Finite Group Databasebeta

← C13×#14892 #15701231

Subgroups — C13×#14892 #15701231

Order 3328.

1786 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#117C211yesmaximal, characteristic
2C2×C13×#397C212yesmaximal
3C2×C13×#385C211yesmaximal, characteristic
4C13×#1444C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1441C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1440C212yesmaximal
9C13×#1436C212yesmaximal, complemented
10C13×#1436C212yesmaximal, complemented
11C13×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C2×C13×#117—24no—
14C2×C13×#117—28no—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2212yes—
23C22×C13×C22⋊C4C2212yes—
24C22×C42×C13C2212yes—
25C13×#397—28no—
26C13×#385—24no—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C25×C13C2311yescharacteristic
40C23×C4×C13—24no—
41C23×C4×C13—24no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13D414yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C13×#117—232no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—24no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—42no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—42no—
78C2×C13×C22⋊C4D418yes—
79C2×C42×C13—24no—
80C2×C42×C13—24no—
81C2×C42×C13—24no—
82C13×#95—22no—
83C13×#95—22no—
84C13×#95—24no—
85C13×#95—24no—
86C13×#95—24no—
87C13×#95—24no—
88C13×#95—24no—
89C13×#95—22no—
90C13×#95—24no—
91C13×#95—24no—
92C13×#95—22no—
93C13×#95—42no—
94#14892C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—21no—
96C24×C13—21no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—21no—
100C24×C13—21no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13C2×D412yes—
105C24×C13C2×D414yes—
106C24×C13C2411yescharacteristic
107C22×C4×C13—216no—
108C22×C4×C13—216no—
109C22×C4×C13—28no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—28no—
116C22×C4×C13—28no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13C2×D414yes—
163C22×C4×C13C2×D414yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13#4112yes—
167C22×C4×C13#4112yes—
168C22×C4×C13#4114yes—
169C22×C4×C13#4114yes—
170C22×C4×C13#4112yes—
171C22×C4×C13#4112yes—
172C13×C4⋊C4—28no—
173C13×C4⋊C4—28no—
174C13×C4⋊C4—48no—
175C13×C4⋊C4—44no—
176C13×C4⋊C4—44no—
177C13×C22⋊C4—28no—
178C13×C22⋊C4—216no—
179C13×C22⋊C4—48no—
180C13×C22⋊C4—44no—
181C42×C13—216no—
182C22×#117C2×C1311yescharacteristic
183C2×#397C2×C1312yes—
184C2×#385C2×C1311yescharacteristic
185#1444C2×C1311yescharacteristic, complemented
186#1442C2×C1311yescharacteristic, complemented
187#1441C2×C1311yescharacteristic, complemented
188#1441C2×C1311yescharacteristic, complemented
189#1440C2×C1312yes—
190#1436C2×C1312yescomplemented
191#1436C2×C1312yescomplemented
192C22⋊#95C2×C1311yescharacteristic
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—24no—
197C23×C13—24no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—24no—
204C23×C13—24no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—42no—
214C23×C13—41no—
215C23×C13#12014yes—
216C23×C13C22×D411yescharacteristic
217C23×C13C22×D412yes—
218C23×C13C2×#4112yes—
219C23×C13C2×#4111yescharacteristic
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4111yescharacteristic
222C23×C13C2×#4111yescharacteristic
223C23×C13C2×#4112yes—
224C23×C13H(5,𝔽2)11yescharacteristic
225C23×C132−1+412yes—
226C23×C132−1+411yescharacteristic
227C2×C4×C13—232no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—41no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—41no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13#12314yes—
287C2×C4×C13#12314yes—
288C24×C4C22×C1311yescharacteristic
289C2×#117—24no—
290C2×#117—28no—
291C22×C4⋊C4C22×C1311yescharacteristic
292C22×C4⋊C4C22×C1311yescharacteristic
293C22×C4⋊C4C22×C1311yescharacteristic
294C22×C4⋊C4C22×C1311yescharacteristic
295C22×C4⋊C4C22×C1312yes—
296C22×C22⋊C4C22×C1311yescharacteristic
297C22×C22⋊C4C22×C1311yescharacteristic
298C22×C22⋊C4C22×C1312yes—
299C22×C22⋊C4C22×C1312yes—
300C22×C42C22×C1312yes—
301#397—28no—
302#385—24no—
303C2×#95C22×C1312yes—
304C2×#95C22×C1312yes—
305C2×#95C22×C1312yes—
306C2×#95C22×C1312yes—
307C2×#95C22×C1311yescharacteristic
308C2×#95C22×C1311yescharacteristic
309C2×#95C22×C1311yescharacteristic
310C2×#95C22×C1312yes—
311C2×#95C22×C1312yes—
312C2×#95C22×C1312yes—
313C2×#95C22×C1311yescharacteristic
314C2×#95C22×C1312yes—
315C22×C13—24no—
316C22×C13—24no—
317C22×C13—24no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—44no—
323C22×C13—44no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13C2×#12011yescharacteristic
327C22×C13C2×#12311yescharacteristic
328C22×C13C2×#12311yescharacteristic
329C22×C13#52512yes—
330C22×C13#52512yes—
