Finite Group Databasebeta

← C13×#14641 #15700980

Subgroups — C13×#14641 #15700980

Order 3328.

1486 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#394C211yesmaximal, characteristic
2C13×#1445C211yesmaximal, characteristic, complemented
3C13×#1442C212yesmaximal, complemented
4C13×#1440C212yesmaximal, complemented
5C13×#1439C212yesmaximal, complemented
6C13×#1439C212yesmaximal, complemented
7C13×#1438C212yesmaximal
8C13×#1437C212yesmaximal, complemented
9C13×#1436C211yesmaximal, characteristic, complemented
10C23×D4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2212yes—
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2212yes—
19C22×C42×C13C2211yescharacteristic
20C13×#394C418yescomplemented
21C2×C13×#95C2212yes—
22C2×C13×#95C2212yes—
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2212yes—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C25×C13C2312yes—
33C22×D4×C13—42no—
34C22×D4×C13—42no—
35C22×D4×C13—41no—
36C22×D4×C13—41no—
37C22×D4×C13C2×C414yes—
38C23×C4×C13C2312yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C2×C13×C4⋊C4—41no—
47C2×C13×C4⋊C4—41no—
48C2×C13×C4⋊C4—42no—
49C2×C13×C4⋊C4—42no—
50C2×C13×C4⋊C4—42no—
51C2×C13×C4⋊C4C2×C414yes—
52C2×C13×C22⋊C4—24no—
53C2×C13×C22⋊C4—24no—
54C2×C13×C22⋊C4—42no—
55C2×C13×C22⋊C4—42no—
56C2×C13×C22⋊C4—42no—
57C2×C13×C22⋊C4—42no—
58C2×C13×C22⋊C4—42no—
59C2×C13×C22⋊C4—42no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4—42no—
62C2×C13×C22⋊C4—42no—
63C2×C13×C22⋊C4—42no—
64C2×C13×C22⋊C4—42no—
65C2×C13×C22⋊C4—42no—
66C2×C13×C22⋊C4—42no—
67C2×C13×C22⋊C4—42no—
68C2×C13×C22⋊C4C2×C418yes—
69C2×C13×C22⋊C4C2×C418yes—
70C2×C42×C13—42no—
71C2×C42×C13—41no—
72C13×#95—24no—
73C13×#95—42no—
74C13×#95—42no—
75C13×#95—42no—
76C13×#95—42no—
77C13×#95—42no—
78C13×#95—41no—
79C13×#95—41no—
80C13×#95—41no—
81C13×#95—42no—
82C13×#95C2×C414yes—
83#14641C1311yesmaximal, characteristic, direct product factor, Sylow
84C24×C13—22no—
85C24×C13—22no—
86C24×C13—22no—
87C24×C13—22no—
88C24×C13—22no—
89C24×C13—22no—
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13C22×C414yes—
99C24×C13C2411yescharacteristic
100C2×D4×C13—44no—
101C2×D4×C13—48no—
102C2×D4×C13—48no—
103C2×D4×C13—44no—
104C2×D4×C13—44no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
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—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—22no—
149C22×C4×C13—22no—
150C22×C4×C13C22×C414yes—
151C22×C4×C13C22×C412yes—
152C22×C4×C13C22×C412yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13#4114yes—
155C13×C4⋊C4—44no—
156C13×C4⋊C4—48no—
157C13×C22⋊C4—48no—
158C13×C22⋊C4—48no—
159C13×C22⋊C4—48no—
160C13×C22⋊C4—48no—
161C13×C22⋊C4—48no—
162C13×C22⋊C4—48no—
163C42×C13—44no—
164C2×#394C2×C1311yescharacteristic
165#1445C2×C1311yescharacteristic, complemented
166#1442C2×C1312yescomplemented
167#1440C2×C1312yescomplemented
168#1439C2×C1312yescomplemented
169#1439C2×C1312yescomplemented
170#1438C2×C1312yes—
171#1437C2×C1312yescomplemented
172#1436C2×C1311yescharacteristic, complemented
173C23×C13—24no—
174C23×C13—24no—
175C23×C13—24no—
176C23×C13—24no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—24no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—42no—
195C23×C13—42no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13C23×C411yescharacteristic
209C23×C13C2×#4112yes—
210C23×C13H(5,𝔽2)11yescharacteristic
211C23×C13H(5,𝔽2)12yes—
212C23×C13H(5,𝔽2)12yes—
213C23×C13H(5,𝔽2)11yescharacteristic
214C23×C13H(5,𝔽2)12yes—
215C23×C13H(5,𝔽2)12yes—
216C23×C132−1+412yes—
217D4×C13—416no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—41no—
240C2×C4×C13—42no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
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—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C23×D4C22×C1311yescharacteristic
269C22×C4⋊C4C22×C1312yes—
270C22×C4⋊C4C22×C1311yescharacteristic
271C22×C22⋊C4C22×C1312yes—
272C22×C22⋊C4C22×C1312yes—
273C22×C22⋊C4C22×C1312yes—
274C22×C22⋊C4C22×C1312yes—
275C22×C22⋊C4C22×C1312yes—
276C22×C22⋊C4C22×C1312yes—
277C22×C42C22×C1311yescharacteristic
278#394C4×C1318yescomplemented
279C2×#95C22×C1312yes—
280C2×#95C22×C1312yes—
281C2×#95C22×C1311yescharacteristic
282C2×#95C22×C1312yes—
283C2×#95C22×C1312yes—
284C2×#95C22×C1312yes—
285C2×#95C22×C1312yes—
286C2×#95C22×C1311yescharacteristic
287C2×#95C22×C1312yes—
288C2×#95C22×C1311yescharacteristic
