Finite Group Databasebeta

← C13×#14719 #15701058

Subgroups — C13×#14719 #15701058

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic
2C23×C13×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C13×#394C212yesmaximal, complemented
4C2×C13×#386C212yesmaximal, complemented
5C2×C13×#386C212yesmaximal, complemented
6C13×#1441C212yesmaximal, complemented
7C13×#1439C214yesmaximal, complemented
8C13×C22⋊#95C211yesmaximal, characteristic, complemented
9C23×D4×C13C2212yes—
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C24×C4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C2×C13×#121—28no—
15C2×C13×#121—24no—
16C22×C13×C4⋊C4—24no—
17C22×C13×C4⋊C4—28no—
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2212yes—
21C22×C13×C22⋊C4C2212yes—
22C22×C13×C22⋊C4C2214yes—
23C22×C13×C22⋊C4C2212yes—
24C22×C13×C22⋊C4C2214yes—
25C13×#394—28no—
26C13×#386—28no—
27C13×#386—28no—
28C2×C13×#95C2214yes—
29C2×C13×#95C2214yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C25×C13C2312yes—
33C25×C13C2311yescharacteristic
34C22×D4×C13—24no—
35C22×D4×C13—24no—
36C22×D4×C13—24no—
37C22×D4×C13—24no—
38C22×D4×C13—24no—
39C22×D4×C13—24no—
40C22×D4×C13—24no—
41C22×D4×C13—22no—
42C22×D4×C13—24no—
43C22×D4×C13—42no—
44C22×D4×C13D418yes—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—24no—
48C23×C4×C13—24no—
49C23×C4×C13—22no—
50C23×C4×C13—24no—
51C23×C4×C13—24no—
52C23×C4×C13—24no—
53C23×C4×C13—24no—
54C23×C4×C13—42no—
55C23×C4×C13—42no—
56C23×C4×C13D414yes—
57C23×C4×C13D414yescomplemented
58C23×C4×C13C2314yes—
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2312yes—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2312yes—
64C13×#121—232no—
65C2×C13×C4⋊C4—232no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—24no—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—24no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—24no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4D418yescomplemented
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—28no—
78C2×C13×C22⋊C4—24no—
79C2×C13×C22⋊C4—24no—
80C2×C13×C22⋊C4—24no—
81C2×C13×C22⋊C4—28no—
82C2×C13×C22⋊C4—28no—
83C2×C13×C22⋊C4—28no—
84C2×C13×C22⋊C4—28no—
85C2×C13×C22⋊C4—44no—
86C13×#95—28no—
87C13×#95—28no—
88C13×#95—24no—
89C13×#95—42no—
90#14719C1311yesmaximal, characteristic, direct product factor, Sylow
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—24no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—24no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—24no—
104C24×C13—24no—
105C24×C13C2×D414yes—
106C24×C13C2×D414yes—
107C24×C13C2×D412yes—
108C24×C13C2×D412yes—
109C24×C13#4112yes—
110C24×C13#4114yes—
111C24×C13C2411yescharacteristic
112C2×D4×C13—28no—
113C2×D4×C13—216no—
114C2×D4×C13—216no—
115C2×D4×C13—216no—
116C2×D4×C13—416no—
117C2×D4×C13—44no—
118C2×D4×C13—48no—
119C2×D4×C13—48no—
120C2×D4×C13—48no—
121C2×D4×C13—48no—
122C2×D4×C13—44no—
123C22×C4×C13—28no—
124C22×C4×C13—216no—
125C22×C4×C13—28no—
126C22×C4×C13—28no—
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—216no—
134C22×C4×C13—28no—
135C22×C4×C13—28no—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
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—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—24no—
149C22×C4×C13—28no—
150C22×C4×C13—24no—
151C22×C4×C13—24no—
152C22×C4×C13—24no—
153C22×C4×C13—24no—
154C22×C4×C13—24no—
155C22×C4×C13—24no—
156C22×C4×C13—24no—
157C22×C4×C13—44no—
158C22×C4×C13—416no—
159C22×C4×C13—416no—
160C22×C4×C13—44no—
161C22×C4×C13—44no—
162C22×C4×C13C2×D414yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D414yes—
165C22×C4×C13C2×D414yes—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D414yes—
168C22×C4×C13C2×D414yes—
169C22×C4×C13#4114yes—
170C13×C4⋊C4—216no—
171C13×C4⋊C4—28no—
172C13×C4⋊C4—216no—
173C13×C22⋊C4—216no—
174C13×C22⋊C4—416no—
175C13×C22⋊C4—48no—
176C13×C22⋊C4—416no—
177C22×#121C2×C1311yescharacteristic
178C23×C4⋊C4C2×C1311yescharacteristic, complemented
179C2×#394C2×C1312yescomplemented
180C2×#386C2×C1312yescomplemented
181C2×#386C2×C1312yescomplemented
182#1441C2×C1312yescomplemented
