Finite Group Databasebeta

← C13×#18447 #15704786

Subgroups — C13×#18447 #15704786

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3534C211yesmaximal, characteristic
2C13×#3193C211yesmaximal, characteristic, complemented
3C13×#3190C211yesmaximal, characteristic, complemented
4C13×#2814C211yesmaximal, characteristic, complemented
5C13×#1612C211yesmaximal, characteristic, complemented
6C13×#1610C211yesmaximal, characteristic, complemented
7C13×#1609C211yesmaximal, characteristic, complemented
8C13×#1607C211yesmaximal, characteristic, complemented
9C13×#1606C211yesmaximal, characteristic, complemented
10C13×#1604C211yesmaximal, characteristic, complemented
11C13×#1603C211yesmaximal, characteristic, complemented
12C13×#1601C211yesmaximal, 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×C22⋊Q8C2211yescharacteristic, complemented
35C2×C13×#121C2211yescharacteristic
36C13×#485—21no—
37C13×#484—21no—
38C13×#483C2211yescharacteristic, complemented
39C13×#480C2211yescharacteristic
40C13×#480C2211yescharacteristic, complemented
41C13×#480C2211yescharacteristic, complemented
42C13×#468—21no—
43C13×#468—21no—
44C13×#467—21no—
45C13×#465—21no—
46C13×#452—21no—
47C13×#451C2211yescharacteristic, complemented
48C13×#450—21no—
49C13×#448C2211yescharacteristic
50C13×#448C2211yescharacteristic, complemented
51C13×#448C2211yescharacteristic, complemented
52C13×#407C2211yescharacteristic, complemented
53C2×C13×C22⋊C8C2211yescharacteristic, complemented
54C13×#398—21no—
55C13×#398C2211yescharacteristic, complemented
56C13×#397—21no—
57C13×#397C2211yescharacteristic, complemented
58C13×#396—21no—
59C13×#395C2211yescharacteristic, complemented
60C13×#394—21no—
61C13×#393C2211yescharacteristic, 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
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13D411yescharacteristic
82C22×D4×C13D411yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C2×C13×Q16—21no—
85C2×C13×SD16—21no—
86C2×C13×SD16—21no—
87C2×C13×SD16—21no—
88C2×C13×M16—21no—
89C22×C8×C13—21no—
90C13×#127—21no—
91C13×#126—21no—
92C13×#126—21no—
93C13×#126—21no—
94C13×#126—21no—
95C13×#125—21no—
96C13×#125—21no—
97C13×#124—21no—
98C13×#124—21no—
99C13×#124—21no—
100C13×#123—21no—
101C13×#123—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×C22⋊Q8—21no—
115C13×C22⋊Q8—21no—
116C13×C22⋊Q8—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⋊Q8D411yescharacteristic
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×#121—21no—
138C13×#121—21no—
139C13×#121—21no—
140C13×#121D411yescharacteristic
141C13×#121D411yescharacteristic
142C13×#121D411yescharacteristic
143C13×#121C2311yescharacteristic
144C13×#121C2311yescharacteristic
145C13×#121C2311yescharacteristic
146C13×#120—21no—
147C13×#120—21no—
148C13×#120—21no—
149C13×#120—21no—
150C13×#120—21no—
151C13×#120—21no—
152C13×#120—21no—
153C13×#120—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—
161C4×D4×C13—21no—
162C13×#117—21no—
163C13×#117D411yescharacteristic
164C2×C13×C4⋊C4—21no—
165C2×C13×C4⋊C4—21no—
166C2×C13×C4⋊C4—21no—
167C2×C13×C4⋊C4—21no—
168C2×C13×C4⋊C4D411yescharacteristic
169C2×C13×C4⋊C4D411yescharacteristic
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⋊C4D411yescharacteristic
180C2×C13×C22⋊C4D411yescharacteristic
181C2×C13×C22⋊C4C2311yescharacteristic
182C13×#107—21no—
183C13×#107—21no—
184C13×#107—21no—
185C13×#106—21no—
186C13×#103—21no—
187C13×#103—21no—
188C13×#103—21no—
189C13×#103—21no—
190C13×#103—21no—
191C13×#102—21no—
192C13×#102—21no—
193C13×#102—21no—
194C13×C22⋊C8—21no—
195C13×C22⋊C8—21no—
196C13×C22⋊C8C2311yescharacteristic
197C13×C22⋊C8C2311yescharacteristic
198C13×C22⋊C8C2311yescharacteristic
199C13×C22⋊C8C2311yescharacteristic
200C13×#95—21no—
201C13×#95—21no—
202C13×#95—21no—
203C13×#95—21no—
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#18447C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C24×C13C2×D411yescharacteristic
210C24×C13C2×D411yescharacteristic
211C13×#41—81no—
212C13×#41—81no—
213C13×#41—81no—
214C2×Q8×C13—21no—
215C2×Q8×C13—21no—
216C2×Q8×C13—21no—
217C2×Q8×C13—81no—
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—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—81no—
