Finite Group Databasebeta

← #15930946

Subgroups — #15930946

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117850C211yesmaximal, characteristic, complemented
2#13116146C211yesmaximal, characteristic, complemented
3#13116018C211yesmaximal, characteristic, complemented
4#13115969C211yesmaximal, characteristic, complemented
5#13115832C211yesmaximal, characteristic
6#13115789C211yesmaximal, characteristic, complemented
7#13115522C211yesmaximal, characteristic, complemented
8#13115453C211yesmaximal, characteristic, complemented
9#13115444C211yesmaximal, characteristic, complemented
10#13115407C211yesmaximal, characteristic, complemented
11#13115187C211yesmaximal, characteristic, complemented
12#13115154C211yesmaximal, characteristic, complemented
13#13114920C211yesmaximal, characteristic, complemented
14C4×#88049C211yesmaximal, characteristic, complemented
15C13×#2491C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#124—21no—
18C2×C13×#121C2211yescharacteristic
19C22×#6104C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C2×#88135—21no—
23C2×C4×D52C2211yescharacteristic
24C13×#394—21no—
25C13×#393—21no—
26C13×#390C2211yescharacteristic
27C13×#390C2211yescharacteristic
28C13×#388—21no—
29C13×#380C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31C4×C13×C22⋊C4C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718619—21no—
42#11718600C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718331—21no—
48#11718329—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×D4×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C22×C22⋊D13—21no—
64C23×Dic13—21no—
65C22×D52C2311yescharacteristic
66C22×C4×D13—21no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8—41no—
69C13×#124—44no—
70C13×#121—22no—
71C13×#121—41no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×#6104—22no—
88C2×#6104—41no—
89C2×#6104—41no—
90#88184—22no—
91#88184—22no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—41no—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×#6101—21no—
103C2×C4×Dic13—21no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88135—44no—
109C4×D52—22no—
110C4×D52—41no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95D411yescharacteristic
114C13×#95D411yescharacteristic
115#88072—22no—
116#88072—22no—
117#88072—41no—
118#88071—21no—
119#88071—21no—
120C22⋊#1055—41no—
121C22⋊#1055—41no—
122#88049—22no—
123#88049—22no—
124#88049—41no—
125#88047—22no—
126C4⋊#1055—41no—
127C4×#1055—41no—
128#26720—131nomaximal, Sylow
129C24×C13—21no—
130C24×C13C2×D411yescharacteristic
131C23×D13—21no—
132C2×Q8×C13—42no—
133C2×Q8×C13—42no—
134C2×Q8×C13—81no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—42no—
142C2×D4×C13—42no—
143C2×D4×C13—81no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2411yescharacteristic
159C2×C22⋊D13—24no—
160C2×C22⋊D13—42no—
161C2×C22⋊D13—42no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—42no—
166C22×Dic13—42no—
167C22×Dic13—81no—
168C2×D52—21no—
169C2×D52—21no—
170C2×D52—21no—
171C2×D52—21no—
172C2×D52—21no—
173C2×D52#4112yes—
174C2×C4×D13—42no—
175C2×C4×D13—42no—
176C2×C4×D13—81no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4#4112yes—
184C13×C22⋊C4—41no—
185C13×C22⋊C4—42no—
186C13×C22⋊C4—42no—
187C13×C22⋊C4—42no—
188C13×C22⋊C4—42no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—81no—
191C13×C22⋊C4D814yescomplemented
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13—42no—
197#6104—44no—
198#6103—24no—
199#6103—42no—
200#6103—42no—
201#6103—81no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—42no—
207C4⋊Dic13#4112yes—
208C4⋊Dic13#4112yes—
209#6101—42no—
210C4×Dic13—42no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223#2491D1311yescharacteristic, complemented
224#2361—131no—
225#2054—131no—
226#2033—131no—
227#2023—131no—
228#1999—131no—
229#1988—131no—
230#1934—131no—
231#1925—131no—
232#1923—131no—
233#1918—131no—
234#1879—131no—
235#1874—131no—
236#1823—131no—
237C4×#102—131no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13C2×D812yes—
