Finite Group Databasebeta

← C13×#14632 #15700971

Subgroups — C13×#14632 #15700971

Order 3328.

1586 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#394C211yesmaximal, characteristic
2C2×C13×#388C212yesmaximal, complemented
3C13×#1442C212yesmaximal, complemented
4C13×#1441C211yesmaximal, characteristic, complemented
5C13×#1439C212yesmaximal, complemented
6C13×#1439C212yesmaximal, complemented
7C13×#1439C212yesmaximal, complemented
8C13×#1438C212yesmaximal
9C13×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2212yes—
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2212yes—
21C22×C42×C13C2211yescharacteristic
22C13×#394C418yescomplemented
23C13×#388—28no—
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2211yescharacteristic
33C25×C13C2312yes—
34C22×D4×C13—42no—
35C22×D4×C13—42no—
36C22×D4×C13—41no—
37C22×D4×C13—41no—
38C22×D4×C13C2×C414yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C2×C13×C4⋊C4—24no—
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4—41no—
50C2×C13×C4⋊C4—41no—
51C2×C13×C4⋊C4—41no—
52C2×C13×C4⋊C4—41no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C4⋊C4—41no—
57C2×C13×C4⋊C4C2×C414yes—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—24no—
61C2×C13×C22⋊C4—24no—
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⋊C4—42no—
69C2×C13×C22⋊C4—42no—
70C2×C13×C22⋊C4—42no—
71C2×C13×C22⋊C4—42no—
72C2×C13×C22⋊C4—42no—
73C2×C13×C22⋊C4—42no—
74C2×C13×C22⋊C4C2×C418yes—
75C2×C13×C22⋊C4C2×C418yes—
76C2×C42×C13—41no—
77C2×C42×C13—41no—
78C2×C42×C13D414yescomplemented
79C13×#95—24no—
80C13×#95—24no—
81C13×#95—42no—
82C13×#95—42no—
83C13×#95—42no—
84C13×#95—41no—
85C13×#95—42no—
86C13×#95—42no—
87C13×#95C2×C414yes—
88#14632C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13C22×C414yes—
104C24×C13C2411yescharacteristic
105C2×D4×C13—44no—
106C2×D4×C13—48no—
107C2×D4×C13—44no—
108C2×D4×C13—48no—
109C2×D4×C13—44no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
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—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
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×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13C22×C414yes—
156C22×C4×C13C22×C412yes—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C22×C412yes—
159C22×C4×C13C2×D414yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13#4112yes—
162C13×C4⋊C4—44no—
163C13×C4⋊C4—44no—
164C13×C4⋊C4—48no—
165C13×C4⋊C4—44no—
166C13×C22⋊C4—216no—
167C13×C22⋊C4—48no—
168C13×C22⋊C4—48no—
169C13×C22⋊C4—48no—
170C13×C22⋊C4—48no—
171C13×C22⋊C4—48no—
172C42×C13—44no—
173C2×#394C2×C1311yescharacteristic
174C2×#388C2×C1312yescomplemented
175#1442C2×C1312yescomplemented
176#1441C2×C1311yescharacteristic, complemented
177#1439C2×C1312yescomplemented
178#1439C2×C1312yescomplemented
179#1439C2×C1312yescomplemented
180#1438C2×C1312yes—
181C4⋊#95C2×C1311yescharacteristic, complemented
182C23×C13—24no—
183C23×C13—24no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—24no—
188C23×C13—24no—
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×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13C23×C411yescharacteristic
218C23×C13C22×D411yescharacteristic
219C23×C13C2×#4111yescharacteristic
220C23×C13H(5,𝔽2)11yescharacteristic
221C23×C13H(5,𝔽2)12yes—
