541C2×#41—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4C23×C1311yescharacteristic
545C23×C4—21no—
546C2×SD16—21no—
547C2×D8—21no—
548C2×D8—21no—
549C2×D8—21no—
550C4⋊Q8—21no—
551C4⋊Q8D4×C1311yescharacteristic, complemented
552#127D4×C1311yescharacteristic, complemented
553#126—21no—
554#126—21no—
555#126—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#125D4×C1311yescharacteristic, complemented
565#124—21no—
566#124—21no—
567#124—21no—
568#124—21no—
569#124D4×C1311yescharacteristic, complemented
570#123—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—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8C23×C1311yescharacteristic
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121C23×C1311yescharacteristic
603#121C23×C1311yescharacteristic
604#121C23×C1311yescharacteristic
605#120—21no—
606#120—21no—
607#120—21no—
608#120—21no—
609#120—21no—
610C4×Q8D4×C1311yescharacteristic, complemented
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4D4×C1311yescharacteristic, complemented
624C4×D4D4×C1311yescharacteristic, complemented
625C4×D4D4×C1311yescharacteristic, complemented
626#117—21no—
627#117—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4D4×C1311yescharacteristic
631C2×C4⋊C4D4×C1311yescharacteristic
632C2×C4⋊C4C23×C1311yescharacteristic
633C2×C4⋊C4C23×C1311yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C1311yescharacteristic
642C2×C22⋊C4D4×C1311yescharacteristic
643C2×C22⋊C4C23×C1311yescharacteristic
644C2×C42—21no—
645C2×C42C23×C1311yescharacteristic
646#107—21no—
647#107—21no—
648#107—21no—
649#106—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652#103—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#102—21no—
657#102—21no—
658#102—21no—
659#102—21no—
660C22⋊C8C23×C1311yescharacteristic
661C22⋊C8C23×C1311yescharacteristic
662C22⋊C8C23×C1311yescharacteristic
663C22⋊C8C23×C1311yescharacteristic
664#97—21no—
665C4×C8—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95C23×C1311yescharacteristic
670#95C23×C1311yescharacteristic
671C2×C13—21no—
672C2×C13—21no—
673C2×C13—81no—
674C2×C13—82no—
675C2×C13—81no—
676C2×C13—81no—
677C2×C13—81no—
678C2×C13#300811yescharacteristic
679C2×C13#301811yescharacteristic
680C2×C13#302511yescharacteristic
681C24—21no—
682C24—21no—
683C24C2×D4×C1311yescharacteristic
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C2×D4×C1311yescharacteristic
691C2×D4—21no—
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—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C1311yescharacteristic
712C2×D4C2×D4×C1311yescharacteristic
713C2×D4C2×D4×C1311yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C1311yescharacteristic
730C22×C4C2×D4×C1311yescharacteristic
731C22×C4C2×D4×C1311yescharacteristic
732C22×C4C2×D4×C1311yescharacteristic
733C22×C4C2×D4×C1311yescharacteristic
734C22×C4C24×C1311yescharacteristic
735SD16—42no—
736D8—42no—
737D8—42no—
738D8—42no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—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—81no—
763C4⋊C4C2×D4×C1311yescharacteristic
764C4⋊C4C2×D4×C1311yescharacteristic
765C4⋊C4C2×D4×C1311yescharacteristic
766C4⋊C4C2×D4×C1311yescharacteristic
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
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—42no—
793C22⋊C4—42no—
794C22⋊C4—41no—
795C22⋊C4—41no—
796C22⋊C4—81no—
797C22⋊C4—81no—
798C42—21no—
799C42—21no—
800C42—21no—
801C42—42no—
802C42C2×D4×C1311yescharacteristic
803C42C2×D4×C1311yescharacteristic
804C42C2×D4×C1311yescharacteristic
805C42C2×D4×C1311yescharacteristic
