Finite Group Databasebeta

← C13×#15463 #15701802

Subgroups — C13×#15463 #15701802

Order 3328.

2042 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic
2C2×C13×#397C212yesmaximal, complemented
3C2×C13×#386C211yesmaximal, characteristic
4C13×#1442C212yesmaximal, complemented
5C13×#1441C212yesmaximal, complemented
6C13×#1439C212yesmaximal, complemented
7C13×#1438C211yesmaximal, characteristic
8C13×C22⋊#95C212yesmaximal, complemented
9C13×C22⋊#95C212yesmaximal, complemented
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C24×C4×C13C2211yescharacteristic
13C2×C13×#123—24no—
14C2×C13×#123—28no—
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2212yes—
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2212yes—
21C22×C13×C22⋊C4C2212yes—
22C22×C13×C22⋊C4C2212yes—
23C13×#397—28no—
24C13×#386—24no—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C25×C13C2311yescharacteristic
36C25×C13C2311yescharacteristic
37C22×D4×C13—24no—
38C22×D4×C13—24no—
39C22×D4×C13—41no—
40C22×D4×C13—41no—
41C22×D4×C13D414yes—
42C23×C4×C13—22no—
43C23×C4×C13—24no—
44C23×C4×C13—22no—
45C23×C4×C13—24no—
46C23×C4×C13—24no—
47C23×C4×C13—41no—
48C23×C4×C13—41no—
49C23×C4×C13—41no—
50C23×C4×C13—41no—
51C23×C4×C13—42no—
52C23×C4×C13C2312yes—
53C23×C4×C13C2312yes—
54C23×C4×C13C2312yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2312yes—
58C23×C4×C13C2312yes—
59C13×#123—232no—
60C2×C13×C4⋊C4—24no—
61C2×C13×C4⋊C4—24no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—24no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—42no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—24no—
68C2×C13×C22⋊C4—24no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4—42no—
79C2×C13×C22⋊C4—42no—
80C2×C13×C22⋊C4—42no—
81C2×C13×C22⋊C4D418yes—
82C13×#95—24no—
83C13×#95—24no—
84C13×#95—24no—
85C13×#95—24no—
86C13×#95—24no—
87C13×#95—41no—
88C13×#95—42no—
89C13×#95—42no—
90C13×#95—42no—
91C13×#95—41no—
92#15463C1311yesmaximal, characteristic, direct product factor, Sylow
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—21no—
102C24×C13—21no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13C2×D414yes—
108C24×C13C2×D412yes—
109C24×C13C2×D412yes—
110C24×C13#4114yes—
111C24×C13C2411yescharacteristic
112C2×D4×C13—28no—
113C2×D4×C13—28no—
114C2×D4×C13—44no—
115C2×D4×C13—48no—
116C2×D4×C13—48no—
117C22×C4×C13—28no—
118C22×C4×C13—22no—
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—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—44no—
161C22×C4×C13—48no—
162C22×C4×C13—48no—
163C22×C4×C13—48no—
164C22×C4×C13—48no—
165C22×C4×C13—44no—
166C22×C4×C13—44no—
167C22×C4×C13—44no—
168C22×C4×C13—44no—
169C22×C4×C13C2×D414yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D414yes—
172C22×C4×C13#4114yes—
173C22×C4×C13#4114yes—
174C13×C4⋊C4—216no—
175C13×C4⋊C4—48no—
176C13×C22⋊C4—28no—
177C13×C22⋊C4—216no—
178C13×C22⋊C4—48no—
179C13×C22⋊C4—48no—
180C13×C22⋊C4—48no—
181C13×C22⋊C4—44no—
182C22×#123C2×C1311yescharacteristic
183C2×#397C2×C1312yescomplemented
184C2×#386C2×C1311yescharacteristic
185#1442C2×C1312yescomplemented
186#1441C2×C1312yescomplemented
187#1439C2×C1312yescomplemented
188#1438C2×C1311yescharacteristic
189C22⋊#95C2×C1312yescomplemented
190C22⋊#95C2×C1312yescomplemented
