Finite Group Databasebeta

← C13×#18264 #15704603

Subgroups — C13×#18264 #15704603

Order 3328.

1068 conjugacy classes of subgroups.

The subgroup lattice has 646 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×#480C211yesmaximal, characteristic, complemented
4C13×#2504C211yesmaximal, characteristic, complemented
5C13×#1612C214yesmaximal, complemented
6C13×#1607C214yesmaximal, 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×#121C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic, complemented
26C13×#484—21no—
27C13×#483C2212yescomplemented
28C13×#481—21no—
29C13×#480—22no—
30C13×#480C2214yescomplemented
31C13×#480C2212yescomplemented
32C13×#428—21no—
33C2×C13×#107—21no—
34C13×#417—21no—
35C2×C13×#102—21no—
36C13×#407C2211yescharacteristic, complemented
37C2×C13×C22⋊C8C2211yescharacteristic, complemented
38C13×#397C2214yescomplemented
39C13×#390—21no—
40C13×#386—22no—
41C13×#382—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×C13D412yes—
53C22×D4×C13D411yescharacteristic
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×C22⋊Q8D411yescharacteristic
71C13×C22⋊Q8C2311yescharacteristic
72C13×#121—22no—
73C13×#121—21no—
74C13×#121—21no—
75C13×#121—22no—
76C13×#121—22no—
77C13×#121—22no—
78C13×#121—22no—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—21no—
82C13×#121—21no—
83C13×#121—21no—
84C13×#121—21no—
85C13×#121—22no—
86C13×#121D412yes—
87C13×#121D411yescharacteristic
88C13×#121C2312yes—
89C13×#121C2311yescharacteristic
90C13×#120—22no—
91C13×#120—22no—
92C13×#120—22no—
93C13×#120—21no—
94C13×#120—22no—
95C13×#120—22no—
96C13×#120—22no—
97C4×D4×C13—22no—
98C4×D4×C13—21no—
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—22no—
103C13×#117—21no—
104C13×#117D411yescharacteristic
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4C2312yes—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4C2312yes—
117C2×C42×C13—21no—
118C13×#107—24no—
119C13×#107—22no—
120C13×#106—22no—
121C13×#103—22no—
122C13×#102—24no—
123C13×#102—22no—
124C13×C22⋊C8—21no—
125C13×C22⋊C8—21no—
126C13×C22⋊C8C2312yes—
127C13×C22⋊C8C2312yes—
128C13×#95—24no—
129C13×#95C2312yes—
130#18264C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—22no—
132C24×C13—21no—
133C24×C13C2×D411yescharacteristic
134C24×C13C2×D412yes—
135C13×#41—42no—
136C2×Q8×C13C2×D411yescharacteristic
137C2×D4×C13—22no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—21no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—42no—
153C2×D4×C13—42no—
154C2×D4×C13—44no—
155C2×D4×C13—82no—
156C2×D4×C13—82no—
157C2×D4×C13—84no—
158C2×D4×C13—84no—
159C2×D4×C13C2×D411yescharacteristic
160C2×D4×C13C2×D412yes—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—42no—
168C22×C4×C13—41no—
169C22×C4×C13—41no—
170C22×C4×C13—82no—
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2411yescharacteristic
178C13×M16—42no—
179C2×C8×C13—22no—
180C2×C8×C13—22no—
181C2×C8×C13—42no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—41no—
192C13×C4⋊C4—41no—
193C13×C4⋊C4C2×D411yescharacteristic
194C13×C4⋊C4C2×D412yes—
195C13×C4⋊C4C2×D411yescharacteristic
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—21no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—21no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—21no—
210C13×C22⋊C4—42no—
211C13×C22⋊C4—84no—
212C42×C13—22no—
213C42×C13—21no—
214C42×C13—42no—
215#3537C2×C1311yescharacteristic
216#3092C2×C1311yescharacteristic, complemented
217C2×#480C2×C1311yescharacteristic, complemented
218#2504C2×C1311yescharacteristic, complemented
219#1612C2×C1314yescomplemented
220#1607C2×C1314yescomplemented
221#1507C2×C1311yescharacteristic, complemented
222#1501C2×C1311yescharacteristic, complemented
223#1471C2×C1311yescharacteristic, complemented