222C23×C13H(5,𝔽2)11yescharacteristic
223C23×C13H(5,𝔽2)12yes—
224C23×C13H(5,𝔽2)11yescharacteristic
225C23×C13H(5,𝔽2)12yes—
226C23×C132−1+411yescharacteristic
227C23×C132−1+412yes—
228D4×C13—416no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
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—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—41no—
254C2×C4×C13—42no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
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—
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×C13C4×D414yes—
281C23×D4C22×C1311yescharacteristic
282C22×C4⋊C4C22×C1311yescharacteristic
283C22×C4⋊C4C22×C1312yes—
284C22×C4⋊C4C22×C1311yescharacteristic
285C22×C4⋊C4C22×C1311yescharacteristic
286C22×C22⋊C4C22×C1312yes—
287C22×C22⋊C4C22×C1312yes—
288C22×C22⋊C4C22×C1312yes—
289C22×C22⋊C4C22×C1312yes—
290C22×C22⋊C4C22×C1312yes—
291C22×C22⋊C4C22×C1312yes—
292C22×C42C22×C1311yescharacteristic
293#394C4×C1318yescomplemented
294#388—28no—
295C2×#95C22×C1312yes—
296C2×#95C22×C1312yes—
297C2×#95C22×C1312yes—
298C2×#95C22×C1312yes—
299C2×#95C22×C1312yes—
300C2×#95C22×C1311yescharacteristic
301C2×#95C22×C1312yes—
302C2×#95C22×C1312yes—
303C2×#95C22×C1311yescharacteristic
304C22×C13—44no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—44no—
309C22×C13—44no—
310C22×C13—44no—
311C22×C13—82no—
312C22×C13—82no—
313C22×C13—82no—
314C22×C13—82no—
315C22×C13—82no—
316C22×C13—82no—
317C22×C13—82no—
318C22×C13—82no—
319C22×C13C2×C4×D411yescharacteristic
320C22×C13#51812yes—
321C22×C13#51811yescharacteristic
322C22×C13#52012yes—
323C22×C13#52011yescharacteristic
324C22×C13#53411yescharacteristic
325C22×C13#53512yes—
326C22×C13#53711yescharacteristic
327C22×C13#53712yes—
328C22×C13#53811yescharacteristic
329C22×C13#53911yescharacteristic
330C22×C13#54012yes—
331C22×C13#54212yes—
332C22×C13#56011yescharacteristic
333C22×C13#56012yes—
334C22×C13#56012yes—
335C22×C13H(3,𝔽4)11yescharacteristic
336C22×C13H(3,𝔽4)11yescharacteristic
337C22×C13#56212yes—
338C22×C13#56212yes—
339C22×C13#56212yes—
340C22×C13#56311yescharacteristic
341C22×C13#56312yes—
342C4×C13—24no—
343C4×C13—44no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—44no—
347C4×C13—82no—
348C4×C13—82no—
349C4×C13—82no—
350C25C23×C1312yes—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—41no—
354C22×D4—41no—
355C22×D4C2×C4×C1314yes—
356C23×C4C23×C1312yes—
357C23×C4C23×C1312yes—
358C23×C4C23×C1312yes—
359C23×C4C23×C1311yescharacteristic
360C23×C4C23×C1312yes—
361C23×C4C23×C1311yescharacteristic
362C23×C4C23×C1312yes—
363C23×C4C23×C1311yescharacteristic
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4C2×C4×C1314yes—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4C2×C4×C1318yes—
392C2×C22⋊C4C2×C4×C1318yes—
393C2×C42—41no—
394C2×C42—41no—
395C2×C42D4×C1314yescomplemented
396#95—24no—
397#95—24no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—41no—
402#95—42no—
403#95—42no—
404#95C2×C4×C1314yes—
405C2×C13—84no—
406C2×C13#232412yes—
407C2×C13#232511yescharacteristic
408C2×C13#237511yescharacteristic
409C2×C13#237612yes—
410C2×C13#237911yescharacteristic
411C2×C13#281312yes—
412C2×C13#281911yescharacteristic
413C2×C13#282311yescharacteristic
414C2×C13#282811yescharacteristic
