Finite Group Databasebeta

← C13×#18446 #15704785

Subgroups — C13×#18446 #15704785

Order 3328.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3534C211yesmaximal, characteristic, complemented
2C13×#3192C211yesmaximal, characteristic, complemented
3C13×#3188C211yesmaximal, characteristic, complemented
4C13×#2813C211yesmaximal, characteristic, complemented
5C13×#1618C211yesmaximal, characteristic, complemented
6C13×#1616C211yesmaximal, characteristic, complemented
7C13×#1615C211yesmaximal, characteristic, complemented
8C13×#1613C211yesmaximal, characteristic, complemented
9C13×#1600C211yesmaximal, characteristic, complemented
10C13×#1598C211yesmaximal, characteristic, complemented
11C13×#1597C211yesmaximal, characteristic, complemented
12C13×#1595C211yesmaximal, characteristic, complemented
13C13×#1519C211yesmaximal, characteristic, complemented
14C13×#1513C211yesmaximal, characteristic, complemented
15C13×#1468C211yesmaximal, characteristic, complemented
16C13×#562—21no—
17C13×#560—21no—
18C13×#553—21no—
19C13×#551—21no—
20C13×#546—21no—
21C13×#546—21no—
22C13×#546—21no—
23D42×C13—21no—
24C13×#540—21no—
25C13×#539—21no—
26C13×#539C2211yescharacteristic
27C13×#538—21no—
28C13×#538C2211yescharacteristic
29C13×#537C2211yescharacteristic
30C13×#534—21no—
31C13×#534C2211yescharacteristic
32C13×#525C2211yescharacteristic
33C2×C13×#123C2211yescharacteristic
34C2×C13×#121C2211yescharacteristic
35C2×C13×#121C2211yescharacteristic, complemented
36C13×#484C2211yescharacteristic, complemented
37C13×#482—21no—
38C13×#481—21no—
39C13×#481C2211yescharacteristic
40C13×#481C2211yescharacteristic, complemented
41C13×#481C2211yescharacteristic, complemented
42C13×#469—21no—
43C13×#469—21no—
44C13×#466—21no—
45C13×#465—21no—
46C13×#450C2211yescharacteristic, complemented
47C13×#449—21no—
48C13×#447—21no—
49C13×#447C2211yescharacteristic
50C13×#447C2211yescharacteristic, complemented
51C13×#447C2211yescharacteristic, complemented
52C13×#407C2211yescharacteristic, complemented
53C2×C13×C22⋊C8C2211yescharacteristic, complemented
54C13×#400C2211yescharacteristic, complemented
55C13×#399C2211yescharacteristic, complemented
56C13×#396—21no—
57C13×#394—21no—
58C13×#394—21no—
59C13×#394C2211yescharacteristic, complemented
60C13×#392—21no—
61C13×#392C2211yescharacteristic, complemented
62C13×#380C2211yescharacteristic, complemented
63C13×#328C2211yescharacteristic, complemented
64C13×#328C2211yescharacteristic, complemented
65C13×#327C2211yescharacteristic
66C13×#327C2211yescharacteristic
67C13×#327C2211yescharacteristic, complemented
68C13×#327C2211yescharacteristic, complemented
69C13×#327C2211yescharacteristic, complemented
70C13×#327C2211yescharacteristic, complemented
71C13×#324C2211yescharacteristic, complemented
72C13×#324C2211yescharacteristic, complemented
73C13×#323C2211yescharacteristic, complemented
74C13×#323C2211yescharacteristic, complemented
75C2×C13×#41—21no—
76C2×C13×#41D411yescharacteristic, complemented
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13—21no—
82C22×D4×C13D411yescharacteristic
83C22×D4×C13D411yescharacteristic, complemented
84C22×D4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C2×C13×SD16—21no—
