Finite Group Databasebeta

← C13×#18265 #15704604

Subgroups — C13×#18265 #15704604

Order 3328.

1124 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3537C211yesmaximal, characteristic
2C13×#3092C211yesmaximal, characteristic, complemented
3C2×C13×#481C211yesmaximal, characteristic, complemented
4C13×#2501C211yesmaximal, characteristic, complemented
5C13×#1618C214yesmaximal, complemented
6C13×#1613C214yesmaximal, complemented
7C13×#1507C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic, complemented
9C13×#1471C211yesmaximal, characteristic, complemented
10C13×#560—22no—
11C13×#553—21no—
12C13×#553—21no—
13D42×C13—22no—
14D42×C13—21no—
15D42×C13—21no—
16C13×#540—21no—
17C13×#538—21no—
18C13×#538C2212yes—
19C13×#535—21no—
20C13×#534—21no—
21C13×#534C2212yes—
22C13×#525C2211yescharacteristic
23C2×C13×#123—22no—
24C2×C13×#121C2211yescharacteristic
25C2×C13×#121C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic, complemented
27C13×#484C2212yescomplemented
28C13×#483—21no—
29C13×#481—22no—
30C13×#481C2214yescomplemented
31C13×#481C2212yescomplemented
32C13×#480—21no—
33C13×#428—21no—
34C2×C13×#106—21no—
35C13×#417—21no—
36C2×C13×#102—21no—
37C13×#407C2211yescharacteristic, complemented
38C2×C13×C22⋊C8C2211yescharacteristic, complemented
39C13×#399C2214yescomplemented
40C13×#390—21no—
41C13×#384—21no—
42C4×C13×C22⋊C4C2211yescharacteristic, complemented
43C13×#328C2212yescomplemented
44C13×#327C2212yescomplemented
45C13×#327C2214yescomplemented
46C13×#323C2214yescomplemented
47C2×C13×#41D411yescharacteristic
48C22×D4×C13—22no—
49C22×D4×C13—21no—
50C22×D4×C13—21no—
51C22×D4×C13—22no—
52C22×D4×C13D411yescharacteristic
53C22×D4×C13D412yes—
54C22×D4×C13D411yescharacteristic
55C23×C4×C13—21no—
56C23×C4×C13C2311yescharacteristic
57C2×C13×M16—21no—
58C22×C8×C13—21no—
59C13×#127—22no—
60C13×#127—21no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#125—21no—
64C13×#124—22no—
65C13×#123—22no—
66C13×#123—21no—
67C13×#123—22no—
68C13×#123—22no—
69C13×#123—22no—
70C13×#123—48no—
71C13×C22⋊Q8D411yescharacteristic
72C13×C22⋊Q8C2311yescharacteristic
73C13×#121—22no—
74C13×#121—21no—
75C13×#121—21no—
76C13×#121—22no—
77C13×#121—22no—
78C13×#121—22no—
79C13×#121—22no—
80C13×#121—21no—
81C13×#121—21no—
82C13×#121—21no—
83C13×#121—21no—
84C13×#121—21no—
85C13×#121—21no—
86C13×#121—22no—
87C13×#121D411yescharacteristic
88C13×#121D412yes—
89C13×#121C2312yes—
90C13×#121C2311yescharacteristic
91C13×#120—22no—
92C13×#120—22no—
93C13×#120—22no—
94C13×#120—21no—
95C13×#120—22no—
96C13×#120—22no—
97C13×#120—22no—
98C4×D4×C13—22no—
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13—22no—
104C13×#117—21no—
105C13×#117D411yescharacteristic
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4C2312yes—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4C2312yes—
119C2×C42×C13—21no—
120C13×#107—22no—
121C13×#106—24no—
122C13×#106—22no—
123C13×#103—22no—
124C13×#102—24no—
125C13×#102—22no—
126C13×C22⋊C8—21no—
127C13×C22⋊C8—21no—
128C13×C22⋊C8C2312yes—
129C13×C22⋊C8C2312yes—
130C13×#95C2312yes—
131#18265C1311yesmaximal, characteristic, direct product factor, Sylow
132C24×C13—22no—
133C24×C13—21no—
134C24×C13C2×D411yescharacteristic
135C24×C13C2×D412yes—
136C13×#41—42no—
137C2×Q8×C13C2×D411yescharacteristic
138C2×D4×C13—22no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—42no—
154C2×D4×C13—42no—
155C2×D4×C13—44no—
156C2×D4×C13—82no—
157C2×D4×C13—82no—
158C2×D4×C13—84no—
159C2×D4×C13—84no—
160C2×D4×C13C2×D411yescharacteristic
161C2×D4×C13C2×D412yes—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—22no—
168C22×C4×C13—42no—
169C22×C4×C13—44no—
170C22×C4×C13—41no—
171C22×C4×C13—41no—
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2411yescharacteristic
179C13×M16—42no—
180C2×C8×C13—22no—
181C2×C8×C13—22no—
182C2×C8×C13—42no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—48no—
193C13×C4⋊C4—41no—
194C13×C4⋊C4—41no—
195C13×C4⋊C4C2×D412yes—
196C13×C4⋊C4C2×D411yescharacteristic
197C13×C4⋊C4C2×D411yescharacteristic
198C13×C22⋊C4—24no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—21no—
206C13×C22⋊C4—21no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—21no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—21no—