415C2×C13#283211yescharacteristic
416C2×C13#283712yes—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24C22×C4×C1314yes—
432C24C24×C1311yescharacteristic
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—44no—
437C2×D4—44no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
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—21no—
458C22×C4—21no—
459C22×C4—21no—
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—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4C22×C4×C1314yes—
484C22×C4C22×C4×C1312yes—
485C22×C4C22×C4×C1312yes—
486C22×C4C22×C4×C1312yes—
487C22×C4C2×D4×C1314yes—
488C22×C4C2×D4×C1312yes—
489C22×C4C13×#4112yes—
490C4⋊C4—44no—
491C4⋊C4—44no—
492C4⋊C4—48no—
493C4⋊C4—44no—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C22⋊C4—48no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C22⋊C4—48no—
500C42—44no—
501C13#1463211yescharacteristic, direct product factor, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C23×C4×C1311yescharacteristic
538C23C22×D4×C1311yescharacteristic
539C23C2×C13×#4111yescharacteristic
540C23C13×H(5,𝔽2)11yescharacteristic
541C23C13×H(5,𝔽2)12yes—
542C23C13×H(5,𝔽2)11yescharacteristic
543C23C13×H(5,𝔽2)12yes—
544C23C13×H(5,𝔽2)11yescharacteristic
545C23C13×H(5,𝔽2)12yes—
546C23C13×2−1+411yescharacteristic
547C23C13×2−1+412yes—
548D4—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
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×C4C4×D4×C1314yes—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22C2×C4×D4×C1311yescharacteristic
617C22C13×#51812yes—
618C22C13×#51811yescharacteristic
619C22C13×#52012yes—
620C22C13×#52011yescharacteristic
621C22C13×#53411yescharacteristic
622C22C13×#53512yes—
623C22C13×#53712yes—
624C22C13×#53711yescharacteristic
625C22C13×#53811yescharacteristic
626C22C13×#53911yescharacteristic
627C22C13×#54012yes—
628C22C13×#54212yes—
629C22C13×#56012yes—
630C22C13×#56012yes—
631C22C13×#56011yescharacteristic
632C22C13×H(3,𝔽4)11yescharacteristic
633C22C13×H(3,𝔽4)11yescharacteristic
634C22C13×#56212yes—
635C22C13×#56212yes—
636C22C13×#56212yes—
637C22C13×#56311yescharacteristic
638C22C13×#56312yes—
639C4—24no—
640C4—44no—
641C4—44no—
642C4—42no—
643C4—42no—
644C4—82no—
645C4—82no—
646C4—82no—
647C2—84no—
648C2C13×#232412yes—
649C2C13×#232511yescharacteristic
650C2C13×#237511yescharacteristic
651C2C13×#237612yes—
652C2C13×#237911yescharacteristic
653C2C13×#281312yes—
654C2C13×#281911yescharacteristic
655C2C13×#282311yescharacteristic
656C2C13×#282811yescharacteristic
657C2C13×#283211yescharacteristic
658C2C13×#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. C2×C13×#388C2semidirect
3. C13×#1442C2semidirect
4. C13×#1441C2semidirect
5. C13×#1439C2semidirect
6. C13×#1439C2semidirect
7. C13×#1439C2semidirect
9. C13×C4⋊#95C2semidirect
22. C13×#394C4semidirect
78. C2×C42×C13D4semidirect
88. #14632C13direct (N × H)
174. C2×#388C2×C13semidirect
175. #1442C2×C13semidirect
176. #1441C2×C13semidirect
177. #1439C2×C13semidirect
178. #1439C2×C13semidirect
179. #1439C2×C13semidirect
181. C4⋊#95C2×C13semidirect
293. #394C4×C13semidirect
395. C2×C42D4×C13semidirect
501. C13#14632direct (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
C2×C13×#3882
C13×#14422
C13×#14412
C13×#14392
C13×#14382
C13×C4⋊#952
#1463213