Finite Group Databasebeta

← C13×#18267 #15704606

Subgroups — C13×#18267 #15704606

Order 3328.

1056 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3536C211yesmaximal, characteristic
2C13×#3092C211yesmaximal, characteristic, complemented
3C2×C13×#484C211yesmaximal, characteristic, complemented
4C13×#2501C211yesmaximal, characteristic, complemented
5C13×#1618C214yesmaximal, complemented
6C13×#1614C214yesmaximal, complemented
7C13×#1508C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic, complemented
9C13×#1471C211yesmaximal, characteristic, complemented
10C13×#562—22no—
11C13×#554—21no—
12C13×#548—21no—
13C13×#547—21no—
14C13×#546—22no—
15C13×#546—21no—
16C13×#543C2212yes—
17C13×#542—21no—
18C13×#539—21no—
19C13×#538C2212yes—
20C13×#537—21no—
21C13×#537—21no—
22C13×#525C2211yescharacteristic
23C2×C13×#123—22no—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×#121C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C13×#484—22no—
28C13×#484C2214yes—
29C13×#484C2212yes—
30C13×#483—21no—
31C13×#481C2212yes—
32C13×#480—21no—
33C13×#428—21no—
34C2×C13×#107—21no—
35C13×#417—21no—
36C2×C13×#103—21no—
37C13×#407C2211yescharacteristic
38C2×C13×C22⋊C8C2211yescharacteristic
39C13×#399C2214yes—
40C13×#390—21no—
41C13×#384—21no—
42C4×C13×C22⋊C4C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#323C2214yes—
47C2×C13×#41—22no—
48C2×C13×#41—21no—
49C2×C13×#41D411yescharacteristic
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13D411yescharacteristic
52C22×D4×C13D412yes—
53C23×C4×C13—21no—
54C23×C4×C13C2311yescharacteristic
55C2×C13×M16—21no—
56C22×C8×C13—21no—
57C13×C4⋊Q8—21no—
58C13×#126—22no—
59C13×#125—22no—
60C13×#124—21no—
61C13×#124—22no—
62C13×#124—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×#123—22no—
66C13×#123—21no—
67C13×#123—22no—
68C13×#123—48no—
69C13×C22⋊Q8—21no—
70C13×C22⋊Q8—22no—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8—22no—
73C13×C22⋊Q8—21no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8D411yescharacteristic
79C13×C22⋊Q8D412yes—
80C13×C22⋊Q8C2312yes—
81C13×C22⋊Q8C2311yescharacteristic
82C13×#121—21no—
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#121—22no—
87C13×#121—22no—
88C13×#121—21no—
89C13×#121—21no—
90C13×#121—21no—
91C13×#121—21no—
92C13×#121D411yescharacteristic
93C13×#121C2311yescharacteristic
94C13×#120—21no—
95C13×#120—22no—
96C4×Q8×C13—21no—
97C4×D4×C13—22no—
98C4×D4×C13—21no—
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13—22no—
102C13×#117D411yescharacteristic
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
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⋊C4—24no—
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4C2312yes—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—22no—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4C2312yes—
119C2×C42×C13—21no—
120C13×#107—24no—
121C13×#107—22no—
122C13×#106—22no—
123C13×#103—24no—
124C13×#103—22no—
125C13×#102—22no—
126C13×C22⋊C8—21no—
127C13×C22⋊C8—21no—
128C13×C22⋊C8C2312yes—
129C13×C22⋊C8C2312yes—
130C13×#95C2312yes—
131#18267C1311yesmaximal, characteristic, direct product factor, Sylow
132C24×C13C2×D411yescharacteristic
133C24×C13C2×D412yes—
134C13×#41—42no—
135C13×#41—84no—
136C13×#41—82no—
137C2×Q8×C13—22no—
138C2×Q8×C13—21no—
139C2×Q8×C13—42no—
140C2×Q8×C13C2×D411yescharacteristic
141C2×Q8×C13C2×D412yes—
142C2×D4×C13—21no—
143C2×D4×C13—22no—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—42no—
152C2×D4×C13—44no—
153C2×D4×C13C2×D411yescharacteristic
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—42no—
163C22×C4×C13—44no—
164C22×C4×C13—41no—
165C22×C4×C13—41no—
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2411yescharacteristic
173C13×M16—42no—