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—24no—
204C23×C13—24no—
205C23×C13—24no—
206C23×C13—24no—
207C23×C13—24no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—41no—
222C23×C13—42no—
223C23×C13—41no—
224C23×C13—42no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13#12014yes—
232C23×C13#12314yes—
233C23×C13C22×D411yescharacteristic
234C23×C13C22×D412yes—
235C23×C13C2×#4112yes—
236C23×C13C2×#4112yes—
237C23×C13C2×#4112yes—
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C13H(5,𝔽2)12yes—
241C23×C132−1+412yes—
242D4×C13—416no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—416no—
259C2×C4×C13—416no—
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—42no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
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—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—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C23×D4C22×C1311yescharacteristic
293C24×C4C22×C1311yescharacteristic
294C24×C4C22×C1311yescharacteristic
295C2×#123—24no—
296C2×#123—28no—
297C22×C4⋊C4C22×C1312yes—
298C22×C4⋊C4C22×C1312yes—
299C22×C22⋊C4C22×C1311yescharacteristic
300C22×C22⋊C4C22×C1311yescharacteristic
301C22×C22⋊C4C22×C1312yes—
302C22×C22⋊C4C22×C1312yes—
303C22×C22⋊C4C22×C1312yes—
304C22×C22⋊C4C22×C1312yes—
305#397—28no—
306#386—24no—
307C2×#95C22×C1312yes—
308C2×#95C22×C1312yes—
309C2×#95C22×C1312yes—
310C2×#95C22×C1312yes—
311C2×#95C22×C1312yes—
312C2×#95C22×C1312yes—
313C2×#95C22×C1312yes—
314C2×#95C22×C1312yes—
315C2×#95C22×C1311yescharacteristic
316C2×#95C22×C1311yescharacteristic
317C22×C13—24no—
318C22×C13—24no—
319C22×C13—28no—
320C22×C13—28no—
321C22×C13—44no—
322C22×C13—44no—
323C22×C13—44no—
324C22×C13—44no—
325C22×C13—44no—
326C22×C13—44no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—44no—
332C22×C13—44no—
333C22×C13—44no—
334C22×C13—44no—
335C22×C13C2×#12011yescharacteristic
336C22×C13C2×#12311yescharacteristic
337C22×C13#52912yes—
338C22×C13#53212yes—
339C22×C13#53411yescharacteristic
340C22×C13#53712yes—
341C22×C13#53812yes—
342C22×C13#53912yes—
343C22×C13#53912yes—
344C22×C13#54612yes—
345C22×C13#54612yes—
346C22×C13#54612yes—
347C22×C13#54612yes—
348C22×C13#54712yes—
349C22×C13#54712yes—
350C22×C13#55112yes—
351C22×C13#55111yescharacteristic
352C22×C13#55212yes—
353C22×C13#55911yescharacteristic
354C22×C13#56011yescharacteristic
355C22×C13#56311yescharacteristic
356C4×C13—44no—
357C4×C13—42no—
358C4×C13—44no—
359C4×C13—44no—
360C4×C13—44no—
361C4×C13—82no—
362C4×C13—82no—
363C25C23×C1311yescharacteristic
364C25C23×C1311yescharacteristic
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4D4×C1314yes—
370C23×C4—22no—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—41no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4—42no—
380C23×C4C23×C1312yes—
381C23×C4C23×C1312yes—
382C23×C4C23×C1312yes—
383C23×C4C23×C1312yes—
384C23×C4C23×C1311yescharacteristic
385C23×C4C23×C1312yes—
386C23×C4C23×C1312yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—42no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4D4×C1318yes—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—41no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—41no—
420C2×C13—44no—
421C2×C13—44no—