87C2×C13×D8—21no—
88C2×C13×D8—21no—
89C2×C13×D8—21no—
90C2×C13×M16—21no—
91C22×C8×C13—21no—
92C13×#127—21no—
93C13×#126—21no—
94C13×#126—21no—
95C13×#126—21no—
96C13×#126—21no—
97C13×#125—21no—
98C13×#125—21no—
99C13×#124—21no—
100C13×#124—21no—
101C13×#124—21no—
102C13×#123—21no—
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×#123—21no—
112C13×#123—21no—
113C13×#123—21no—
114C13×#123—21no—
115C13×#123—21no—
116C13×C22⋊Q8—21no—
117C13×C22⋊Q8—21no—
118C13×C22⋊Q8—21no—
119C13×C22⋊Q8—21no—
120C13×C22⋊Q8—21no—
121C13×C22⋊Q8D411yescharacteristic, complemented
122C13×C22⋊Q8C2311yescharacteristic
123C13×#121—21no—
124C13×#121—21no—
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×#121—21no—
138C13×#121—21no—
139C13×#121—21no—
140C13×#121—21no—
141C13×#121—21no—
142C13×#121D411yescharacteristic, complemented
143C13×#121D411yescharacteristic, complemented
144C13×#121D411yescharacteristic, complemented
145C13×#121C2311yescharacteristic
146C13×#121C2311yescharacteristic
147C13×#121C2311yescharacteristic
148C13×#120—21no—
149C13×#120—21no—
150C13×#120—21no—
151C13×#120—21no—
152C13×#120—21no—
153C13×#120—21no—
154C13×#120—21no—
155C13×#120—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×C13—21no—
163C4×D4×C13—21no—
164C13×#117—21no—
165C13×#117D411yescharacteristic, complemented
166C2×C13×C4⋊C4—21no—
167C2×C13×C4⋊C4—21no—
168C2×C13×C4⋊C4D411yescharacteristic
169C2×C13×C4⋊C4D411yescharacteristic, complemented
170C2×C13×C4⋊C4C2311yescharacteristic
171C2×C13×C4⋊C4C2311yescharacteristic
172C2×C13×C22⋊C4—21no—
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×#106—21no—
186C13×#106—21no—
187C13×#106—21no—
188C13×#103—21no—
189C13×#102—21no—
190C13×#102—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#18446C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C24×C13—21no—
210C24×C13C2×D411yescharacteristic
211C24×C13C2×D411yescharacteristic
212C13×#41—81no—
213C13×#41—81no—
214C13×#41—81no—
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—21no—
232C2×D4×C13—21no—
233C2×D4×C13—21no—
234C2×D4×C13—21no—
235C2×D4×C13—21no—
236C2×D4×C13—41no—
237C2×D4×C13—41no—
238C2×D4×C13—81no—
239C2×D4×C13—81no—
240C2×D4×C13—81no—
241C2×D4×C13—81no—
242C2×D4×C13—81no—
243C2×D4×C13—81no—
244C2×D4×C13—81no—
245C2×D4×C13—81no—
246C2×D4×C13—81no—
247C2×D4×C13—81no—
248C2×D4×C13—81no—
249C2×D4×C13—81no—
250C2×D4×C13—82no—
251C2×D4×C13C2×D411yescharacteristic
252C2×D4×C13C2×D411yescharacteristic
253C2×D4×C13C2×D411yescharacteristic
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—81no—
265C22×C4×C13C2×D411yescharacteristic
266C22×C4×C13C2×D411yescharacteristic
267C22×C4×C13C2×D411yescharacteristic
268C22×C4×C13C2×D411yescharacteristic
269C22×C4×C13C2×D411yescharacteristic
270C22×C4×C13C2×D411yescharacteristic
271C22×C4×C13C2×D411yescharacteristic
272C22×C4×C13C2×D411yescharacteristic
273C22×C4×C13C2411yescharacteristic
274C13×SD16—81no—
275C13×D8—81no—
276C13×D8—81no—
277C13×D8—81no—
278C13×M16—81no—
279C2×C8×C13—21no—
280C2×C8×C13—21no—
281C2×C8×C13—21no—
282C2×C8×C13—21no—
283C2×C8×C13—81no—
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—21no—
294C13×C4⋊C4—21no—