174C2×C8×C13—22no—
175C2×C8×C13—22no—
176C2×C8×C13—42no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—48no—
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—24no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—21no—
207C13×C22⋊C4—21no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—21no—
211C13×C22⋊C4—48no—
212C42×C13—22no—
213C42×C13—21no—
214C42×C13—42no—
215#3536C2×C1311yescharacteristic
216#3092C2×C1311yescharacteristic, complemented
217C2×#484C2×C1311yescharacteristic, complemented
218#2501C2×C1311yescharacteristic, complemented
219#1618C2×C1314yescomplemented
220#1614C2×C1314yescomplemented
221#1508C2×C1311yescharacteristic, complemented
222#1501C2×C1311yescharacteristic, complemented
223#1471C2×C1311yescharacteristic, complemented
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—21no—
228C23×C13—24no—
229C23×C13—41no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13#12011yescharacteristic
233C23×C13#12011yescharacteristic
234C23×C13C22×D411yescharacteristic
235Q8×C13—42no—
236Q8×C13—41no—
237Q8×C13—42no—
238Q8×C13—82no—
239D4×C13—41no—
240D4×C13—42no—
241D4×C13—44no—
242D4×C13—42no—
243D4×C13—42no—
244D4×C13—81no—
245D4×C13—82no—
246D4×C13—81no—
247D4×C13—82no—
248D4×C13—82no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—24no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—22no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—44no—
268C2×C4×C13—42no—
269C2×C4×C13—81no—
270C2×C4×C13—82no—
271C2×C4×C13—82no—
272C2×C4×C13—82no—
273C2×C4×C13—82no—
274C2×C4×C13—82no—
275C2×C4×C13#12011yescharacteristic
276C2×C4×C13#12011yescharacteristic
277C2×C4×C13C22×D411yescharacteristic
278C2×C4×C13C22×D411yescharacteristic
279C8×C13—42no—
280C8×C13—42no—
281#562—22no—
282#554—21no—
283#548—21no—
284#547—21no—
285#546—22no—
286#546—21no—
287#543C22×C1312yes—
288#542—21no—
289#539—21no—
290#538C22×C1312yes—
291#537—21no—
292#537—21no—
293#525C22×C1311yescharacteristic
294C2×#123—22no—
295C2×C22⋊Q8C22×C1311yescharacteristic
296C2×#121C22×C1311yescharacteristic
297C22×C4⋊C4C22×C1311yescharacteristic
298#484—22no—
299#484C22×C1314yes—
300#484C22×C1312yes—
301#483—21no—
302#481C22×C1312yes—
303#480—21no—
304#428—21no—
305C2×#107—21no—
306#417—21no—
307C2×#103—21no—
308#407C22×C1311yescharacteristic
309C2×C22⋊C8C22×C1311yescharacteristic
310#399C22×C1314yes—
311#390—21no—
312#384—21no—
313C4×C22⋊C4C22×C1311yescharacteristic
314#328C22×C1312yes—
315#328C22×C1314yes—
316#327C22×C1312yes—
317#323C22×C1314yes—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—44no—
326C22×C13—41no—
327C22×C13—42no—
328C22×C13—41no—
329C22×C13—42no—
330C22×C13—41no—
331C22×C13—42no—
332C22×C13—84no—
333C22×C13#45312yes—
334C22×C13C2×#12011yescharacteristic
335C22×C13#57812yes—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—44no—
340C4×C13—41no—
341C4×C13—42no—
342C4×C13—42no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—42no—
346C4×C13—82no—
347C4×C13#45812yes—
348C2×#41—22no—
349C2×#41—21no—
350C2×#41D4×C1311yescharacteristic
351C22×Q8D4×C1311yescharacteristic
352C22×D4D4×C1312yes—
353C22×D4D4×C1311yescharacteristic
354C23×C4—21no—
355C23×C4C23×C1311yescharacteristic
356C2×M16—21no—
357C22×C8—21no—
358C4⋊Q8—21no—
359#126—22no—
360#125—22no—
361#124—21no—
362#124—22no—
363#124—22no—
364#123—22no—
365#123—22no—
366#123—22no—
367#123—21no—
368#123—22no—
369#123—48no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8D4×C1312yes—
380C22⋊Q8D4×C1311yescharacteristic
381C22⋊Q8C23×C1312yes—
382C22⋊Q8C23×C1311yescharacteristic
383#121—21no—
384#121—22no—
385#121—22no—
386#121—22no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#121D4×C1311yescharacteristic
394#121C23×C1311yescharacteristic