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—21no—
229C23×C13—24no—
230C23×C13—41no—
231C23×C13—42no—
232C23×C13—42no—
233C23×C13—42no—
234C23×C13—81no—
235C23×C13—81no—
236C23×C13—82no—
237C23×C13—82no—
238C23×C13—82no—
239C23×C13#12011yescharacteristic
240C23×C13#12011yescharacteristic
241C23×C13C22×D411yescharacteristic
242Q8×C13—41no—
243D4×C13—42no—
244D4×C13—41no—
245D4×C13—44no—
246D4×C13—42no—
247D4×C13—44no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—42no—
251D4×C13—81no—
252D4×C13—82no—
253D4×C13—82no—
254D4×C13—81no—
255D4×C13—82no—
256D4×C13—82no—
257D4×C13—82no—
258D4×C13—82no—
259D4×C13—82no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—42no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—44no—
278C2×C4×C13—81no—
279C2×C4×C13—82no—
280C2×C4×C13—82no—
281C2×C4×C13—82no—
282C2×C4×C13—82no—
283C2×C4×C13#12011yescharacteristic
284C2×C4×C13#12011yescharacteristic
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C22×D411yescharacteristic
287C8×C13—42no—
288C8×C13—42no—
289#560—22no—
290#553—21no—
291#553—21no—
292D42—22no—
293D42—21no—
294D42—21no—
295#540—21no—
296#538—21no—
297#538C22×C1312yes—
298#535—21no—
299#534—21no—
300#534C22×C1312yes—
301#525C22×C1311yescharacteristic
302C2×#121C22×C1311yescharacteristic
303C2×#121C22×C1311yescharacteristic
304C22×C4⋊C4C22×C1311yescharacteristic, complemented
305#484—21no—
306#483C22×C1312yescomplemented
307#481—21no—
308#480—22no—
309#480C22×C1314yescomplemented
310#480C22×C1312yescomplemented
311#428—21no—
312C2×#107—21no—
313#417—21no—
314C2×#102—21no—
315#407C22×C1311yescharacteristic, complemented
316C2×C22⋊C8C22×C1311yescharacteristic, complemented
317#397C22×C1314yescomplemented
318#390—21no—
319#386—22no—
320#382—21no—
321C4×C22⋊C4C22×C1311yescharacteristic, complemented
322#328C22×C1312yescomplemented
323#327C22×C1312yescomplemented
324#327C22×C1314yescomplemented
325#323C22×C1314yescomplemented
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—44no—
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—41no—
337C22×C13—42no—
338C22×C13—42no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—42no—
342C22×C13—42no—
343C22×C13—84no—
344C22×C13—162no—
345C22×C13—164no—
346C22×C13#45512yes—
347C22×C13C2×#12011yescharacteristic
348C22×C13#57612yes—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—42no—
353C4×C13—41no—
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—82no—
358C4×C13—82no—
359C4×C13#45812yes—
360C2×#41D4×C1311yescharacteristic
361C22×D4—22no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—22no—
365C22×D4D4×C1312yes—
366C22×D4D4×C1311yescharacteristic
367C22×D4D4×C1311yescharacteristic
368C23×C4—21no—
369C23×C4C23×C1311yescharacteristic
370C2×M16—21no—
371C22×C8—21no—
372#127—22no—
373#127—21no—
374#126—22no—
375#126—22no—
376#125—21no—
377#124—22no—
378#123—22no—
379#123—21no—
380#123—22no—
381#123—22no—
382#123—22no—
383C22⋊Q8D4×C1311yescharacteristic
384C22⋊Q8C23×C1311yescharacteristic
385#121—22no—
386#121—21no—
387#121—21no—
388#121—22no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—22no—
399#121D4×C1312yes—
400#121D4×C1311yescharacteristic
401#121C23×C1312yes—
402#121C23×C1311yescharacteristic
403#120—22no—
404#120—22no—
405#120—22no—
406#120—21no—
407#120—22no—
408#120—22no—
409#120—22no—
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—22no—
416#117—21no—
417#117D4×C1311yescharacteristic
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4D4×C1311yescharacteristic
424C2×C4⋊C4D4×C1311yescharacteristic
425C2×C4⋊C4C23×C1312yes—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4C23×C1312yes—
430C2×C42—21no—
431#107—24no—
432#107—22no—
433#106—22no—
434#103—22no—
435#102—24no—
436#102—22no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8C23×C1312yes—