331C22×C13#52511yescharacteristic
332C22×C13#52912yes—
333C22×C13#52912yes—
334C22×C13#53211yescharacteristic
335C22×C13#53611yescharacteristic
336C22×C13#53711yescharacteristic
337C22×C13#54112yes—
338C22×C13#54212yes—
339C22×C13#54612yes—
340C22×C13#54712yes—
341C22×C13#54712yes—
342C22×C13#54712yes—
343C22×C13#55212yes—
344C22×C13#55211yescharacteristic
345C22×C13#55311yescharacteristic
346C22×C13#55511yescharacteristic
347C22×C13#55612yes—
348C22×C13#55611yescharacteristic
349C4×C13—24no—
350C4×C13—24no—
351C4×C13—42no—
352C4×C13—44no—
353C4×C13—44no—
354C4×C13—44no—
355C4×C13—42no—
356C4×C13—81no—
357C4×C13—81no—
358C4×C13—82no—
359C25C23×C1311yescharacteristic
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4D4×C1314yes—
365C23×C4C23×C1311yescharacteristic
366C23×C4C23×C1311yescharacteristic
367C23×C4C23×C1312yes—
368C23×C4C23×C1312yes—
369C23×C4C23×C1312yes—
370C23×C4C23×C1312yes—
371C23×C4C23×C1311yescharacteristic
372C23×C4C23×C1311yescharacteristic
373C23×C4C23×C1311yescharacteristic
374C23×C4C23×C1311yescharacteristic
375#117—232no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—42no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4D4×C1318yes—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402#95—22no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—22no—
410#95—24no—
411#95—24no—
412#95—22no—
413#95—42no—
414C2×C13—44no—
415C2×C13#239511yescharacteristic
416C2×C13#240611yescharacteristic
417C2×C13#243011yescharacteristic
418C2×C13#247012yes—
419C2×C13#247412yes—
420C2×C13#247812yes—
421C2×C13#247812yes—
422C2×C13#248511yescharacteristic
423C2×C13#249911yescharacteristic
424C2×C13#262511yescharacteristic
425C2×C13#284911yescharacteristic
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24C2×D4×C1312yes—
436C24C2×D4×C1314yes—
437C24C24×C1311yescharacteristic
438C22×C4—216no—
439C22×C4—216no—
440C22×C4—28no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4C2×D4×C1314yes—
494C22×C4C2×D4×C1314yes—
495C22×C4C2×D4×C1312yes—
496C22×C4C2×D4×C1312yes—
497C22×C4C13×#4112yes—
498C22×C4C13×#4112yes—
499C22×C4C13×#4114yes—
500C22×C4C13×#4114yes—
501C22×C4C13×#4112yes—
502C22×C4C13×#4112yes—
503C4⋊C4—28no—
504C4⋊C4—28no—
505C4⋊C4—48no—
506C4⋊C4—44no—
507C4⋊C4—44no—
508C22⋊C4—28no—
509C22⋊C4—216no—
510C22⋊C4—48no—
511C22⋊C4—44no—
512C42—216no—
513C13#1489211yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—22no—
516C23—22no—
517C23—24no—
518C23—24no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—41no—
536C23C13×#12014yes—
537C23C22×D4×C1311yescharacteristic
538C23C22×D4×C1312yes—
539C23C2×C13×#4112yes—
540C23C2×C13×#4111yescharacteristic
541C23C2×C13×#4111yescharacteristic
542C23C2×C13×#4111yescharacteristic
543C23C2×C13×#4111yescharacteristic
544C23C2×C13×#4112yes—
545C23C13×H(5,𝔽2)11yescharacteristic
546C23C13×2−1+412yes—
547C23C13×2−1+411yescharacteristic
548C2×C4—232no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4C13×#12314yes—
608C2×C4C13×#12314yes—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22C2×C13×#12011yescharacteristic
621C22C2×C13×#12311yescharacteristic
622C22C2×C13×#12311yescharacteristic
623C22C13×#52512yes—
624C22C13×#52512yes—
625C22C13×#52511yescharacteristic
626C22C13×#52912yes—
627C22C13×#52912yes—
628C22C13×#53211yescharacteristic
629C22C13×#53611yescharacteristic
630C22C13×#53711yescharacteristic
631C22C13×#54112yes—
632C22C13×#54212yes—
633C22C13×#54612yes—
634C22C13×#54712yes—
635C22C13×#54712yes—
636C22C13×#54712yes—
637C22C13×#55212yes—
638C22C13×#55211yescharacteristic
639C22C13×#55311yescharacteristic
640C22C13×#55511yescharacteristic
641C22C13×#55612yes—
642C22C13×#55611yescharacteristic
643C4—24no—
644C4—24no—
645C4—42no—
646C4—44no—
647C4—44no—
648C4—44no—
649C4—42no—
650C4—81no—
651C4—81no—
652C4—82no—
653C2—44no—
654C2C13×#239511yescharacteristic
655C2C13×#240611yescharacteristic
656C2C13×#243011yescharacteristic
657C2C13×#247012yes—
658C2C13×#247412yes—
659C2C13×#247812yes—
660C2C13×#247812yes—
661C2C13×#248511yescharacteristic
662C2C13×#249911yescharacteristic
663C2C13×#262511yescharacteristic
664C2C13×#284911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1444C2semidirect
5. C13×#1442C2semidirect
6. C13×#1441C2semidirect
7. C13×#1441C2semidirect
9. C13×#1436C2semidirect
10. C13×#1436C2semidirect
94. #14892C13direct (N × H)
185. #1444C2×C13semidirect
186. #1442C2×C13semidirect
187. #1441C2×C13semidirect
188. #1441C2×C13semidirect
190. #1436C2×C13semidirect
191. #1436C2×C13semidirect
513. C13#14892direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1172
C2×C13×#3972
C2×C13×#3852
C13×#14442
C13×#14422
C13×#14412
C13×#14402
C13×#14362
C13×C22⋊#952
#1489213