183#1439C2×C1314yescomplemented
184C22⋊#95C2×C1311yescharacteristic, complemented
185C23×C13—22no—
186C23×C13—24no—
187C23×C13—22no—
188C23×C13—24no—
189C23×C13—22no—
190C23×C13—22no—
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—28no—
194C23×C13—28no—
195C23×C13—28no—
196C23×C13—28no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—28no—
201C23×C13—28no—
202C23×C13—42no—
203C23×C13—44no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—44no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—44no—
213C23×C13—44no—
214C23×C13—44no—
215C23×C13—44no—
216C23×C13—44no—
217C23×C13—44no—
218C23×C13—44no—
219C23×C13—44no—
220C23×C13#12014yes—
221C23×C13#12118yes—
222C23×C13#12114yes—
223C23×C13#12318yes—
224C23×C13#12414yes—
225C23×C13C22×D411yescharacteristic
226C23×C13C22×D412yes—
227C23×C13C22×D412yes—
228C23×C13C22×D411yescharacteristic
229C23×C13C2×#4111yescharacteristic
230C23×C13C2×#4112yes—
231C23×C13C2×#4112yes—
232C23×C13H(5,𝔽2)12yes—
233C23×C132−1+412yes—
234D4×C13—416no—
235D4×C13—432no—
236C2×C4×C13—232no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—28no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—22no—
253C2×C4×C13—28no—
254C2×C4×C13—416no—
255C2×C4×C13—416no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—44no—
263C2×C4×C13—44no—
264C2×C4×C13—44no—
265C2×C4×C13—44no—
266C2×C4×C13—44no—
267C2×C4×C13—44no—
268C2×C4×C13—44no—
269C2×C4×C13—44no—
270C2×C4×C13—44no—
271C2×C4×C13#12014yes—
272C2×C4×C13#12118yescomplemented
273C23×D4C22×C1312yes—
274C23×D4C22×C1311yescharacteristic
275C24×C4C22×C1311yescharacteristic
276C24×C4C22×C1311yescharacteristic
277C24×C4C22×C1311yescharacteristic
278C2×#121—28no—
279C2×#121—24no—
280C22×C4⋊C4—24no—
281C22×C4⋊C4—28no—
282C22×C4⋊C4C22×C1312yes—
283C22×C4⋊C4C22×C1311yescharacteristic
284C22×C4⋊C4C22×C1312yes—
285C22×C22⋊C4C22×C1314yes—
286C22×C22⋊C4C22×C1312yes—
287C22×C22⋊C4C22×C1312yes—
288C22×C22⋊C4C22×C1314yes—
289#394—28no—
290#386—28no—
291#386—28no—
292C2×#95C22×C1312yes—
293C2×#95C22×C1314yes—
294C2×#95C22×C1314yes—
295C2×#95C22×C1312yes—
296C22×C13—24no—
297C22×C13—24no—
298C22×C13—24no—
299C22×C13—24no—
300C22×C13—24no—
301C22×C13—216no—
302C22×C13—24no—
303C22×C13—216no—
304C22×C13—44no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13—48no—
308C22×C13—48no—
309C22×C13—82no—
310C22×C13—82no—
311C22×C13—82no—
312C22×C13—84no—
313C22×C13—82no—
314C22×C13—84no—
315C22×C13#39418yescomplemented
316C22×C13C2×#12011yescharacteristic
317C22×C13C2×#12011yescharacteristic
318C22×C13C2×#12111yescharacteristic
319C22×C13C2×#12112yes—
320C22×C13C2×#12112yes—
321C22×C13C2×#12312yes—
322C22×C13#52511yescharacteristic
323C22×C13#52512yes—
324C22×C13C2×#12411yescharacteristic
325C22×C13#53411yescharacteristic
326C22×C13#53611yescharacteristic
327C22×C13#53712yes—
328C22×C13#53912yes—
329C22×C13D4214yes—
330C22×C13#54714yes—
331C22×C13#54814yes—
332C22×C13#55314yes—
333C4×C13—28no—
334C4×C13—24no—
335C4×C13—44no—
336C4×C13—42no—
337C4×C13—44no—
338C4×C13—84no—
339C25C23×C1312yes—
340C25C23×C1311yescharacteristic
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—42no—
351C22×D4D4×C1318yes—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—22no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4D4×C1314yes—
364C23×C4D4×C1314yescomplemented
365C23×C4C23×C1314yes—
366C23×C4C23×C1312yes—
367C23×C4C23×C1311yescharacteristic
368C23×C4C23×C1312yes—
369C23×C4C23×C1311yescharacteristic
370C23×C4C23×C1312yes—
371#121—232no—
372C2×C4⋊C4—232no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4D4×C1318yescomplemented
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—44no—
393#95—28no—
394#95—28no—
395#95—24no—
396#95—42no—
397C2×C13—28no—
398C2×C13—84no—
399C2×C13C2×#39411yescharacteristic
400C2×C13#240311yescharacteristic
401C2×C13#240611yescharacteristic
402C2×C13#241614yes—
403C2×C13#243611yescharacteristic
404C2×C13#244314yes—
405C2×C13#259111yescharacteristic
406C2×C13#261811yescharacteristic
407C2×C13#284711yescharacteristic
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—24no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24C2×D4×C1314yes—
