Finite Group Databasebeta

← C13×#14918 #15701257

Subgroups — C13×#14918 #15701257

Order 3328.

3366 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C13×C22⋊C4C211yesmaximal, characteristic
2C2×C13×#385C211yesmaximal, characteristic, complemented
3C2×C13×#381C211yesmaximal, characteristic, complemented
4C2×C13×#381C211yesmaximal, characteristic, complemented
5C2×C13×#379C211yesmaximal, characteristic
6C2×C13×#379C211yesmaximal, characteristic
7C13×#1440C214yesmaximal, complemented
8C13×#1439C214yesmaximal, complemented
9C13×C22⋊#95C211yesmaximal, characteristic, complemented
10C26×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2212yescomplemented
14C22×C13×C22⋊C4—24no—
15C22×C13×C22⋊C4—24no—
16C22×C13×C22⋊C4—24no—
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C13×C22⋊C4C2214yes—
22C22×C13×C22⋊C4C2214yes—
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2212yes—
25C13×#385—24no—
26C13×#381—24no—
27C13×#381—24no—
28C13×#379—24no—
29C13×#379—24no—
30C2×C13×#95C2212yescomplemented
31C2×C13×#95C2214yescomplemented
32C2×C13×#95C2212yescomplemented
33C2×C13×#95C2212yescomplemented
34C2×C13×#95C2214yescomplemented
35C25×C13—22no—
36C25×C13—22no—
37C25×C13—28no—
38C25×C13—22no—
39C25×C13—22no—
40C25×C13—22no—
41C25×C13—22no—
42C25×C13—44no—
43C25×C13D414yes—
44C25×C13C2312yes—
45C25×C13C2311yescharacteristic
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—44no—
55C23×C4×C13D414yes—
56C23×C4×C13D414yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2312yes—
60C23×C4×C13C2312yes—
61C23×C4×C13C2312yes—
62C23×C4×C13C2312yes—
63C23×C4×C13C2312yes—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—44no—
66C2×C13×C22⋊C4—232no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—28no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—28no—
71C2×C13×C22⋊C4—28no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—28no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—28no—
85C2×C13×C22⋊C4—28no—
86C2×C13×C22⋊C4—44no—
87C2×C13×C22⋊C4—44no—
88C2×C13×C22⋊C4D414yes—
89C13×#95—28no—
90C13×#95—24no—
91C13×#95—24no—
92C13×#95—24no—
93C13×#95—44no—
94#14918C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—24no—
96C24×C13—24no—
97C24×C13—216no—
98C24×C13—216no—
99C24×C13—28no—
100C24×C13—216no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—24no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—24no—
109C24×C13—24no—
110C24×C13—28no—
111C24×C13—28no—
112C24×C13—48no—
113C24×C13—416no—
114C24×C13—416no—
115C24×C13—416no—
116C24×C13—416no—
117C24×C13—48no—
118C24×C13—48no—
119C24×C13—44no—
120C24×C13—44no—
121C24×C13—44no—
122C24×C13—44no—
123C24×C13C2×D414yes—
124C24×C13C2×D412yes—
125C24×C13C2×D412yes—
126C24×C13C2×D412yes—
127C24×C13C2×D412yes—
128C24×C13#4118yes—
129C24×C13#4112yes—
130C24×C13#4112yes—
131C24×C13#4112yes—
132C24×C13C2411yescharacteristic
133C22×C4×C13—28no—
134C22×C4×C13—28no—
135C22×C4×C13—28no—
136C22×C4×C13—28no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—24no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—24no—