237C2×D4×C13—81no—
238C2×D4×C13—81no—
239C2×D4×C13—81no—
240C2×D4×C13—81no—
241C2×D4×C13—81no—
242C2×D4×C13—82no—
243C2×D4×C13C2×D411yescharacteristic
244C2×D4×C13C2×D411yescharacteristic
245C2×D4×C13C2×D411yescharacteristic
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×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—81no—
258C22×C4×C13C2×D411yescharacteristic
259C22×C4×C13C2×D411yescharacteristic
260C22×C4×C13C2×D411yescharacteristic
261C22×C4×C13C2×D411yescharacteristic
262C22×C4×C13C2×D411yescharacteristic
263C22×C4×C13C2×D411yescharacteristic
264C22×C4×C13C2×D411yescharacteristic
265C22×C4×C13C2×D411yescharacteristic
266C22×C4×C13C2411yescharacteristic
267C13×Q16—81no—
268C13×SD16—81no—
269C13×SD16—81no—
270C13×SD16—81no—
271C13×M16—81no—
272C2×C8×C13—21no—
273C2×C8×C13—21no—
274C2×C8×C13—21no—
275C2×C8×C13—21no—
276C2×C8×C13—81no—
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—41no—
293C13×C4⋊C4—41no—
294C13×C4⋊C4—81no—
295C13×C4⋊C4—81no—
296C13×C4⋊C4—81no—
297C13×C4⋊C4C2×D411yescharacteristic
298C13×C4⋊C4C2×D411yescharacteristic
299C13×C4⋊C4C2×D411yescharacteristic
300C13×C4⋊C4C2×D411yescharacteristic
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—21no—
323C13×C22⋊C4—21no—
324C13×C22⋊C4—21no—
325C13×C22⋊C4—21no—
326C13×C22⋊C4—41no—
327C13×C22⋊C4—41no—
328C13×C22⋊C4—81no—
329C13×C22⋊C4—81no—
330C13×C22⋊C4—81no—
331C42×C13—21no—
332C42×C13—21no—
333C42×C13—21no—
334#3534C2×C1311yescharacteristic
335#3193C2×C1311yescharacteristic, complemented
336#3190C2×C1311yescharacteristic, complemented
337#2814C2×C1311yescharacteristic, complemented
338#1612C2×C1311yescharacteristic, complemented
339#1610C2×C1311yescharacteristic, complemented
340#1609C2×C1311yescharacteristic, complemented
341#1607C2×C1311yescharacteristic, complemented
342#1606C2×C1311yescharacteristic, complemented
343#1604C2×C1311yescharacteristic, complemented
344#1603C2×C1311yescharacteristic, complemented
345#1601C2×C1311yescharacteristic, complemented
346#1519C2×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—21no—
356C23×C13—21no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—42no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—81no—
363C23×C13—81no—
364C23×C13—81no—
365C23×C13—81no—
366C23×C13—81no—
367C23×C13#12011yescharacteristic
368C23×C13#12011yescharacteristic
369C23×C13C22×D411yescharacteristic
370Q8×C13—41no—
371Q8×C13—41no—
372Q8×C13—41no—
373Q8×C13—41no—
374Q8×C13—41no—
375Q8×C13—81no—
376D4×C13—41no—
377D4×C13—41no—
378D4×C13—41no—
379D4×C13—42no—
380D4×C13—42no—
381D4×C13—41no—
382D4×C13—41no—
383D4×C13—41no—
384D4×C13—41no—
385D4×C13—41no—
386D4×C13—41no—
387D4×C13—81no—
388D4×C13—81no—
389D4×C13—81no—
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—
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—21no—
406C2×C4×C13—21no—
407C2×C4×C13—21no—
408C2×C4×C13—21no—
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—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—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—81no—
430C2×C4×C13—81no—
431C2×C4×C13—81no—
432C2×C4×C13—81no—
433C2×C4×C13—81no—
434C2×C4×C13—81no—
435C2×C4×C13—81no—
436C2×C4×C13#12011yescharacteristic
437C2×C4×C13#12011yescharacteristic
438C2×C4×C13C22×D411yescharacteristic
439C2×C4×C13C22×D411yescharacteristic
440C8×C13—41no—
441C8×C13—41no—
442C8×C13—41no—
443C8×C13—41no—
444#562—21no—
445#560—21no—
446#553—21no—
447#551—21no—
448#546—21no—
449#546—21no—
450#546—21no—
451D42—21no—
452#540—21no—
453#539—21no—
454#539C22×C1311yescharacteristic
455#538—21no—
456#538C22×C1311yescharacteristic
457#537C22×C1311yescharacteristic
458#534—21no—
459#534C22×C1311yescharacteristic
460#525C22×C1311yescharacteristic
461C2×#123C22×C1311yescharacteristic
462C2×C22⋊Q8C22×C1311yescharacteristic, complemented
463C2×#121C22×C1311yescharacteristic
464#485—21no—
465#484—21no—
466#483C22×C1311yescharacteristic, complemented
467#480C22×C1311yescharacteristic
468#480C22×C1311yescharacteristic, complemented
469#480C22×C1311yescharacteristic, complemented
470#468—21no—
471#468—21no—
472#467—21no—
473#465—21no—
474#452—21no—