422C2×C13#240511yescharacteristic
423C2×C13#241912yes—
424C2×C13#243012yes—
425C2×C13#255312yes—
426C2×C13#255712yes—
427C2×C13#269312yes—
428C2×C13#269512yes—
429C2×C13#269711yescharacteristic
430C2×C13#272411yescharacteristic
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24C2×D4×C1314yes—
446C24C2×D4×C1312yes—
447C24C2×D4×C1312yes—
448C24C13×#4114yes—
449C24C24×C1311yescharacteristic
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—44no—
453C2×D4—48no—
454C2×D4—48no—
455C22×C4—28no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4C2×D4×C1314yes—
508C22×C4C2×D4×C1312yes—
509C22×C4C2×D4×C1314yes—
510C22×C4C13×#4114yes—
511C22×C4C13×#4114yes—
512C4⋊C4—216no—
513C4⋊C4—48no—
514C22⋊C4—28no—
515C22⋊C4—216no—
516C22⋊C4—48no—
517C22⋊C4—48no—
518C22⋊C4—48no—
519C22⋊C4—44no—
520C13#1546311yescharacteristic, direct product factor, Sylow
521C23—22no—
522C23—22no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—22no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—41no—
552C23—41no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C13×#12014yes—
562C23C13×#12314yes—
563C23C22×D4×C1311yescharacteristic
564C23C22×D4×C1312yes—
565C23C2×C13×#4112yes—
566C23C2×C13×#4112yes—
567C23C2×C13×#4112yes—
568C23C13×H(5,𝔽2)11yescharacteristic
569C23C13×H(5,𝔽2)11yescharacteristic
570C23C13×H(5,𝔽2)12yes—
571C23C13×2−1+412yes—
572D4—416no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—416no—
589C2×C4—416no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
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—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C22—24no—
623C22—24no—
624C22—28no—
625C22—28no—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—44no—
634C22—44no—
635C22—44no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22C2×C13×#12011yescharacteristic
641C22C2×C13×#12311yescharacteristic
642C22C13×#52912yes—
643C22C13×#53212yes—
644C22C13×#53411yescharacteristic
645C22C13×#53712yes—
646C22C13×#53812yes—
647C22C13×#53912yes—
648C22C13×#53912yes—
649C22C13×#54612yes—
650C22C13×#54612yes—
651C22C13×#54612yes—
652C22C13×#54612yes—
653C22C13×#54712yes—
654C22C13×#54712yes—
655C22C13×#55111yescharacteristic
656C22C13×#55112yes—
657C22C13×#55212yes—
658C22C13×#55911yescharacteristic
659C22C13×#56011yescharacteristic
660C22C13×#56311yescharacteristic
661C4—44no—
662C4—42no—
663C4—44no—
664C4—44no—
665C4—44no—
666C4—82no—
667C4—82no—
668C2—44no—
669C2—44no—
670C2C13×#240511yescharacteristic
671C2C13×#241912yes—
672C2C13×#243012yes—
673C2C13×#255312yes—
674C2C13×#255712yes—
675C2C13×#269312yes—
676C2C13×#269512yes—
677C2C13×#269711yescharacteristic
678C2C13×#272411yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×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×#397C2semidirect
4. C13×#1442C2semidirect
5. C13×#1441C2semidirect
6. C13×#1439C2semidirect
8. C13×C22⋊#95C2semidirect
9. C13×C22⋊#95C2semidirect
92. #15463C13direct (N × H)
183. C2×#397C2×C13semidirect
185. #1442C2×C13semidirect
186. #1441C2×C13semidirect
187. #1439C2×C13semidirect
189. C22⋊#95C2×C13semidirect
190. C22⋊#95C2×C13semidirect
520. C13#15463direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C2×C13×#3972
C2×C13×#3862
C13×#14422
C13×#14412
C13×#14392
C13×#14382
C13×C22⋊#952
#1546313