164C22×C4×C13—24no—
165C22×C4×C13—24no—
166C22×C4×C13—24no—
167C22×C4×C13—24no—
168C22×C4×C13—24no—
169C22×C4×C13—48no—
170C22×C4×C13—48no—
171C22×C4×C13—48no—
172C22×C4×C13—44no—
173C22×C4×C13—44no—
174C22×C4×C13—44no—
175C22×C4×C13—44no—
176C22×C4×C13C2×D414yes—
177C22×C4×C13C2×D414yes—
178C22×C4×C13C2×D414yes—
179C13×C4⋊C4—48no—
180C13×C22⋊C4—232no—
181C13×C22⋊C4—28no—
182C13×C22⋊C4—416no—
183C13×C22⋊C4—48no—
184C13×C22⋊C4—44no—
185C13×C22⋊C4—44no—
186C13×C22⋊C4—44no—
187C13×C22⋊C4—48no—
188C23×C22⋊C4C2×C1311yescharacteristic
189C2×#385C2×C1311yescharacteristic, complemented
190C2×#381C2×C1311yescharacteristic, complemented
191C2×#381C2×C1311yescharacteristic, complemented
192C2×#379C2×C1311yescharacteristic
193C2×#379C2×C1311yescharacteristic
194#1440C2×C1314yescomplemented
195#1439C2×C1314yescomplemented
196C22⋊#95C2×C1311yescharacteristic, complemented
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—28no—
204C23×C13—28no—
205C23×C13—28no—
206C23×C13—28no—
207C23×C13—232no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—28no—
213C23×C13—28no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13—28no—
217C23×C13—28no—
218C23×C13—28no—
219C23×C13—28no—
220C23×C13—432no—
221C23×C13—432no—
222C23×C13—432no—
223C23×C13—416no—
224C23×C13—432no—
225C23×C13—432no—
226C23×C13—432no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13—44no—
232C23×C13—44no—
233C23×C13—44no—
234C23×C13—44no—
235C23×C13—44no—
236C23×C13—44no—
237C23×C13—416no—
238C23×C13#12014yes—
239C23×C13#12114yes—
240C23×C13#12114yes—
241C23×C13#12114yes—
242C23×C13#12318yes—
243C23×C13#12314yes—
244C23×C13#12314yes—
245C23×C13#12414yes—
246C23×C13C22×D411yescharacteristic
247C23×C13C22×D411yescharacteristic
248C23×C13C22×D411yescharacteristic
249C23×C13C22×D411yescharacteristic
250C23×C13C2×#4111yescharacteristic
251C23×C13C2×#4111yescharacteristic
252C23×C13C2×#4111yescharacteristic
253C23×C13C2×#4114yes—
254C23×C13H(5,𝔽2)14yes—
255C2×C4×C13—24no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—24no—
259C2×C4×C13—24no—
260C2×C4×C13—24no—
261C2×C4×C13—24no—
262C2×C4×C13—28no—
263C2×C4×C13—416no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—44no—
271C2×C4×C13—44no—
272C2×C4×C13—44no—
273C2×C4×C13—416no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
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—42no—
287C2×C4×C13—42no—
288C2×C4×C13—44no—
289C2×C4×C13—44no—
290C2×C4×C13—44no—
291C2×C4×C13—44no—
292C26C22×C1311yescharacteristic
293C24×C4C22×C1311yescharacteristic
294C24×C4C22×C1311yescharacteristic
295C22×C4⋊C4C22×C1312yescomplemented
296C22×C22⋊C4—24no—
297C22×C22⋊C4—24no—
298C22×C22⋊C4—24no—
299C22×C22⋊C4C22×C1314yes—
300C22×C22⋊C4C22×C1311yescharacteristic
301C22×C22⋊C4C22×C1311yescharacteristic
302C22×C22⋊C4C22×C1312yes—
303C22×C22⋊C4C22×C1311yescharacteristic
304C22×C22⋊C4C22×C1314yes—
305C22×C22⋊C4C22×C1311yescharacteristic
306C22×C22⋊C4C22×C1312yes—
307#385—24no—
308#381—24no—
309#381—24no—
310#379—24no—
311#379—24no—