475#451C22×C1311yescharacteristic, complemented
476#450—21no—
477#448C22×C1311yescharacteristic
478#448C22×C1311yescharacteristic, complemented
479#448C22×C1311yescharacteristic, complemented
480#407C22×C1311yescharacteristic, complemented
481C2×C22⋊C8C22×C1311yescharacteristic, complemented
482#398—21no—
483#398C22×C1311yescharacteristic, complemented
484#397—21no—
485#397C22×C1311yescharacteristic, complemented
486#396—21no—
487#395C22×C1311yescharacteristic, complemented
488#394—21no—
489#393C22×C1311yescharacteristic, complemented
490#380C22×C1311yescharacteristic, complemented
491#328C22×C1311yescharacteristic, complemented
492#328C22×C1311yescharacteristic, complemented
493#327C22×C1311yescharacteristic
494#327C22×C1311yescharacteristic
495#327C22×C1311yescharacteristic, complemented
496#327C22×C1311yescharacteristic, complemented
497#327C22×C1311yescharacteristic, complemented
498#327C22×C1311yescharacteristic, complemented
499#324C22×C1311yescharacteristic, complemented
500#324C22×C1311yescharacteristic, complemented
501#323C22×C1311yescharacteristic, complemented
502#323C22×C1311yescharacteristic, complemented
503C22×C13—21no—
504C22×C13—21no—
505C22×C13—21no—
506C22×C13—21no—
507C22×C13—21no—
508C22×C13—21no—
509C22×C13—21no—
510C22×C13—21no—
511C22×C13—41no—
512C22×C13—41no—
513C22×C13—41no—
514C22×C13—41no—
515C22×C13—41no—
516C22×C13—41no—
517C22×C13—41no—
518C22×C13—41no—
519C22×C13—41no—
520C22×C13—41no—
521C22×C13—41no—
522C22×C13—41no—
523C22×C13—81no—
524C22×C13—81no—
525C22×C13—81no—
526C22×C13—81no—
527C22×C13—162no—
528C22×C13—162no—
529C22×C13C2×#12011yescharacteristic
530C22×C13#57611yescharacteristic
531C22×C13#57711yescharacteristic
532C4×C13—21no—
533C4×C13—21no—
534C4×C13—21no—
535C4×C13—21no—
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—
546C4×C13—81no—
547C4×C13—81no—
548C2×#41—21no—
549C2×#41D4×C1311yescharacteristic
550C22×Q8C23×C1311yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4D4×C1311yescharacteristic
555C22×D4D4×C1311yescharacteristic
556C23×C4C23×C1311yescharacteristic
557C2×Q16—21no—
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×M16—21no—
562C22×C8—21no—
563#127—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125—21no—
570#124—21no—
571#124—21no—
572#124—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—
585#123—21no—
586#123—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⋊Q8D4×C1311yescharacteristic
597C22⋊Q8C23×C1311yescharacteristic
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
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#121D4×C1311yescharacteristic
614#121D4×C1311yescharacteristic
615#121D4×C1311yescharacteristic
616#121C23×C1311yescharacteristic
617#121C23×C1311yescharacteristic
618#121C23×C1311yescharacteristic
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624#120—21no—
625#120—21no—
626#120—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635#117—21no—
636#117D4×C1311yescharacteristic
637C2×C4⋊C4—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×C4⋊C4C23×C1311yescharacteristic
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
655#107—21no—
656#107—21no—
657#107—21no—
658#106—21no—
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#103—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8C23×C1311yescharacteristic
670C22⋊C8C23×C1311yescharacteristic
671C22⋊C8C23×C1311yescharacteristic
672C22⋊C8C23×C1311yescharacteristic
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95C23×C1311yescharacteristic
678#95C23×C1311yescharacteristic
679C2×C13—21no—
680C2×C13—21no—
681C2×C13—41no—
682C2×C13—41no—
683C2×C13—81no—
684C2×C13—81no—
685C2×C13—81no—
686C2×C13—81no—
687C2×C13#301211yescharacteristic
688C2×C13#302211yescharacteristic
689C2×C13#302611yescharacteristic
690C24—21no—
691C24—21no—
692C24C2×D4×C1311yescharacteristic
693C24C2×D4×C1311yescharacteristic
694#41—81no—
695#41—81no—
696#41—81no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—81no—
701C2×Q8C2×D4×C1311yescharacteristic
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—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—82no—
726C2×D4C2×D4×C1311yescharacteristic
727C2×D4C2×D4×C1311yescharacteristic