440C22⋊C8C23×C1312yes—
441#95—24no—
442#95C23×C1312yes—
443C2×C13—22no—
444C2×C13—22no—
445C2×C13—41no—
446C2×C13—82no—
447C2×C13—82no—
448C2×C13—81no—
449C2×C13#300811yescharacteristic
450C2×C13C2×#45511yescharacteristic
451C2×C13C2×#45811yescharacteristic
452C24—22no—
453C24—21no—
454C24C2×D4×C1311yescharacteristic
455C24C2×D4×C1312yes—
456#41—42no—
457C2×Q8C2×D4×C1311yescharacteristic
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—82no—
477C2×D4—82no—
478C2×D4—84no—
479C2×D4—84no—
480C2×D4C2×D4×C1311yescharacteristic
481C2×D4C2×D4×C1312yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—82no—
492C22×C4C2×D4×C1311yescharacteristic
493C22×C4C2×D4×C1311yescharacteristic
494C22×C4C2×D4×C1311yescharacteristic
495C22×C4C2×D4×C1312yes—
496C22×C4C2×D4×C1311yescharacteristic
497C22×C4C2×D4×C1311yescharacteristic
498C22×C4C24×C1311yescharacteristic
499M16—42no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—42no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4C2×D4×C1311yescharacteristic
515C4⋊C4C2×D4×C1312yes—
516C4⋊C4C2×D4×C1311yescharacteristic
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—42no—
532C22⋊C4—84no—
533C42—22no—
534C42—21no—
535C42—42no—
536C13#1826411yescharacteristic, direct product factor, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—21no—
542C23—24no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23C13×#12011yescharacteristic
553C23C13×#12011yescharacteristic
554C23C22×D4×C1311yescharacteristic
555Q8—41no—
556D4—42no—
557D4—41no—
558D4—44no—
559D4—42no—
560D4—44no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—81no—
565D4—82no—
566D4—82no—
567D4—81no—
568D4—82no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4—82no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—44no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4C13×#12011yescharacteristic
597C2×C4C13×#12011yescharacteristic
598C2×C4C22×D4×C1311yescharacteristic
599C2×C4C22×D4×C1311yescharacteristic
600C8—42no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—41no—
617C22—42no—
618C22—42no—
619C22—84no—
620C22—162no—
621C22—164no—
622C22C13×#45512yes—
623C22C2×C13×#12011yescharacteristic
624C22C13×#57612yes—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—82no—
634C4—82no—
635C4C13×#45812yes—
636C2—22no—
637C2—22no—
638C2—41no—
639C2—82no—
640C2—82no—
641C2—81no—
642C2C13×#300811yescharacteristic
643C2C2×C13×#45511yescharacteristic
644C2C2×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×#480C2semidirect
4. C13×#2504C2semidirect
5. C13×#1612C2semidirect
6. C13×#1607C2semidirect
7. C13×#1507C2semidirect
8. C13×#1501C2semidirect
9. C13×#1471C2semidirect
25. C22×C13×C4⋊C4C22semidirect
27. C13×#483C22semidirect
30. C13×#480C22semidirect
31. C13×#480C22semidirect
36. C13×#407C22semidirect
37. C2×C13×C22⋊C8C22semidirect
38. C13×#397C22semidirect
42. C4×C13×C22⋊C4C22semidirect
43. C13×#328C22semidirect
44. C13×#327C22semidirect
45. C13×#327C22semidirect
46. C13×#323C22semidirect
130. #18264C13direct (N × H)
216. #3092C2×C13semidirect
217. C2×#480C2×C13semidirect
218. #2504C2×C13semidirect
219. #1612C2×C13semidirect
220. #1607C2×C13semidirect
221. #1507C2×C13semidirect
222. #1501C2×C13semidirect
223. #1471C2×C13semidirect
304. C22×C4⋊C4C22×C13semidirect
306. #483C22×C13semidirect
309. #480C22×C13semidirect
310. #480C22×C13semidirect
315. #407C22×C13semidirect
316. C2×C22⋊C8C22×C13semidirect
317. #397C22×C13semidirect
321. C4×C22⋊C4C22×C13semidirect
322. #328C22×C13semidirect
323. #327C22×C13semidirect
324. #327C22×C13semidirect
325. #323C22×C13semidirect
536. C13#18264direct (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×#4802
C13×#25042
C13×#16122
C13×#16072
C13×#15072
C13×#15012
C13×#14712
#1826413