Finite Group Databasebeta

← C13×#18434 #15704773

Subgroups — C13×#18434 #15704773

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3560C211yesmaximal, characteristic, complemented
2C13×#3213C211yesmaximal, characteristic, complemented
3C13×#3211C211yesmaximal, characteristic, complemented
4C13×#2662C211yesmaximal, characteristic, complemented
5C13×#1606C211yesmaximal, characteristic, complemented
6C13×#1604C211yesmaximal, characteristic, complemented
7C13×#1603C211yesmaximal, characteristic, complemented
8C13×#1601C211yesmaximal, characteristic, complemented
9C13×#1600C211yesmaximal, characteristic, complemented
10C13×#1598C211yesmaximal, characteristic, complemented
11C13×#1597C211yesmaximal, characteristic, complemented
12C13×#1595C211yesmaximal, characteristic, complemented
13C13×#1509C211yesmaximal, characteristic, complemented
14C13×#1502C211yesmaximal, 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×C13×#124C2211yescharacteristic, complemented
36C13×#496—21no—
37C13×#495—21no—
38C13×#489—21no—
39C13×#488—21no—
40C13×#464—21no—
41C13×#463—21no—
42C13×#463—21no—
43C13×#463—21no—
44C13×#451C2211yescharacteristic, complemented
45C13×#450C2211yescharacteristic, complemented
46C13×#448C2211yescharacteristic
47C13×#448C2211yescharacteristic
48C13×#448C2211yescharacteristic, complemented
49C13×#447C2211yescharacteristic
50C13×#447C2211yescharacteristic
51C13×#447C2211yescharacteristic, complemented
52C13×#432C2211yescharacteristic, complemented
53C13×#431C2211yescharacteristic, complemented
54C13×#396—21no—
55C13×#395C2211yescharacteristic, complemented
56C13×#394—21no—
57C13×#394C2211yescharacteristic, complemented
58C13×#393C2211yescharacteristic
59C13×#392C2211yescharacteristic
60C13×#390—21no—
61C13×#388—21no—
62C4×C13×C4⋊C4C2211yescharacteristic, 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×Q8×C13C2311yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13C2311yescharacteristic
81C2×C13×Q16—21no—
82C2×C13×SD16—21no—
83C2×C13×SD16—21no—
84C2×C13×SD16—21no—
85C2×C13×SD16—21no—
86C2×C13×D8—21no—
87C2×C13×D8—21no—
88C2×C13×D8—21no—
89C13×C4⋊Q8—21no—
90C13×C4⋊Q8D411yescharacteristic, complemented
91C13×#127D411yescharacteristic, complemented
92C13×#126—21no—
93C13×#126—21no—
94C13×#126—21no—
95C13×#126—21no—
96C13×#126—21no—
97C13×#126—21no—
98C13×#126—21no—
99C13×#126—21no—
100C13×#126—21no—
101C13×#125—21no—
102C13×#125—21no—
103C13×#125D411yescharacteristic, complemented
104C13×#124—21no—
105C13×#124—21no—
106C13×#124—21no—
107C13×#124—21no—
108C13×#124—21no—
109C13×#124—21no—
110C13×#124—21no—
111C13×#124—21no—
112C13×#124D411yescharacteristic, complemented
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×#123—21no—
122C13×#123—21no—
123C13×#123—21no—
124C13×#123—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⋊Q8C2311yescharacteristic
133C13×#121—21no—
134C13×#121—21no—
135C13×#121—21no—
136C13×#121—21no—
137C13×#121—21no—
138C13×#121—21no—
139C13×#121—21no—
140C13×#121—21no—
141C13×#121—21no—
142C13×#121—21no—
143C13×#121—21no—
144C13×#121—21no—
145C13×#121C2311yescharacteristic
146C13×#121C2311yescharacteristic
147C13×#121C2311yescharacteristic
148C13×#120—21no—
149C13×#120—21no—
150C13×#120—21no—
151C13×#120—21no—
152C13×#120—21no—
153C4×Q8×C13D411yescharacteristic, complemented
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—
161C4×D4×C13—21no—
162C4×D4×C13D411yescharacteristic, complemented
163C4×D4×C13D411yescharacteristic, complemented