213C13×C22⋊C4—48no—
214C42×C13—22no—
215C42×C13—21no—
216C42×C13—42no—
217#3537C2×C1311yescharacteristic
218#3092C2×C1311yescharacteristic, complemented
219C2×#481C2×C1311yescharacteristic, complemented
220#2501C2×C1311yescharacteristic, complemented
221#1618C2×C1314yescomplemented
222#1613C2×C1314yescomplemented
223#1507C2×C1311yescharacteristic, complemented
224#1501C2×C1311yescharacteristic, complemented
225#1471C2×C1311yescharacteristic, complemented
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—21no—
231C23×C13—24no—
232C23×C13—41no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—42no—
236C23×C13—81no—
237C23×C13—81no—
238C23×C13—82no—
239C23×C13—82no—
240C23×C13—82no—
241C23×C13#12011yescharacteristic
242C23×C13#12011yescharacteristic
243C23×C13C22×D411yescharacteristic
244Q8×C13—41no—
245D4×C13—42no—
246D4×C13—41no—
247D4×C13—44no—
248D4×C13—42no—
249D4×C13—44no—
250D4×C13—42no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—81no—
254D4×C13—82no—
255D4×C13—82no—
256D4×C13—81no—
257D4×C13—82no—
258D4×C13—82no—
259D4×C13—82no—
260D4×C13—82no—
261D4×C13—82no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—24no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—44no—
279C2×C4×C13—42no—
280C2×C4×C13—81no—
281C2×C4×C13—82no—
282C2×C4×C13—82no—
283C2×C4×C13—82no—
284C2×C4×C13—82no—
285C2×C4×C13#12011yescharacteristic
286C2×C4×C13#12011yescharacteristic
287C2×C4×C13C22×D411yescharacteristic
288C2×C4×C13C22×D411yescharacteristic
289C8×C13—42no—
290C8×C13—42no—
291#560—22no—
292#553—21no—
293#553—21no—
294D42—22no—
295D42—21no—
296D42—21no—
297#540—21no—
298#538—21no—
299#538C22×C1312yes—
300#535—21no—
301#534—21no—
302#534C22×C1312yes—
303#525C22×C1311yescharacteristic
304C2×#123—22no—
305C2×#121C22×C1311yescharacteristic
306C2×#121C22×C1311yescharacteristic
307C22×C4⋊C4C22×C1311yescharacteristic, complemented
308#484C22×C1312yescomplemented
309#483—21no—
310#481—22no—
311#481C22×C1314yescomplemented
312#481C22×C1312yescomplemented
313#480—21no—
314#428—21no—
315C2×#106—21no—
316#417—21no—
317C2×#102—21no—
318#407C22×C1311yescharacteristic, complemented
319C2×C22⋊C8C22×C1311yescharacteristic, complemented
320#399C22×C1314yescomplemented
321#390—21no—
322#384—21no—
323C4×C22⋊C4C22×C1311yescharacteristic, complemented
324#328C22×C1312yescomplemented
325#327C22×C1312yescomplemented
326#327C22×C1314yescomplemented
327#323C22×C1314yescomplemented
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—44no—
336C22×C13—42no—
337C22×C13—42no—
338C22×C13—41no—
339C22×C13—42no—
340C22×C13—42no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—84no—
346C22×C13—162no—
347C22×C13—164no—
348C22×C13#45312yes—
349C22×C13C2×#12011yescharacteristic
350C22×C13#57712yes—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—44no—
355C4×C13—42no—
356C4×C13—41no—
357C4×C13—42no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—82no—
361C4×C13#45812yes—
362C2×#41D4×C1311yescharacteristic
363C22×D4—22no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4D4×C1312yes—
368C22×D4D4×C1311yescharacteristic
369C22×D4D4×C1311yescharacteristic
370C23×C4—21no—
371C23×C4C23×C1311yescharacteristic
372C2×M16—21no—
373C22×C8—21no—
374#127—22no—
375#127—21no—
376#126—22no—
377#126—22no—
378#125—21no—
379#124—22no—
380#123—22no—
381#123—21no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—48no—
386C22⋊Q8D4×C1311yescharacteristic
387C22⋊Q8C23×C1311yescharacteristic
388#121—22no—
389#121—21no—
390#121—21no—
391#121—22no—
392#121—22no—
393#121—22no—
394#121—22no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—22no—
402#121D4×C1312yes—
403#121D4×C1311yescharacteristic
404#121C23×C1312yes—
405#121C23×C1311yescharacteristic
406#120—22no—
407#120—22no—
408#120—22no—
409#120—21no—
410#120—22no—
411#120—22no—
412#120—22no—
413C4×D4—22no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—22no—
419#117—21no—
420#117D4×C1311yescharacteristic
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4D4×C1311yescharacteristic
428C2×C4⋊C4D4×C1311yescharacteristic
429C2×C4⋊C4C23×C1312yes—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4C23×C1312yes—
434C2×C42—21no—