806C13#1828011yescharacteristic, direct product factor, Sylow
807C23—22no—
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—81no—
823C23—81no—
824C23—81no—
825C23C22×D4×C1311yescharacteristic
826Q8—41no—
827Q8—81no—
828Q8—81no—
829D4—22no—
830D4—22no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
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—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—82no—
881C2×C4—82no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4C13×#12011yescharacteristic
888C2×C4C13×#12011yescharacteristic
889C2×C4C13×#12011yescharacteristic
890C2×C4C13×#12011yescharacteristic
891C2×C4C22×D4×C1311yescharacteristic
892C2×C4C22×D4×C1311yescharacteristic
893C8—41no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—21no—
898C22—21no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—162no—
921C22C2×C13×#12011yescharacteristic
922C22C13×#57611yescharacteristic
923C22C13×#57611yescharacteristic
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—81no—
940C4—81no—
941C2—21no—
942C2—21no—
943C2—82no—
944C2—81no—
945C2—81no—
946C2—81no—
947C2—81no—
948C2C13×#300811yescharacteristic
949C2C13×#301811yescharacteristic
950C2C13×#302511yescharacteristic
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×#3114C2semidirect
3. C13×#3100C2semidirect
4. C13×#2603C2semidirect
5. C13×#1612C2semidirect
6. C13×#1610C2semidirect
7. C13×#1609C2semidirect
8. C13×#1607C2semidirect
9. C13×#1600C2semidirect
10. C13×#1598C2semidirect
11. C13×#1597C2semidirect
12. C13×#1595C2semidirect
13. C13×#1505C2semidirect
14. C13×#1500C2semidirect
15. C13×#1473C2semidirect
35. C2×C4×D4×C13C22semidirect
36. C13×#483C22semidirect
39. C13×#480C22semidirect
44. C13×#450C22semidirect
47. C13×#447C22semidirect
52. C13×#432C22semidirect
53. C13×#431C22semidirect
54. C13×#398C22semidirect
56. C13×#394C22semidirect
62. C13×#376C22semidirect
63. C13×#328C22semidirect
64. C13×#328C22semidirect
69. C13×#327C22semidirect
70. C13×#327C22semidirect
71. C13×#324C22semidirect
72. C13×#324C22semidirect
86. C13×C4⋊Q8D4semidirect
87. C13×#127D4semidirect
99. C13×#125D4semidirect
104. C13×#124D4semidirect
145. C4×Q8×C13D4semidirect
158. C4×D4×C13D4semidirect
159. C4×D4×C13D4semidirect
160. C4×D4×C13D4semidirect
206. #18280C13direct (N × H)
332. #3560C2×C13semidirect
333. #3114C2×C13semidirect
334. #3100C2×C13semidirect
335. #2603C2×C13semidirect
336. #1612C2×C13semidirect
337. #1610C2×C13semidirect
338. #1609C2×C13semidirect
339. #1607C2×C13semidirect
340. #1600C2×C13semidirect
341. #1598C2×C13semidirect
342. #1597C2×C13semidirect
343. #1595C2×C13semidirect
344. #1505C2×C13semidirect
345. #1500C2×C13semidirect
346. #1473C2×C13semidirect
456. C2×C4×D4C22×C13semidirect
457. #483C22×C13semidirect
460. #480C22×C13semidirect
465. #450C22×C13semidirect
468. #447C22×C13semidirect
473. #432C22×C13semidirect
474. #431C22×C13semidirect
475. #398C22×C13semidirect
477. #394C22×C13semidirect
483. #376C22×C13semidirect
484. #328C22×C13semidirect
485. #328C22×C13semidirect
490. #327C22×C13semidirect
491. #327C22×C13semidirect
492. #324C22×C13semidirect
493. #324C22×C13semidirect
551. C4⋊Q8D4×C13semidirect
552. #127D4×C13semidirect
564. #125D4×C13semidirect
569. #124D4×C13semidirect
610. C4×Q8D4×C13semidirect
623. C4×D4D4×C13semidirect
624. C4×D4D4×C13semidirect
625. C4×D4D4×C13semidirect
806. C13#18280direct (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×#31142
C13×#31002
C13×#26032
C13×#16122
C13×#16102
C13×#16092
C13×#16072
C13×#16002
C13×#15982
C13×#15972
C13×#15952
C13×#15052
C13×#15002
C13×#14732
#1828013