164C4×D4×C13D411yescharacteristic, complemented
165C13×#117—21no—
166C13×#117—21no—
167C2×C13×C4⋊C4—21no—
168C2×C13×C4⋊C4—21no—
169C2×C13×C4⋊C4—21no—
170C2×C13×C4⋊C4D411yescharacteristic
171C2×C13×C4⋊C4D411yescharacteristic
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
184C2×C42×C13—21no—
185C2×C42×C13C2311yescharacteristic
186C13×C4⋊C8—21no—
187C13×C4⋊C8—21no—
188C13×#103—21no—
189C13×#103—21no—
190C13×#103—21no—
191C13×#103—21no—
192C13×#102—21no—
193C13×#102—21no—
194C13×#102—21no—
195C13×#102—21no—
196C13×C22⋊C8C2311yescharacteristic
197C13×C22⋊C8C2311yescharacteristic
198C13×C22⋊C8C2311yescharacteristic
199C13×C22⋊C8C2311yescharacteristic
200C13×#97—21no—
201C4×C8×C13—21no—
202C13×#95—21no—
203C13×#95—21no—
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#18434C1311yesmaximal, 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×C13—21no—
217C2×Q8×C13—21no—
218C2×Q8×C13—81no—
219C2×Q8×C13C2×D411yescharacteristic
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—21no—
232C2×D4×C13—21no—
233C2×D4×C13—21no—
234C2×D4×C13—42no—
235C2×D4×C13—81no—
236C2×D4×C13—81no—
237C2×D4×C13—81no—
238C2×D4×C13—81no—
239C2×D4×C13—81no—
240C2×D4×C13C2×D411yescharacteristic
241C2×D4×C13C2×D411yescharacteristic
242C2×D4×C13C2×D411yescharacteristic
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—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13C2×D411yescharacteristic
255C22×C4×C13C2×D411yescharacteristic
256C22×C4×C13C2×D411yescharacteristic
257C22×C4×C13C2×D411yescharacteristic
258C22×C4×C13C2×D411yescharacteristic
259C22×C4×C13C2411yescharacteristic
260C13×Q16—81no—
261C13×SD16—81no—
262C13×SD16—81no—
263C13×SD16—81no—
264C13×SD16—81no—
265C13×D8—81no—
266C13×D8—81no—
267C13×D8—81no—
268C2×C8×C13—21no—
269C2×C8×C13—21no—
270C2×C8×C13—21no—
271C2×C8×C13—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—42no—
290C13×C4⋊C4—81no—
291C13×C4⋊C4C2×D411yescharacteristic
292C13×C4⋊C4C2×D411yescharacteristic
293C13×C4⋊C4C2×D411yescharacteristic
294C13×C4⋊C4C2×D411yescharacteristic
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—21no—
319C13×C22⋊C4—21no—
320C13×C22⋊C4—42no—
321C13×C22⋊C4—41no—
322C13×C22⋊C4—41no—
323C13×C22⋊C4—41no—
324C13×C22⋊C4—41no—
325C13×C22⋊C4—81no—
326C13×C22⋊C4—81no—
327C13×C22⋊C4—81no—
328C42×C13—21no—
329C42×C13—21no—
330C42×C13—21no—
331C42×C13—81no—
332C42×C13C2×D411yescharacteristic
333C42×C13C2×D411yescharacteristic
334C42×C13C2×D411yescharacteristic
335C42×C13C2×D411yescharacteristic
336#3560C2×C1311yescharacteristic, complemented
337#3213C2×C1311yescharacteristic, complemented
338#3211C2×C1311yescharacteristic, complemented
339#2662C2×C1311yescharacteristic, complemented
340#1606C2×C1311yescharacteristic, complemented
341#1604C2×C1311yescharacteristic, complemented
342#1603C2×C1311yescharacteristic, complemented
343#1601C2×C1311yescharacteristic, complemented
344#1600C2×C1311yescharacteristic, complemented
345#1598C2×C1311yescharacteristic, complemented
346#1597C2×C1311yescharacteristic, complemented
347#1595C2×C1311yescharacteristic, complemented
348#1509C2×C1311yescharacteristic, complemented
349#1502C2×C1311yescharacteristic, complemented
350#1473C2×C1311yescharacteristic, complemented
351C23×C13—21no—
352C23×C13—21no—
353C23×C13—21no—
354C23×C13—21no—
355C23×C13—21no—
356C23×C13—21no—
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—81no—
367C23×C13—81no—
368C23×C13—81no—
369C23×C13C22×D411yescharacteristic