295C13×C4⋊C4—21no—
296C13×C4⋊C4—21no—
297C13×C4⋊C4—21no—
298C13×C4⋊C4—21no—
299C13×C4⋊C4—81no—
300C13×C4⋊C4—81no—
301C13×C4⋊C4C2×D411yescharacteristic
302C13×C4⋊C4C2×D411yescharacteristic
303C13×C4⋊C4C2×D411yescharacteristic
304C13×C4⋊C4C2×D411yescharacteristic
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—21no—
323C13×C22⋊C4—21no—
324C13×C22⋊C4—21no—
325C13×C22⋊C4—21no—
326C13×C22⋊C4—21no—
327C13×C22⋊C4—21no—
328C13×C22⋊C4—21no—
329C13×C22⋊C4—21no—
330C13×C22⋊C4—41no—
331C13×C22⋊C4—41no—
332C13×C22⋊C4—81no—
333C13×C22⋊C4—81no—
334C13×C22⋊C4—81no—
335C13×C22⋊C4—81no—
336C13×C22⋊C4—81no—
337C42×C13—21no—
338C42×C13—21no—
339C42×C13—21no—
340#3534C2×C1311yescharacteristic, complemented
341#3192C2×C1311yescharacteristic, complemented
342#3188C2×C1311yescharacteristic, complemented
343#2813C2×C1311yescharacteristic, complemented
344#1618C2×C1311yescharacteristic, complemented
345#1616C2×C1311yescharacteristic, complemented
346#1615C2×C1311yescharacteristic, complemented
347#1613C2×C1311yescharacteristic, complemented
348#1600C2×C1311yescharacteristic, complemented
349#1598C2×C1311yescharacteristic, complemented
350#1597C2×C1311yescharacteristic, complemented
351#1595C2×C1311yescharacteristic, complemented
352#1519C2×C1311yescharacteristic, complemented
353#1513C2×C1311yescharacteristic, complemented
354#1468C2×C1311yescharacteristic, complemented
355C23×C13—21no—
356C23×C13—21no—
357C23×C13—21no—
358C23×C13—21no—
359C23×C13—21no—
360C23×C13—21no—
361C23×C13—21no—
362C23×C13—21no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—42no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—81no—
376C23×C13—81no—
377C23×C13—81no—
378C23×C13—81no—
379C23×C13—81no—
380C23×C13#12011yescharacteristic
381C23×C13#12011yescharacteristic
382C23×C13C22×D411yescharacteristic
383Q8×C13—41no—
384Q8×C13—81no—
385D4×C13—41no—
386D4×C13—41no—
387D4×C13—41no—
388D4×C13—41no—
389D4×C13—41no—
390D4×C13—41no—
391D4×C13—41no—
392D4×C13—42no—
393D4×C13—42no—
394D4×C13—41no—
395D4×C13—41no—
396D4×C13—41no—
397D4×C13—41no—
398D4×C13—41no—
399D4×C13—41no—
400D4×C13—81no—
401D4×C13—81no—
402D4×C13—81no—
403D4×C13—81no—
404D4×C13—81no—
405D4×C13—81no—
406D4×C13—81no—
407D4×C13—81no—
408D4×C13—81no—
409D4×C13—81no—
410D4×C13—81no—
411D4×C13—81no—
412D4×C13—82no—
413D4×C13—82no—
414D4×C13—84no—
415C2×C4×C13—21no—
416C2×C4×C13—21no—
417C2×C4×C13—21no—
418C2×C4×C13—21no—
419C2×C4×C13—21no—
420C2×C4×C13—21no—
421C2×C4×C13—21no—
422C2×C4×C13—21no—
423C2×C4×C13—21no—
424C2×C4×C13—21no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—81no—
443C2×C4×C13—81no—
444C2×C4×C13—81no—
445C2×C4×C13—81no—
446C2×C4×C13—81no—
447C2×C4×C13—81no—
448C2×C4×C13—81no—
449C2×C4×C13#12011yescharacteristic
450C2×C4×C13#12011yescharacteristic
451C2×C4×C13C22×D411yescharacteristic
452C2×C4×C13C22×D411yescharacteristic
453C8×C13—41no—
454C8×C13—41no—
455C8×C13—41no—
456C8×C13—41no—
457#562—21no—
458#560—21no—
459#553—21no—
460#551—21no—
461#546—21no—
462#546—21no—
463#546—21no—
464D42—21no—
465#540—21no—
466#539—21no—
467#539C22×C1311yescharacteristic
468#538—21no—
469#538C22×C1311yescharacteristic
470#537C22×C1311yescharacteristic