312C2×#95C22×C1312yescomplemented
313C2×#95C22×C1314yescomplemented
314C2×#95C22×C1312yescomplemented
315C2×#95C22×C1312yescomplemented
316C2×#95C22×C1314yescomplemented
317C22×C13—28no—
318C22×C13—24no—
319C22×C13—24no—
320C22×C13—28no—
321C22×C13—28no—
322C22×C13—28no—
323C22×C13—28no—
324C22×C13—28no—
325C22×C13—28no—
326C22×C13—28no—
327C22×C13—28no—
328C22×C13—464no—
329C22×C13—48no—
330C22×C13—44no—
331C22×C13—44no—
332C22×C13—48no—
333C22×C13—44no—
334C22×C13—48no—
335C22×C13—44no—
336C22×C13—48no—
337C22×C13#39418yes—
338C22×C13C2×#12011yescharacteristic
339C22×C13C2×#12111yescharacteristic
340C22×C13C2×#12111yescharacteristic
341C22×C13C2×#12111yescharacteristic
342C22×C13C2×#12312yes—
343C22×C13C2×#12311yescharacteristic
344C22×C13C2×#12311yescharacteristic
345C22×C13#52512yes—
346C22×C13#52512yes—
347C22×C13C2×#12411yescharacteristic
348C22×C13#53412yes—
349C22×C13#53412yes—
350C22×C13#53512yes—
351C22×C13#54614yes—
352C22×C13#55114yes—
353C22×C13#55114yes—
354C22×C13#55114yes—
355C4×C13—44no—
356C4×C13—44no—
357C4×C13—44no—
358C4×C13—81no—
359C4×C13—81no—
360C4×C13—82no—
361C4×C13—82no—
362C25—22no—
363C25—22no—
364C25—28no—
365C25—22no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—44no—
370C25D4×C1314yes—
371C25C23×C1312yes—
372C25C23×C1311yescharacteristic
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—44no—
382C23×C4D4×C1314yes—
383C23×C4D4×C1314yes—
384C23×C4C23×C1311yescharacteristic
385C23×C4C23×C1311yescharacteristic
386C23×C4C23×C1312yes—
387C23×C4C23×C1312yes—
388C23×C4C23×C1312yes—
389C23×C4C23×C1312yes—
390C23×C4C23×C1312yes—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—44no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4D4×C1314yes—
416#95—28no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—44no—
421C2×C13—28no—
422C2×C13—48no—
423C2×C13C2×#39411yescharacteristic
424C2×C13#241112yes—
425C2×C13#241212yes—
426C2×C13#248212yes—
427C2×C13#248312yes—
428C2×C13#253412yes—
429C2×C13#256112yes—
430C2×C13#261311yescharacteristic
431C2×C13#284911yescharacteristic
432C24—24no—
433C24—24no—
434C24—216no—
435C24—216no—
436C24—28no—
437C24—216no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—28no—
448C24—28no—
449C24—48no—
450C24—416no—
451C24—416no—
452C24—416no—
453C24—416no—
454C24—48no—
455C24—48no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24C2×D4×C1314yes—
461C24C2×D4×C1312yes—
462C24C2×D4×C1312yes—
463C24C2×D4×C1312yes—
464C24C2×D4×C1312yes—
465C24C13×#4118yes—
466C24C13×#4112yes—
467C24C13×#4112yes—
468C24C13×#4112yes—
469C24C24×C1311yescharacteristic
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4C2×D4×C1314yes—
514C22×C4C2×D4×C1314yes—
515C22×C4C2×D4×C1314yes—
516C4⋊C4—48no—
517C22⋊C4—232no—
518C22⋊C4—28no—
519C22⋊C4—416no—
520C22⋊C4—48no—
521C22⋊C4—44no—
522C22⋊C4—44no—
523C22⋊C4—44no—
524C22⋊C4—48no—
525C13#1491811yescharacteristic, direct product factor, Sylow
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—28no—
533C23—28no—
534C23—28no—
535C23—28no—
536C23—232no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—28no—