370Q8×C13—41no—
371Q8×C13—41no—
372Q8×C13—41no—
373Q8×C13—41no—
374Q8×C13—41no—
375Q8×C13—81no—
376Q8×C13—81no—
377D4×C13—41no—
378D4×C13—41no—
379D4×C13—41no—
380D4×C13—41no—
381D4×C13—41no—
382D4×C13—41no—
383D4×C13—41no—
384D4×C13—41no—
385D4×C13—41no—
386D4×C13—41no—
387D4×C13—41no—
388D4×C13—41no—
389D4×C13—41no—
390D4×C13—81no—
391D4×C13—81no—
392D4×C13—81no—
393D4×C13—81no—
394D4×C13—81no—
395D4×C13—81no—
396D4×C13—81no—
397D4×C13—81no—
398D4×C13—81no—
399D4×C13—84no—
400C2×C4×C13—21no—
401C2×C4×C13—21no—
402C2×C4×C13—22no—
403C2×C4×C13—21no—
404C2×C4×C13—21no—
405C2×C4×C13—21no—
406C2×C4×C13—21no—
407C2×C4×C13—21no—
408C2×C4×C13—21no—
409C2×C4×C13—21no—
410C2×C4×C13—21no—
411C2×C4×C13—21no—
412C2×C4×C13—21no—
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—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—81no—
426C2×C4×C13—81no—
427C2×C4×C13—81no—
428C2×C4×C13—81no—
429C2×C4×C13—81no—
430C2×C4×C13—81no—
431C2×C4×C13—81no—
432C2×C4×C13—81no—
433C2×C4×C13#12011yescharacteristic
434C2×C4×C13#12011yescharacteristic
435C2×C4×C13#12011yescharacteristic
436C2×C4×C13#12011yescharacteristic
437C2×C4×C13C22×D411yescharacteristic
438C2×C4×C13C22×D411yescharacteristic
439C8×C13—41no—
440C8×C13—41no—
441C8×C13—41no—
442C8×C13—41no—
443#563—21no—
444#560—21no—
445#553—21no—
446#553—21no—
447#551—21no—
448#547—21no—
449#546—21no—
450#546—21no—
451#542—21no—
452#539—21no—
453#539C22×C1311yescharacteristic
454#538—21no—
455#538—21no—
456#538C22×C1311yescharacteristic
457#537C22×C1311yescharacteristic
458#534C22×C1311yescharacteristic
459#532C22×C1311yescharacteristic
460#529C22×C1311yescharacteristic
461C2×#126C22×C1311yescharacteristic
462C2×#124C22×C1311yescharacteristic, complemented
463#496—21no—
464#495—21no—
465#489—21no—
466#488—21no—
467#464—21no—
468#463—21no—
469#463—21no—
470#463—21no—
471#451C22×C1311yescharacteristic, complemented
472#450C22×C1311yescharacteristic, complemented
473#448C22×C1311yescharacteristic
474#448C22×C1311yescharacteristic
475#448C22×C1311yescharacteristic, complemented
476#447C22×C1311yescharacteristic
477#447C22×C1311yescharacteristic
478#447C22×C1311yescharacteristic, complemented
479#432C22×C1311yescharacteristic, complemented
480#431C22×C1311yescharacteristic, complemented
481#396—21no—
482#395C22×C1311yescharacteristic, complemented
483#394—21no—
484#394C22×C1311yescharacteristic, complemented
485#393C22×C1311yescharacteristic
486#392C22×C1311yescharacteristic
487#390—21no—
488#388—21no—
489C4×C4⋊C4C22×C1311yescharacteristic, complemented
490#328C22×C1311yescharacteristic, complemented
491#328C22×C1311yescharacteristic, complemented
492#327C22×C1311yescharacteristic
493#327C22×C1311yescharacteristic
494#327C22×C1311yescharacteristic
495#327C22×C1311yescharacteristic
496#327C22×C1311yescharacteristic, complemented
497#327C22×C1311yescharacteristic, complemented
498#324C22×C1311yescharacteristic, complemented
499#324C22×C1311yescharacteristic, complemented
500#323C22×C1311yescharacteristic
501#323C22×C1311yescharacteristic
502C22×C13—21no—
503C22×C13—21no—
504C22×C13—41no—
505C22×C13—41no—
506C22×C13—41no—
507C22×C13—41no—
508C22×C13—41no—
509C22×C13—41no—
510C22×C13—41no—
511C22×C13—41no—
512C22×C13—41no—
513C22×C13—41no—
514C22×C13—41no—
515C22×C13—41no—
516C22×C13—81no—
517C22×C13—81no—
518C22×C13—81no—
519C22×C13—81no—
520C22×C13—81no—
521C22×C13—81no—
522C22×C13—81no—
523C22×C13—81no—
524C22×C13—81no—
525C22×C13—162no—