471#534—21no—
472#534C22×C1311yescharacteristic
473#525C22×C1311yescharacteristic
474C2×#123C22×C1311yescharacteristic
475C2×#121C22×C1311yescharacteristic
476C2×#121C22×C1311yescharacteristic, complemented
477#484C22×C1311yescharacteristic, complemented
478#482—21no—
479#481—21no—
480#481C22×C1311yescharacteristic
481#481C22×C1311yescharacteristic, complemented
482#481C22×C1311yescharacteristic, complemented
483#469—21no—
484#469—21no—
485#466—21no—
486#465—21no—
487#450C22×C1311yescharacteristic, complemented
488#449—21no—
489#447—21no—
490#447C22×C1311yescharacteristic
491#447C22×C1311yescharacteristic, complemented
492#447C22×C1311yescharacteristic, complemented
493#407C22×C1311yescharacteristic, complemented
494C2×C22⋊C8C22×C1311yescharacteristic, complemented
495#400C22×C1311yescharacteristic, complemented
496#399C22×C1311yescharacteristic, complemented
497#396—21no—
498#394—21no—
499#394—21no—
500#394C22×C1311yescharacteristic, complemented
501#392—21no—
502#392C22×C1311yescharacteristic, complemented
503#380C22×C1311yescharacteristic, complemented
504#328C22×C1311yescharacteristic, complemented
505#328C22×C1311yescharacteristic, complemented
506#327C22×C1311yescharacteristic
507#327C22×C1311yescharacteristic
508#327C22×C1311yescharacteristic, complemented
509#327C22×C1311yescharacteristic, complemented
510#327C22×C1311yescharacteristic, complemented
511#327C22×C1311yescharacteristic, complemented
512#324C22×C1311yescharacteristic, complemented
513#324C22×C1311yescharacteristic, complemented
514#323C22×C1311yescharacteristic, complemented
515#323C22×C1311yescharacteristic, complemented
516C22×C13—21no—
517C22×C13—21no—
518C22×C13—21no—
519C22×C13—21no—
520C22×C13—21no—
521C22×C13—21no—
522C22×C13—21no—
523C22×C13—21no—
524C22×C13—41no—
525C22×C13—41no—
526C22×C13—41no—
527C22×C13—41no—
528C22×C13—41no—
529C22×C13—41no—
530C22×C13—41no—
531C22×C13—41no—
532C22×C13—41no—
533C22×C13—41no—
534C22×C13—41no—
535C22×C13—41no—
536C22×C13—81no—
537C22×C13—81no—
538C22×C13—81no—
539C22×C13—81no—
540C22×C13—81no—
541C22×C13—81no—
542C22×C13—81no—
543C22×C13—81no—
544C22×C13—81no—
545C22×C13—81no—
546C22×C13—81no—
547C22×C13—162no—
548C22×C13—162no—
549C22×C13C2×#12011yescharacteristic
550C22×C13#57611yescharacteristic
551C22×C13#57711yescharacteristic
552C4×C13—21no—
553C4×C13—21no—
554C4×C13—21no—
555C4×C13—21no—
556C4×C13—41no—
557C4×C13—41no—
558C4×C13—41no—
559C4×C13—41no—
560C4×C13—41no—
561C4×C13—41no—
562C4×C13—41no—
563C4×C13—41no—
564C4×C13—81no—
565C4×C13—81no—
566C4×C13—81no—
567C2×#41—21no—
568C2×#41D4×C1311yescharacteristic, complemented
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4D4×C1311yescharacteristic
575C22×D4D4×C1311yescharacteristic, complemented
576C22×D4C23×C1311yescharacteristic
577C23×C4C23×C1311yescharacteristic
578C2×SD16—21no—
579C2×D8—21no—
580C2×D8—21no—
581C2×D8—21no—
582C2×M16—21no—
583C22×C8—21no—
584#127—21no—
585#126—21no—
586#126—21no—
587#126—21no—
588#126—21no—
589#125—21no—
590#125—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607#123—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8D4×C1311yescharacteristic, complemented