542C23—28no—
543C23—24no—
544C23—24no—
545C23—28no—
546C23—28no—
547C23—28no—
548C23—28no—
549C23—432no—
550C23—432no—
551C23—432no—
552C23—432no—
553C23—416no—
554C23—432no—
555C23—432no—
556C23—416no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—44no—
562C23—44no—
563C23—44no—
564C23—44no—
565C23—44no—
566C23—44no—
567C23C13×#12014yes—
568C23C13×#12114yes—
569C23C13×#12114yes—
570C23C13×#12114yes—
571C23C13×#12318yes—
572C23C13×#12314yes—
573C23C13×#12314yes—
574C23C13×#12414yes—
575C23C22×D4×C1311yescharacteristic
576C23C22×D4×C1311yescharacteristic
577C23C22×D4×C1311yescharacteristic
578C23C22×D4×C1311yescharacteristic
579C23C2×C13×#4111yescharacteristic
580C23C2×C13×#4111yescharacteristic
581C23C2×C13×#4111yescharacteristic
582C23C2×C13×#4114yes—
583C23C13×H(5,𝔽2)14yes—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—28no—
592C2×C4—416no—
593C2×C4—416no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C22—28no—
622C22—28no—
623C22—24no—
624C22—24no—
625C22—28no—
626C22—28no—
627C22—28no—
628C22—28no—
629C22—28no—
630C22—28no—
631C22—28no—
632C22—464no—
633C22—48no—
634C22—48no—
635C22—44no—
636C22—44no—
637C22—48no—
638C22—44no—
639C22—48no—
640C22—44no—
641C22C13×#39418yes—
642C22C2×C13×#12011yescharacteristic
643C22C2×C13×#12111yescharacteristic
644C22C2×C13×#12111yescharacteristic
645C22C2×C13×#12111yescharacteristic
646C22C2×C13×#12312yes—
647C22C2×C13×#12311yescharacteristic
648C22C2×C13×#12311yescharacteristic
649C22C13×#52512yes—
650C22C13×#52512yes—
651C22C2×C13×#12411yescharacteristic
652C22C13×#53412yes—
653C22C13×#53412yes—
654C22C13×#53512yes—
655C22C13×#54614yes—
656C22C13×#55114yes—
657C22C13×#55114yes—
658C22C13×#55114yes—
659C4—44no—
660C4—44no—
661C4—44no—
662C4—81no—
663C4—81no—
664C4—82no—
665C4—82no—
666C2—28no—
667C2—48no—
668C2C2×C13×#39411yescharacteristic
669C2C13×#241112yes—
670C2C13×#241212yes—
671C2C13×#248212yes—
672C2C13×#248312yes—
673C2C13×#253412yes—
674C2C13×#256112yes—
675C2C13×#261311yescharacteristic
676C2C13×#284911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC26×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#385C2semidirect
3. C2×C13×#381C2semidirect
4. C2×C13×#381C2semidirect
7. C13×#1440C2semidirect
8. C13×#1439C2semidirect
9. C13×C22⋊#95C2semidirect
13. C22×C13×C4⋊C4C22semidirect
30. C2×C13×#95C22semidirect
31. C2×C13×#95C22semidirect
32. C2×C13×#95C22semidirect
33. C2×C13×#95C22semidirect
34. C2×C13×#95C22semidirect
94. #14918C13direct (N × H)
189. C2×#385C2×C13semidirect
190. C2×#381C2×C13semidirect
191. C2×#381C2×C13semidirect
194. #1440C2×C13semidirect
195. #1439C2×C13semidirect
196. C22⋊#95C2×C13semidirect
295. C22×C4⋊C4C22×C13semidirect
312. C2×#95C22×C13semidirect
313. C2×#95C22×C13semidirect
314. C2×#95C22×C13semidirect
315. C2×#95C22×C13semidirect
316. C2×#95C22×C13semidirect
525. C13#14918direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C13×C22⋊C42
C2×C13×#3852
C2×C13×#3812
C2×C13×#3792
C13×#14402
C13×#14392
C13×C22⋊#952
#1491813