252C23×C13C22×D411yescharacteristic
253C22×D13—22no—
254C22×D13—41no—
255C22×D13—41no—
256C22×D13—41no—
257C22×D13—41no—
258C22×D13—41no—
259C22×D13—41no—
260Q8×C13—84no—
261D4×C13—41no—
262D4×C13—41no—
263D4×C13—41no—
264D4×C13—41no—
265D4×C13—84no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—22no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13C2×D812yes—
293C2×C4×C13C2×D812yes—
294C2×C4×C13C2×#4111yescharacteristic
295C2×C4×C13C2×#4111yescharacteristic
296C2×C4×C13C2×#4111yescharacteristic
297C2×C4×C13C2×#4111yescharacteristic
298C2×C4×C13H(5,𝔽2)11yescharacteristic
299C2×C4×C13H(5,𝔽2)11yescharacteristic
300C22⋊D13—48no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—41no—
310C2×Dic13—84no—
311D52—22no—
312D52—22no—
313D52—41no—
314D52—41no—
315C4×D13—84no—
316#1055—41no—
317#1055—41no—
318#1055—41no—
319#1055—41no—
320C22×D8—131no—
321C2×C4⋊Q8C2×D1311yescharacteristic
322C2×#124—21no—
323C2×#121—131no—
324C2×#121C2×D1311yescharacteristic
325C2×C4×D4—131no—
326C2×C4×D4—261no—
327C22×C4⋊C4—131no—
328C2×#107—131no—
329C2×C4⋊C8—131no—
330C2×#102—131no—
331C2×#102—131no—
332C2×#102—131no—
333C2×#102—131no—
334C2×#102—131no—
335C2×#102—131no—
336C2×C22⋊C8—131no—
337C2×C22⋊C8—131no—
338C2×C4×C8—131no—
339#394—21no—
340#393—21no—
341#390—131no—
342#390C2×D1311yescharacteristic
343#390C2×D1311yescharacteristic
344#389—131no—
345#388—21no—
346#388—261no—
347#386—261no—
348#385—261no—
349#380C2×D1311yescharacteristic
350C4×C4⋊C4—131no—
351C4×C4⋊C4C2×D1311yescharacteristic
352C4×C22⋊C4C2×D1311yescharacteristic
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360#340—131no—
361#336—131no—
362#336—131no—
363C22×C13—22no—
364C22×C13—22no—
365C22×C13—22no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—81no—
371C22×C13—81no—
372C22×C13—81no—
373C22×C13—81no—
374C22×C13—81no—
375C22×C13—81no—
376C22×C13—81no—
377C22×C13#52511yescharacteristic
378C22×C13#54611yescharacteristic
379C22×C13#54611yescharacteristic
380C22×C13C22×D811yescharacteristic
381C22×C13#57511yescharacteristic
382C22×C13#57711yescharacteristic
383C22×C13#57711yescharacteristic
384C2×D13—42no—
385C2×D13—42no—
386C2×D13—42no—
387C2×D13—81no—
388C2×D13—81no—
389C2×D13—81no—
390C2×D13—81no—
391C4×C13—22no—
392C4×C13—22no—
393C4×C13—41no—
394C4×C13—42no—
395C4×C13—41no—
396C4×C13—41no—
397C4×C13—81no—
398C4×C13—81no—
399C4×C13#52911yescharacteristic
400C4×C13#53811yescharacteristic
401C4×C13#55511yescharacteristic
402C4×C13#55911yescharacteristic
403Dic13—42no—
404Dic13—42no—
405Dic13—81no—
406C22×Q8—21no—
407C22×D4—21no—
408C22×D4—131no—
409C22×D4—261no—
410C22×D4C22×D1311yescharacteristic
411C23×C4—261no—
412C23×C4—261no—
413C23×C4C22×D1311yescharacteristic
414C2×D8—262no—
415C2×D8—521no—
416C2×D8—521no—
417C22×C8—131no—
418C22×C8—131no—
419C22×C8—131no—
420C22×C8—131no—
421C4⋊Q8—22no—
422C4⋊Q8—41no—
423#124—44no—
424#121—22no—
425#121—41no—
426#121—262no—
427#121—262no—
428C4×D4—262no—
429C4×D4—521no—
430C4×D4—524no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—262no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4—261no—
438C2×C4⋊C4—521no—
439C2×C4⋊C4C22×D1311yescharacteristic
440C2×C4⋊C4C22×D1311yescharacteristic
441C2×C4⋊C4C22×D1311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—261no—
449C2×C22⋊C4—261no—
450C2×C22⋊C4—261no—
451C2×C22⋊C4—261no—
452C2×C22⋊C4C22⋊D1311yescharacteristic
453C2×C22⋊C4C22⋊D1311yescharacteristic
454C2×C42—21no—
455C2×C42—261no—
456C2×C42C22×D1311yescharacteristic
457C2×C42C22×D1311yescharacteristic
458#107—262no—
459C4⋊C8—521no—
460#102—262no—
461#102—262no—
462#102—262no—
463#102—262no—
464#102—521no—
465#102—521no—
466C22⋊C8—521no—
467C22⋊C8—521no—
468C4×C8—521no—
469#95—21no—
470#95—21no—
471#95—261no—
472#95—261no—
473#95C22⋊D1311yescharacteristic
474#95C22⋊D1311yescharacteristic
475C2×C13—42no—
476C2×C13—161no—
477C2×C13#245911yescharacteristic
478C2×C13#310011yescharacteristic
479C2×C13#312511yescharacteristic
480C2×C13#329411yescharacteristic
481C2×C13#329411yescharacteristic