614C22⋊Q8C23×C1311yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121D4×C1311yescharacteristic, complemented
635#121D4×C1311yescharacteristic, complemented
636#121D4×C1311yescharacteristic, complemented
637#121C23×C1311yescharacteristic
638#121C23×C1311yescharacteristic
639#121C23×C1311yescharacteristic
640#120—21no—
641#120—21no—
642#120—21no—
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656#117—21no—
657#117D4×C1311yescharacteristic, complemented
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4D4×C1311yescharacteristic
661C2×C4⋊C4D4×C1311yescharacteristic, complemented
662C2×C4⋊C4C23×C1311yescharacteristic
663C2×C4⋊C4C23×C1311yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4D4×C1311yescharacteristic
674C2×C22⋊C4D4×C1311yescharacteristic
675C2×C22⋊C4C23×C1311yescharacteristic
676#107—21no—
677#106—21no—
678#106—21no—
679#106—21no—
680#103—21no—
681#102—21no—
682#102—21no—
683#102—21no—
684#102—21no—
685#102—21no—
686#102—21no—
687#102—21no—
688C22⋊C8—21no—
689C22⋊C8—21no—
690C22⋊C8C23×C1311yescharacteristic
691C22⋊C8C23×C1311yescharacteristic
692C22⋊C8C23×C1311yescharacteristic
693C22⋊C8C23×C1311yescharacteristic
694#95—21no—
695#95—21no—
696#95C23×C1311yescharacteristic
697#95C23×C1311yescharacteristic
698C2×C13—21no—
699C2×C13—21no—
700C2×C13—41no—
701C2×C13—41no—
702C2×C13—81no—
703C2×C13—81no—
704C2×C13—81no—
705C2×C13—81no—
706C2×C13—161no—
707C2×C13#301211yescharacteristic
708C2×C13#302111yescharacteristic
709C2×C13#302611yescharacteristic
710C24—21no—
711C24—21no—
712C24—21no—
713C24C2×D4×C1311yescharacteristic
714C24C2×D4×C1311yescharacteristic
715#41—81no—
716#41—81no—
717#41—81no—
718C2×Q8—21no—
719C2×Q8C2×D4×C1311yescharacteristic
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—82no—
754C2×D4C2×D4×C1311yescharacteristic
755C2×D4C2×D4×C1311yescharacteristic
756C2×D4C2×D4×C1311yescharacteristic
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—81no—
768C22×C4C2×D4×C1311yescharacteristic
769C22×C4C2×D4×C1311yescharacteristic
770C22×C4C2×D4×C1311yescharacteristic
771C22×C4C2×D4×C1311yescharacteristic
772C22×C4C2×D4×C1311yescharacteristic
773C22×C4C2×D4×C1311yescharacteristic
774C22×C4C2×D4×C1311yescharacteristic
775C22×C4C2×D4×C1311yescharacteristic
776C22×C4C24×C1311yescharacteristic
777SD16—81no—
778D8—81no—
779D8—81no—
780D8—81no—
781M16—81no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—81no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—81no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C1311yescharacteristic
805C4⋊C4C2×D4×C1311yescharacteristic
806C4⋊C4C2×D4×C1311yescharacteristic
807C4⋊C4C2×D4×C1311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—41no—
834C22⋊C4—41no—
835C22⋊C4—81no—
836C22⋊C4—81no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C13#1844611yescharacteristic, direct product factor, Sylow
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23C13×#12011yescharacteristic
870C23C13×#12011yescharacteristic
871C23C22×D4×C1311yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—82no—
902D4—82no—
903D4—84no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4C13×#12011yescharacteristic
939C2×C4C13×#12011yescharacteristic