395#120—21no—
396#120—22no—
397C4×Q8—21no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—22no—
403#117D4×C1311yescharacteristic
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4D4×C1311yescharacteristic
413C2×C4⋊C4D4×C1311yescharacteristic
414C2×C4⋊C4C23×C1312yes—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4C23×C1312yes—
420C2×C42—21no—
421#107—24no—
422#107—22no—
423#106—22no—
424#103—24no—
425#103—22no—
426#102—22no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8C23×C1312yes—
430C22⋊C8C23×C1312yes—
431#95C23×C1312yes—
432C2×C13—22no—
433C2×C13—22no—
434C2×C13—41no—
435C2×C13—81no—
436C2×C13—82no—
437C2×C13#301111yescharacteristic
438C2×C13C2×#45311yescharacteristic
439C2×C13C2×#45811yescharacteristic
440C24C2×D4×C1311yescharacteristic
441C24C2×D4×C1312yes—
442#41—42no—
443#41—84no—
444#41—82no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—42no—
448C2×Q8C2×D4×C1311yescharacteristic
449C2×Q8C2×D4×C1312yes—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—44no—
461C2×D4C2×D4×C1311yescharacteristic
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—42no—
471C22×C4—44no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4C2×D4×C1311yescharacteristic
475C22×C4C2×D4×C1311yescharacteristic
476C22×C4C2×D4×C1311yescharacteristic
477C22×C4C2×D4×C1312yes—
478C22×C4C2×D4×C1311yescharacteristic
479C22×C4C2×D4×C1311yescharacteristic
480C22×C4C24×C1311yescharacteristic
481M16—42no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—42no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—48no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4C2×D4×C1311yescharacteristic
502C4⋊C4C2×D4×C1312yes—
503C4⋊C4C2×D4×C1311yescharacteristic
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—48no—
520C42—22no—
521C42—21no—
522C42—42no—
523C13#1826711yescharacteristic, direct product factor, Sylow
524C23—22no—
525C23—22no—
526C23—22no—
527C23—21no—
528C23—24no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23C13×#12011yescharacteristic
533C23C13×#12011yescharacteristic
534C23C22×D4×C1311yescharacteristic
535Q8—42no—
536Q8—41no—
537Q8—42no—
538Q8—82no—
539D4—41no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—81no—
545D4—82no—
546D4—81no—
547D4—82no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—81no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4C13×#12011yescharacteristic
576C2×C4C13×#12011yescharacteristic
577C2×C4C22×D4×C1311yescharacteristic
578C2×C4C22×D4×C1311yescharacteristic
579C8—42no—
580C8—42no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—44no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—84no—
596C22C13×#45312yes—
597C22C2×C13×#12011yescharacteristic
598C22C13×#57812yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—44no—
603C4—41no—
604C4—42no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—82no—
610C4C13×#45812yes—
611C2—22no—
612C2—22no—
613C2—41no—
614C2—82no—
615C2—81no—
616C2C13×#301111yescharacteristic
617C2C2×C13×#45311yescharacteristic
618C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3536C2
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×#484C2semidirect
4. C13×#2501C2semidirect
5. C13×#1618C2semidirect
6. C13×#1614C2semidirect
7. C13×#1508C2semidirect
8. C13×#1501C2semidirect
9. C13×#1471C2semidirect
131. #18267C13direct (N × H)
216. #3092C2×C13semidirect
217. C2×#484C2×C13semidirect
218. #2501C2×C13semidirect
219. #1618C2×C13semidirect
220. #1614C2×C13semidirect
221. #1508C2×C13semidirect
222. #1501C2×C13semidirect
223. #1471C2×C13semidirect
523. C13#18267direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35362
C13×#30922
C2×C13×#4842
C13×#25012
C13×#16182
C13×#16142
C13×#15082
C13×#15012
C13×#14712
#1826713