482C2×C13#332111yescharacteristic
483C2×C13#332611yescharacteristic
484D13—82no—
485C24—21no—
486C24—261no—
487C24C2×C22⋊D1311yescharacteristic
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—81no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—132no—
501C2×D4—264no—
502C2×D4—261no—
503C2×D4—261no—
504C2×D4—261no—
505C2×D4—261no—
506C2×D4—261no—
507C2×D4—522no—
508C2×D4—522no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—261no—
521C22×C4—522no—
522C22×C4—522no—
523C22×C4—522no—
524C22×C4—522no—
525C22×C4—1041no—
526C22×C4—1041no—
527C22×C4C2×C22⋊D1311yescharacteristic
528C22×C4C2×C22⋊D1311yescharacteristic
529C22×C4C2×C22⋊D1311yescharacteristic
530C22×C4C2×C22⋊D1311yescharacteristic
531C22×C4C2×C22⋊D1311yescharacteristic
532C22×C4C23×D1311yescharacteristic
533D8—524no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C2×C8—261no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—132no—
553C4⋊C4—132no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—522no—
559C4⋊C4—522no—
560C4⋊C4#612912yes—
561C22⋊C4—41no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—81no—
568C22⋊C4—264no—
569C22⋊C4—522no—
570C22⋊C4—522no—
571C22⋊C4—1041no—
572C22⋊C4#610414yescomplemented
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—522no—
579C13#2672011yescharacteristic, complemented, Sylow
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—262no—
594C23—521no—
595C23—521no—
596C23—521no—
597C23—521no—
598C23—521no—
599C23—521no—
600C23C2×#610412yes—
601C23C22×C22⋊D1311yescharacteristic
602Q8—84no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—84no—
608D4—262no—
609D4—262no—
610D4—528no—
611D4—521no—
612D4—521no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—521no—
644C2×C4—521no—
645C2×C4—521no—
646C2×C4—521no—
647C2×C4—521no—
648C2×C4—1044no—
649C2×C4—1044no—
650C2×C4C2×#610412yes—
651C2×C4C2×#610412yes—
652C2×C4C2×#612911yescharacteristic
653C2×C4#8825111yescharacteristic
654C2×C4#41×D1311yescharacteristic
655C2×C4#41×D1311yescharacteristic
656C2×C4#41×D1311yescharacteristic
657C2×C4#8825611yescharacteristic
658C8—521no—
659C8—521no—
660C8—521no—
661C8—521no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—522no—
677C22—522no—
678C22—522no—
679C22—1041no—
680C22—1041no—
681C22—1041no—
682C22—1041no—
683C22C22×#610411yescharacteristic
684C22#1171951111yescharacteristic
685C22#1171952711yescharacteristic
686C22#1171953311yescharacteristic
687C22#1171953411yescharacteristic
688C22#1171954111yescharacteristic
689C22#1171954211yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—81no—
697C4—81no—
698C4—522no—
699C4—522no—
700C4—1041no—
701C4#1171937511yescharacteristic
702C4#1171938311yescharacteristic
703C4#1171938511yescharacteristic
704C4#1171938611yescharacteristic
705C2—42no—
706C2—161no—
707C2—1042no—
708C2#1311876911yescharacteristic
709C2#1312483211yescharacteristic
710C2#1312510711yescharacteristic
711C2#1312664311yescharacteristic
712C2#1312664911yescharacteristic
713C2#1312701611yescharacteristic
714C2#1312708911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2491C2
socleC23×C13C22×D4
prime radical#13115832C2
hypercenter#2491D13
hypocenterC13#26720
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2491

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13117850C2semidirect
2. #13116146C2semidirect
3. #13116018C2semidirect
4. #13115969C2semidirect
6. #13115789C2semidirect
7. #13115522C2semidirect
8. #13115453C2semidirect
9. #13115444C2semidirect
10. #13115407C2semidirect
11. #13115187C2semidirect
12. #13115154C2semidirect
13. #13114920C2semidirect
14. C4×#88049C2semidirect
15. C13×#2491C2semidirect
191. C13×C22⋊C4D8semidirect
223. #2491D13semidirect
572. C22⋊C4#6104semidirect
579. C13#26720semidirect

Maximal subgroups

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

subgroupindex
#131178502
#131161462
#131160182
#131159692
#131158322
#131157892
#131155222
#131154532
#131154442
#131154072
#131151872
#131151542
#131149202
C4×#880492
C13×#24912
#2672013