423C24C2×D4×C1314yes—
424C24C2×D4×C1312yes—
425C24C2×D4×C1312yes—
426C24C13×#4112yes—
427C24C13×#4114yes—
428C24C24×C1311yescharacteristic
429C2×D4—28no—
430C2×D4—216no—
431C2×D4—216no—
432C2×D4—216no—
433C2×D4—416no—
434C2×D4—44no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—44no—
440C22×C4—28no—
441C22×C4—216no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—216no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
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—24no—
466C22×C4—28no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—44no—
475C22×C4—416no—
476C22×C4—416no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4C2×D4×C1314yes—
480C22×C4C2×D4×C1312yes—
481C22×C4C2×D4×C1314yes—
482C22×C4C2×D4×C1314yes—
483C22×C4C2×D4×C1312yes—
484C22×C4C2×D4×C1314yes—
485C22×C4C2×D4×C1314yes—
486C22×C4C13×#4114yes—
487C4⋊C4—216no—
488C4⋊C4—28no—
489C4⋊C4—216no—
490C22⋊C4—216no—
491C22⋊C4—416no—
492C22⋊C4—48no—
493C22⋊C4—416no—
494C13#1471911yescharacteristic, direct product factor, Sylow
495C23—22no—
496C23—24no—
497C23—22no—
498C23—24no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—28no—
504C23—28no—
505C23—28no—
506C23—28no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—28no—
511C23—28no—
512C23—42no—
513C23—44no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—44no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23C13×#12014yes—
531C23C13×#12118yes—
532C23C13×#12114yes—
533C23C13×#12318yes—
534C23C13×#12414yes—
535C23C22×D4×C1311yescharacteristic
536C23C22×D4×C1312yes—
537C23C22×D4×C1312yes—
538C23C22×D4×C1311yescharacteristic
539C23C2×C13×#4111yescharacteristic
540C23C2×C13×#4112yes—
541C23C2×C13×#4112yes—
542C23C13×H(5,𝔽2)12yes—
543C23C13×2−1+412yes—
544D4—416no—
545D4—432no—
546C2×C4—232no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—28no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—28no—
564C2×C4—416no—
565C2×C4—416no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4C13×#12014yes—
582C2×C4C13×#12118yescomplemented
583C22—24no—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—24no—
588C22—216no—
589C22—24no—
590C22—216no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—48no—
595C22—48no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—84no—
600C22—82no—
601C22—84no—
602C22C13×#39418yescomplemented
603C22C2×C13×#12011yescharacteristic
604C22C2×C13×#12011yescharacteristic
605C22C2×C13×#12111yescharacteristic
606C22C2×C13×#12112yes—
607C22C2×C13×#12112yes—
608C22C2×C13×#12312yes—
609C22C13×#52511yescharacteristic
610C22C13×#52512yes—
611C22C2×C13×#12411yescharacteristic
612C22C13×#53411yescharacteristic
613C22C13×#53611yescharacteristic
614C22C13×#53712yes—
615C22C13×#53912yes—
616C22D42×C1314yes—
617C22C13×#54714yes—
618C22C13×#54814yes—
619C22C13×#55314yes—
620C4—28no—
621C4—24no—
622C4—44no—
623C4—42no—
624C4—44no—
625C4—84no—
626C2—28no—
627C2—84no—
628C2C2×C13×#39411yescharacteristic
629C2C13×#240311yescharacteristic
630C2C13×#240611yescharacteristic
631C2C13×#241614yes—
632C2C13×#243611yescharacteristic
633C2C13×#244314yes—
634C2C13×#259111yescharacteristic
635C2C13×#261811yescharacteristic
636C2C13×#284711yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC22×C13×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C13×C4⋊C4C2semidirect
3. C2×C13×#394C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C13×#1441C2semidirect
7. C13×#1439C2semidirect
8. C13×C22⋊#95C2semidirect
57. C23×C4×C13D4semidirect
73. C2×C13×C4⋊C4D4semidirect
90. #14719C13direct (N × H)
178. C23×C4⋊C4C2×C13semidirect
179. C2×#394C2×C13semidirect
180. C2×#386C2×C13semidirect
181. C2×#386C2×C13semidirect
182. #1441C2×C13semidirect
183. #1439C2×C13semidirect
184. C22⋊#95C2×C13semidirect
272. C2×C4×C13#121semidirect
315. C22×C13#394semidirect
364. C23×C4D4×C13semidirect
380. C2×C4⋊C4D4×C13semidirect
494. C13#14719direct (N × H)
582. C2×C4C13×#121semidirect
602. C22C13×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C23×C13×C4⋊C42
C2×C13×#3942
C2×C13×#3862
C13×#14412
C13×#14392
C13×C22⋊#952
#1471913