289C2×#95C22×C1311yescharacteristic
290C22×C13—44no—
291C22×C13—44no—
292C22×C13—44no—
293C22×C13—44no—
294C22×C13—44no—
295C22×C13—44no—
296C22×C13—44no—
297C22×C13—82no—
298C22×C13—82no—
299C22×C13—82no—
300C22×C13—82no—
301C22×C13—82no—
302C22×C13—82no—
303C22×C13—82no—
304C22×C13—82no—
305C22×C13C4×#4111yescharacteristic
306C22×C13#51811yescharacteristic
307C22×C13#51811yescharacteristic
308C22×C13#51812yes—
309C22×C13#52012yes—
310C22×C13#53812yes—
311C22×C13#53812yes—
312C22×C13#53912yes—
313C22×C13#54012yes—
314C22×C13#54012yes—
315C22×C13#54212yes—
316C22×C13#56012yes—
317C22×C13#56012yes—
318C22×C13#56012yes—
319C22×C13#56011yescharacteristic
320C22×C13H(3,𝔽4)11yescharacteristic
321C22×C13H(3,𝔽4)11yescharacteristic
322C22×C13#56212yes—
323C22×C13#56212yes—
324C22×C13#56212yes—
325C22×C13#56311yescharacteristic
326C4×C13—44no—
327C4×C13—42no—
328C4×C13—42no—
329C4×C13—42no—
330C4×C13—44no—
331C4×C13—82no—
332C4×C13—82no—
333C4×C13—82no—
334C25C23×C1312yes—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4C2×C4×C1314yes—
340C23×C4C23×C1312yes—
341C23×C4C23×C1312yes—
342C23×C4C23×C1312yes—
343C23×C4C23×C1311yescharacteristic
344C23×C4C23×C1312yes—
345C23×C4C23×C1311yescharacteristic
346C23×C4C23×C1311yescharacteristic
347C23×C4C23×C1312yes—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4C2×C4×C1314yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4C2×C4×C1318yes—
371C2×C22⋊C4C2×C4×C1318yes—
372C2×C42—42no—
373C2×C42—41no—
374#95—24no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—41no—
381#95—41no—
382#95—41no—
383#95—42no—
384#95C2×C4×C1314yes—
385C2×C13—84no—
386C2×C13#233311yescharacteristic
387C2×C13#233512yes—
388C2×C13#237511yescharacteristic
389C2×C13#237712yes—
390C2×C13#237911yescharacteristic
391C2×C13#282412yes—
392C2×C13#282812yes—
393C2×C13#282912yes—
394C2×C13#283712yes—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C22×C4×C1314yes—
410C24C24×C1311yescharacteristic
411C2×D4—44no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—44no—
415C2×D4—44no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
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×C4C22×C4×C1314yes—
462C22×C4C22×C4×C1312yes—
463C22×C4C22×C4×C1312yes—
464C22×C4C22×C4×C1312yes—
465C22×C4C13×#4114yes—
466C4⋊C4—44no—
467C4⋊C4—48no—
468C22⋊C4—48no—
469C22⋊C4—48no—
470C22⋊C4—48no—
471C22⋊C4—48no—
472C22⋊C4—48no—
473C22⋊C4—48no—
474C42—44no—
475C13#1464111yescharacteristic, direct product factor, Sylow
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23C23×C4×C1311yescharacteristic
512C23C2×C13×#4112yes—
513C23C13×H(5,𝔽2)11yescharacteristic
514C23C13×H(5,𝔽2)12yes—
515C23C13×H(5,𝔽2)12yes—
516C23C13×H(5,𝔽2)11yescharacteristic
517C23C13×H(5,𝔽2)12yes—
518C23C13×H(5,𝔽2)12yes—
519C23C13×2−1+412yes—
520D4—416no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22C4×C13×#4111yescharacteristic
587C22C13×#51811yescharacteristic
588C22C13×#51811yescharacteristic
589C22C13×#51812yes—
590C22C13×#52012yes—
591C22C13×#53812yes—
592C22C13×#53812yes—
593C22C13×#53912yes—
594C22C13×#54012yes—
595C22C13×#54012yes—
596C22C13×#54212yes—
597C22C13×#56012yes—
598C22C13×#56012yes—
599C22C13×#56012yes—
600C22C13×#56011yescharacteristic
601C22C13×H(3,𝔽4)11yescharacteristic
602C22C13×H(3,𝔽4)11yescharacteristic
603C22C13×#56212yes—
604C22C13×#56212yes—
605C22C13×#56212yes—
606C22C13×#56311yescharacteristic
607C4—44no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—44no—
612C4—82no—
613C4—82no—
614C4—82no—
615C2—84no—
616C2C13×#233311yescharacteristic
617C2C13×#233512yes—
618C2C13×#237511yescharacteristic
619C2C13×#237712yes—
620C2C13×#237911yescharacteristic
621C2C13×#282412yes—
622C2C13×#282812yes—
623C2C13×#282912yes—
624C2C13×#283712yes—
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1445C2semidirect
3. C13×#1442C2semidirect
4. C13×#1440C2semidirect
5. C13×#1439C2semidirect
6. C13×#1439C2semidirect
8. C13×#1437C2semidirect
9. C13×#1436C2semidirect
20. C13×#394C4semidirect
83. #14641C13direct (N × H)
165. #1445C2×C13semidirect
166. #1442C2×C13semidirect
167. #1440C2×C13semidirect
168. #1439C2×C13semidirect
169. #1439C2×C13semidirect
171. #1437C2×C13semidirect
172. #1436C2×C13semidirect
278. #394C4×C13semidirect
475. C13#14641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3942
C13×#14452
C13×#14422
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×#14362
#1464113