526C22×C13C2×#12011yescharacteristic
527C22×C13#57611yescharacteristic
528C22×C13#57711yescharacteristic
529C4×C13—21no—
530C4×C13—21no—
531C4×C13—21no—
532C4×C13—21no—
533C4×C13—21no—
534C4×C13—21no—
535C4×C13—42no—
536C4×C13—41no—
537C4×C13—41no—
538C4×C13—41no—
539C4×C13—41no—
540C4×C13—41no—
541C4×C13—41no—
542C4×C13—41no—
543C4×C13—41no—
544C4×C13—81no—
545C4×C13—81no—
546C2×#41—21no—
547C2×#41—21no—
548C22×Q8C23×C1311yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4C23×C1311yescharacteristic
552C2×Q16—21no—
553C2×SD16—21no—
554C2×SD16—21no—
555C2×SD16—21no—
556C2×SD16—21no—
557C2×D8—21no—
558C2×D8—21no—
559C2×D8—21no—
560C4⋊Q8—21no—
561C4⋊Q8D4×C1311yescharacteristic, complemented
562#127D4×C1311yescharacteristic, complemented
563#126—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125D4×C1311yescharacteristic, complemented
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#124—21no—
583#124D4×C1311yescharacteristic, complemented
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8C23×C1311yescharacteristic
604#121—21no—
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#121—21no—
614#121—21no—
615#121—21no—
616#121C23×C1311yescharacteristic
617#121C23×C1311yescharacteristic
618#121C23×C1311yescharacteristic
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×Q8D4×C1311yescharacteristic, complemented
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4D4×C1311yescharacteristic, complemented
634C4×D4D4×C1311yescharacteristic, complemented
635C4×D4D4×C1311yescharacteristic, complemented
636#117—21no—
637#117—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4D4×C1311yescharacteristic
642C2×C4⋊C4D4×C1311yescharacteristic
643C2×C4⋊C4C23×C1311yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4D4×C1311yescharacteristic
653C2×C22⋊C4D4×C1311yescharacteristic
654C2×C22⋊C4C23×C1311yescharacteristic
655C2×C42—21no—
656C2×C42C23×C1311yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#102—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667C22⋊C8C23×C1311yescharacteristic
668C22⋊C8C23×C1311yescharacteristic
669C22⋊C8C23×C1311yescharacteristic
670C22⋊C8C23×C1311yescharacteristic
671#97—21no—
672C4×C8—21no—
673#95—21no—
674#95—21no—
675#95C23×C1311yescharacteristic
676#95C23×C1311yescharacteristic
677C2×C13—21no—
678C2×C13—21no—
679C2×C13—81no—
680C2×C13—81no—
681C2×C13—81no—
682C2×C13—81no—
683C2×C13—161no—
684C2×C13#301211yescharacteristic
685C2×C13#301811yescharacteristic
686C2×C13#302711yescharacteristic
687C24—21no—
688C24—21no—
689C24C2×D4×C1311yescharacteristic
690#41—81no—
691#41—81no—
692#41—81no—
693#41—81no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—81no—
699C2×Q8C2×D4×C1311yescharacteristic
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—42no—
715C2×D4—81no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4C2×D4×C1311yescharacteristic
721C2×D4C2×D4×C1311yescharacteristic
722C2×D4C2×D4×C1311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4C2×D4×C1311yescharacteristic
735C22×C4C2×D4×C1311yescharacteristic
736C22×C4C2×D4×C1311yescharacteristic
737C22×C4C2×D4×C1311yescharacteristic
738C22×C4C2×D4×C1311yescharacteristic
739C22×C4C24×C1311yescharacteristic
740Q16—81no—
741SD16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745D8—81no—
746D8—81no—
747D8—81no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—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—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—42no—