728C2×D4C2×D4×C1311yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—81no—
741C22×C4C2×D4×C1311yescharacteristic
742C22×C4C2×D4×C1311yescharacteristic
743C22×C4C2×D4×C1311yescharacteristic
744C22×C4C2×D4×C1311yescharacteristic
745C22×C4C2×D4×C1311yescharacteristic
746C22×C4C2×D4×C1311yescharacteristic
747C22×C4C2×D4×C1311yescharacteristic
748C22×C4C2×D4×C1311yescharacteristic
749C22×C4C24×C1311yescharacteristic
750Q16—81no—
751SD16—81no—
752SD16—81no—
753SD16—81no—
754M16—81no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—81no—
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—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—41no—
776C4⋊C4—41no—
777C4⋊C4—81no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C1311yescharacteristic
781C4⋊C4C2×D4×C1311yescharacteristic
782C4⋊C4C2×D4×C1311yescharacteristic
783C4⋊C4C2×D4×C1311yescharacteristic
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—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—41no—
810C22⋊C4—41no—
811C22⋊C4—81no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C13#1844711yescharacteristic, direct product factor, Sylow
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23C13×#12011yescharacteristic
837C23C13×#12011yescharacteristic
838C23C22×D4×C1311yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
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—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
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—41no—
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—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4C13×#12011yescharacteristic
906C2×C4C13×#12011yescharacteristic
907C2×C4C22×D4×C1311yescharacteristic
908C2×C4C22×D4×C1311yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×C13×#12011yescharacteristic
940C22C13×#57611yescharacteristic
941C22C13×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C13×#301211yescharacteristic
967C2C13×#302211yescharacteristic
968C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3534C2
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
2. C13×#3193C2semidirect
3. C13×#3190C2semidirect
4. C13×#2814C2semidirect
5. C13×#1612C2semidirect
6. C13×#1610C2semidirect
7. C13×#1609C2semidirect
8. C13×#1607C2semidirect
9. C13×#1606C2semidirect
10. C13×#1604C2semidirect
11. C13×#1603C2semidirect
12. C13×#1601C2semidirect
13. C13×#1519C2semidirect
14. C13×#1513C2semidirect
15. C13×#1468C2semidirect
34. C2×C13×C22⋊Q8C22semidirect
38. C13×#483C22semidirect
40. C13×#480C22semidirect
41. C13×#480C22semidirect
47. C13×#451C22semidirect
50. C13×#448C22semidirect
51. C13×#448C22semidirect
52. C13×#407C22semidirect
53. C2×C13×C22⋊C8C22semidirect
55. C13×#398C22semidirect
57. C13×#397C22semidirect
59. C13×#395C22semidirect
61. C13×#393C22semidirect
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
206. #18447C13direct (N × H)
335. #3193C2×C13semidirect
336. #3190C2×C13semidirect
337. #2814C2×C13semidirect
338. #1612C2×C13semidirect
339. #1610C2×C13semidirect
340. #1609C2×C13semidirect
341. #1607C2×C13semidirect
342. #1606C2×C13semidirect
343. #1604C2×C13semidirect
344. #1603C2×C13semidirect
345. #1601C2×C13semidirect
346. #1519C2×C13semidirect
347. #1513C2×C13semidirect
348. #1468C2×C13semidirect
462. C2×C22⋊Q8C22×C13semidirect
466. #483C22×C13semidirect
468. #480C22×C13semidirect
469. #480C22×C13semidirect
475. #451C22×C13semidirect
478. #448C22×C13semidirect
479. #448C22×C13semidirect
480. #407C22×C13semidirect
481. C2×C22⋊C8C22×C13semidirect
483. #398C22×C13semidirect
485. #397C22×C13semidirect
487. #395C22×C13semidirect
489. #393C22×C13semidirect
490. #380C22×C13semidirect
491. #328C22×C13semidirect
492. #328C22×C13semidirect
495. #327C22×C13semidirect
496. #327C22×C13semidirect
497. #327C22×C13semidirect
498. #327C22×C13semidirect
499. #324C22×C13semidirect
500. #324C22×C13semidirect
501. #323C22×C13semidirect
502. #323C22×C13semidirect
817. C13#18447direct (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×#31932
C13×#31902
C13×#28142
C13×#16122
C13×#16102
C13×#16092
C13×#16072
C13×#16062
C13×#16042
C13×#16032
C13×#16012
C13×#15192
C13×#15132
C13×#14682
#1844713