940C2×C4C22×D4×C1311yescharacteristic
941C2×C4C22×D4×C1311yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×C13×#12011yescharacteristic
980C22C13×#57611yescharacteristic
981C22C13×#57711yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C13×#301211yescharacteristic
1007C2C13×#302111yescharacteristic
1008C2C13×#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×#3534C2semidirect
2. C13×#3192C2semidirect
3. C13×#3188C2semidirect
4. C13×#2813C2semidirect
5. C13×#1618C2semidirect
6. C13×#1616C2semidirect
7. C13×#1615C2semidirect
8. C13×#1613C2semidirect
9. C13×#1600C2semidirect
10. C13×#1598C2semidirect
11. C13×#1597C2semidirect
12. C13×#1595C2semidirect
13. C13×#1519C2semidirect
14. C13×#1513C2semidirect
15. C13×#1468C2semidirect
35. C2×C13×#121C22semidirect
36. C13×#484C22semidirect
40. C13×#481C22semidirect
41. C13×#481C22semidirect
46. C13×#450C22semidirect
50. C13×#447C22semidirect
51. C13×#447C22semidirect
52. C13×#407C22semidirect
53. C2×C13×C22⋊C8C22semidirect
54. C13×#400C22semidirect
55. C13×#399C22semidirect
59. C13×#394C22semidirect
61. C13×#392C22semidirect
62. C13×#380C22semidirect
63. C13×#328C22semidirect
64. C13×#328C22semidirect
67. C13×#327C22semidirect
68. C13×#327C22semidirect
69. C13×#327C22semidirect
70. C13×#327C22semidirect
71. C13×#324C22semidirect
72. C13×#324C22semidirect
73. C13×#323C22semidirect
74. C13×#323C22semidirect
76. C2×C13×#41D4semidirect
83. C22×D4×C13D4semidirect
121. C13×C22⋊Q8D4semidirect
142. C13×#121D4semidirect
143. C13×#121D4semidirect
144. C13×#121D4semidirect
165. C13×#117D4semidirect
169. C2×C13×C4⋊C4D4semidirect
206. #18446C13direct (N × H)
340. #3534C2×C13semidirect
341. #3192C2×C13semidirect
342. #3188C2×C13semidirect
343. #2813C2×C13semidirect
344. #1618C2×C13semidirect
345. #1616C2×C13semidirect
346. #1615C2×C13semidirect
347. #1613C2×C13semidirect
348. #1600C2×C13semidirect
349. #1598C2×C13semidirect
350. #1597C2×C13semidirect
351. #1595C2×C13semidirect
352. #1519C2×C13semidirect
353. #1513C2×C13semidirect
354. #1468C2×C13semidirect
476. C2×#121C22×C13semidirect
477. #484C22×C13semidirect
481. #481C22×C13semidirect
482. #481C22×C13semidirect
487. #450C22×C13semidirect
491. #447C22×C13semidirect
492. #447C22×C13semidirect
493. #407C22×C13semidirect
494. C2×C22⋊C8C22×C13semidirect
495. #400C22×C13semidirect
496. #399C22×C13semidirect
500. #394C22×C13semidirect
502. #392C22×C13semidirect
503. #380C22×C13semidirect
504. #328C22×C13semidirect
505. #328C22×C13semidirect
508. #327C22×C13semidirect
509. #327C22×C13semidirect
510. #327C22×C13semidirect
511. #327C22×C13semidirect
512. #324C22×C13semidirect
513. #324C22×C13semidirect
514. #323C22×C13semidirect
515. #323C22×C13semidirect
568. C2×#41D4×C13semidirect
575. C22×D4D4×C13semidirect
613. C22⋊Q8D4×C13semidirect
634. #121D4×C13semidirect
635. #121D4×C13semidirect
636. #121D4×C13semidirect
657. #117D4×C13semidirect
661. C2×C4⋊C4D4×C13semidirect
843. C13#18446direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35342
C13×#31922
C13×#31882
C13×#28132
C13×#16182
C13×#16162
C13×#16152
C13×#16132
C13×#16002
C13×#15982
C13×#15972
C13×#15952
C13×#15192
C13×#15132
C13×#14682
#1844613