770C4⋊C4—81no—
771C4⋊C4C2×D4×C1311yescharacteristic
772C4⋊C4C2×D4×C1311yescharacteristic
773C4⋊C4C2×D4×C1311yescharacteristic
774C4⋊C4C2×D4×C1311yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—42no—
801C22⋊C4—41no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C42—21no—
809C42—21no—
810C42—21no—
811C42—81no—
812C42C2×D4×C1311yescharacteristic
813C42C2×D4×C1311yescharacteristic
814C42C2×D4×C1311yescharacteristic
815C42C2×D4×C1311yescharacteristic
816C13#1843411yescharacteristic, direct product factor, Sylow
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C1311yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4C13×#12011yescharacteristic
900C2×C4C13×#12011yescharacteristic
901C2×C4C13×#12011yescharacteristic
902C2×C4C13×#12011yescharacteristic
903C2×C4C22×D4×C1311yescharacteristic
904C2×C4C22×D4×C1311yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×C13×#12011yescharacteristic
934C22C13×#57611yescharacteristic
935C22C13×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C13×#301211yescharacteristic
961C2C13×#301811yescharacteristic
962C2C13×#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×#3213C2semidirect
3. C13×#3211C2semidirect
4. C13×#2662C2semidirect
5. C13×#1606C2semidirect
6. C13×#1604C2semidirect
7. C13×#1603C2semidirect
8. C13×#1601C2semidirect
9. C13×#1600C2semidirect
10. C13×#1598C2semidirect
11. C13×#1597C2semidirect
12. C13×#1595C2semidirect
13. C13×#1509C2semidirect
14. C13×#1502C2semidirect
15. C13×#1473C2semidirect
35. C2×C13×#124C22semidirect
44. C13×#451C22semidirect
45. C13×#450C22semidirect
48. C13×#448C22semidirect
51. C13×#447C22semidirect
52. C13×#432C22semidirect
53. C13×#431C22semidirect
55. C13×#395C22semidirect
57. C13×#394C22semidirect
62. C4×C13×C4⋊C4C22semidirect
63. C13×#328C22semidirect
64. C13×#328C22semidirect
69. C13×#327C22semidirect
70. C13×#327C22semidirect
71. C13×#324C22semidirect
72. C13×#324C22semidirect
90. C13×C4⋊Q8D4semidirect
91. C13×#127D4semidirect
103. C13×#125D4semidirect
112. C13×#124D4semidirect
153. C4×Q8×C13D4semidirect
162. C4×D4×C13D4semidirect
163. C4×D4×C13D4semidirect
164. C4×D4×C13D4semidirect
206. #18434C13direct (N × H)
336. #3560C2×C13semidirect
337. #3213C2×C13semidirect
338. #3211C2×C13semidirect
339. #2662C2×C13semidirect
340. #1606C2×C13semidirect
341. #1604C2×C13semidirect
342. #1603C2×C13semidirect
343. #1601C2×C13semidirect
344. #1600C2×C13semidirect
345. #1598C2×C13semidirect
346. #1597C2×C13semidirect
347. #1595C2×C13semidirect
348. #1509C2×C13semidirect
349. #1502C2×C13semidirect
350. #1473C2×C13semidirect
462. C2×#124C22×C13semidirect
471. #451C22×C13semidirect
472. #450C22×C13semidirect
475. #448C22×C13semidirect
478. #447C22×C13semidirect
479. #432C22×C13semidirect
480. #431C22×C13semidirect
482. #395C22×C13semidirect
484. #394C22×C13semidirect
489. C4×C4⋊C4C22×C13semidirect
490. #328C22×C13semidirect
491. #328C22×C13semidirect
496. #327C22×C13semidirect
497. #327C22×C13semidirect
498. #324C22×C13semidirect
499. #324C22×C13semidirect
561. C4⋊Q8D4×C13semidirect
562. #127D4×C13semidirect
574. #125D4×C13semidirect
583. #124D4×C13semidirect
624. C4×Q8D4×C13semidirect
633. C4×D4D4×C13semidirect
634. C4×D4D4×C13semidirect
635. C4×D4D4×C13semidirect
816. C13#18434direct (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×#32132
C13×#32112
C13×#26622
C13×#16062
C13×#16042
C13×#16032
C13×#16012
C13×#16002
C13×#15982
C13×#15972
C13×#15952
C13×#15092
C13×#15022
C13×#14732
#1843413