435#107—22no—
436#106—24no—
437#106—22no—
438#103—22no—
439#102—24no—
440#102—22no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8C23×C1312yes—
444C22⋊C8C23×C1312yes—
445#95C23×C1312yes—
446C2×C13—22no—
447C2×C13—22no—
448C2×C13—41no—
449C2×C13—82no—
450C2×C13—82no—
451C2×C13—81no—
452C2×C13#300911yescharacteristic
453C2×C13C2×#45311yescharacteristic
454C2×C13C2×#45811yescharacteristic
455C24—22no—
456C24—21no—
457C24C2×D4×C1311yescharacteristic
458C24C2×D4×C1312yes—
459#41—42no—
460C2×Q8C2×D4×C1311yescharacteristic
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—44no—
479C2×D4—82no—
480C2×D4—82no—
481C2×D4—84no—
482C2×D4—84no—
483C2×D4C2×D4×C1311yescharacteristic
484C2×D4C2×D4×C1312yes—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4C2×D4×C1311yescharacteristic
496C22×C4C2×D4×C1311yescharacteristic
497C22×C4C2×D4×C1311yescharacteristic
498C22×C4C2×D4×C1312yes—
499C22×C4C2×D4×C1311yescharacteristic
500C22×C4C2×D4×C1311yescharacteristic
501C22×C4C24×C1311yescharacteristic
502M16—42no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—42no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—48no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4C2×D4×C1312yes—
519C4⋊C4C2×D4×C1311yescharacteristic
520C4⋊C4C2×D4×C1311yescharacteristic
521C22⋊C4—24no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—48no—
537C42—22no—
538C42—21no—
539C42—42no—
540C13#1826511yescharacteristic, direct product factor, Sylow
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—21no—
546C23—24no—
547C23—41no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—81no—
552C23—81no—
553C23—82no—
554C23—82no—
555C23—82no—
556C23C13×#12011yescharacteristic
557C23C13×#12011yescharacteristic
558C23C22×D4×C1311yescharacteristic
559Q8—41no—
560D4—42no—
561D4—41no—
562D4—44no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—81no—
569D4—82no—
570D4—82no—
571D4—81no—
572D4—82no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—44no—
594C2×C4—42no—
595C2×C4—81no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4C13×#12011yescharacteristic
601C2×C4C13×#12011yescharacteristic
602C2×C4C22×D4×C1311yescharacteristic
603C2×C4C22×D4×C1311yescharacteristic
604C8—42no—
605C8—42no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—44no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—42no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—84no—
624C22—162no—
625C22—164no—
626C22C13×#45312yes—
627C22C2×C13×#12011yescharacteristic
628C22C13×#57712yes—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—42no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—82no—
639C4C13×#45812yes—
640C2—22no—
641C2—22no—
642C2—41no—
643C2—82no—
644C2—82no—
645C2—81no—
646C2C13×#300911yescharacteristic
647C2C2×C13×#45311yescharacteristic
648C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3537C2
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×#3092C2semidirect
3. C2×C13×#481C2semidirect
4. C13×#2501C2semidirect
5. C13×#1618C2semidirect
6. C13×#1613C2semidirect
7. C13×#1507C2semidirect
8. C13×#1501C2semidirect
9. C13×#1471C2semidirect
26. C22×C13×C4⋊C4C22semidirect
27. C13×#484C22semidirect
30. C13×#481C22semidirect
31. C13×#481C22semidirect
37. C13×#407C22semidirect
38. C2×C13×C22⋊C8C22semidirect
39. C13×#399C22semidirect
42. C4×C13×C22⋊C4C22semidirect
43. C13×#328C22semidirect
44. C13×#327C22semidirect
45. C13×#327C22semidirect
46. C13×#323C22semidirect
131. #18265C13direct (N × H)
218. #3092C2×C13semidirect
219. C2×#481C2×C13semidirect
220. #2501C2×C13semidirect
221. #1618C2×C13semidirect
222. #1613C2×C13semidirect
223. #1507C2×C13semidirect
224. #1501C2×C13semidirect
225. #1471C2×C13semidirect
307. C22×C4⋊C4C22×C13semidirect
308. #484C22×C13semidirect
311. #481C22×C13semidirect
312. #481C22×C13semidirect
318. #407C22×C13semidirect
319. C2×C22⋊C8C22×C13semidirect
320. #399C22×C13semidirect
323. C4×C22⋊C4C22×C13semidirect
324. #328C22×C13semidirect
325. #327C22×C13semidirect
326. #327C22×C13semidirect
327. #323C22×C13semidirect
540. C13#18265direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35372
C13×#30922
C2×C13×#4812
C13×#25012
C13×#16182
C13×#16132
C13×#15072
C13×#15012
C13×#14712
#1826513