Finite Group Databasebeta

← C13×#14666 #15701005

Subgroups — C13×#14666 #15701005

Order 3328.

1602 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#386C211yesmaximal, characteristic
2C13×#1443C212yesmaximal, complemented
3C13×#1442C212yesmaximal, complemented
4C13×#1440C212yesmaximal, complemented
5C13×#1439C212yesmaximal, complemented
6C13×#1439C212yesmaximal, complemented
7C13×#1438C211yesmaximal, characteristic
8C13×#1438C211yesmaximal, characteristic
9C13×C22⋊#95C212yesmaximal, complemented
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C22⋊C4C2212yes—
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2212yes—
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C13×#386C418yescomplemented
21C2×C13×#95C2212yes—
22C2×C13×#95C2212yes—
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C25×C13C2311yescharacteristic
33C25×C13C2311yescharacteristic
34C22×D4×C13—24no—
35C22×D4×C13—42no—
36C22×D4×C13—41no—
37C22×D4×C13—41no—
38C22×D4×C13C2×C414yes—
39C23×C4×C13—41no—
40C23×C4×C13—41no—
41C23×C4×C13—42no—
42C23×C4×C13—42no—
43C23×C4×C13C2×C414yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2312yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2311yescharacteristic
51C2×C13×C4⋊C4—42no—
52C2×C13×C4⋊C4—42no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C22⋊C4—24no—
55C2×C13×C22⋊C4—24no—
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—41no—
64C2×C13×C22⋊C4—41no—
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⋊C4C2×C414yes—
71C2×C13×C22⋊C4C2×C418yes—
72C13×#95—42no—
73C13×#95—42no—
74C13×#95—42no—
75C13×#95—42no—
76C13×#95—42no—
77C13×#95—42no—
78C13×#95—42no—
79C13×#95—41no—
80C13×#95—41no—
81C13×#95—42no—
82C13×#95C2×C418yes—
83#14666C1311yesmaximal, characteristic, direct product factor, Sylow
84C24×C13—22no—
85C24×C13—22no—
86C24×C13—22no—
87C24×C13—22no—
88C24×C13—21no—
89C24×C13—21no—
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—21no—
96C24×C13—22no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13C22×C412yes—
100C24×C13C22×C412yes—
101C24×C13#4114yes—
102C24×C13C2411yescharacteristic
103C2×D4×C13—28no—
104C2×D4×C13—44no—
105C2×D4×C13—44no—
106C2×D4×C13—48no—
107C2×D4×C13—48no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
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—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—48no—
153C22×C4×C13—44no—
154C22×C4×C13—48no—
155C22×C4×C13—44no—
156C22×C4×C13—44no—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C22×C414yes—
159C22×C4×C13C22×C414yes—
160C13×C4⋊C4—48no—
161C13×C22⋊C4—48no—
162C13×C22⋊C4—44no—
163C13×C22⋊C4—48no—
164C13×C22⋊C4—48no—
165C13×C22⋊C4—44no—
166C13×C22⋊C4—48no—
167C13×C22⋊C4—44no—
168C2×#386C2×C1311yescharacteristic
169#1443C2×C1312yescomplemented
170#1442C2×C1312yescomplemented
171#1440C2×C1312yescomplemented
172#1439C2×C1312yescomplemented
173#1439C2×C1312yescomplemented
174#1438C2×C1311yescharacteristic
175#1438C2×C1311yescharacteristic
176C22⋊#95C2×C1312yescomplemented
177C23×C13—22no—
178C23×C13—22no—
179C23×C13—24no—
180C23×C13—24no—
181C23×C13—24no—
182C23×C13—24no—
183C23×C13—24no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—22no—
188C23×C13—24no—
189C23×C13—22no—
190C23×C13—22no—
191C23×C13—24no—
192C23×C13—42no—
193C23×C13—41no—
194C23×C13—42no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—41no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—42no—
213C23×C13—41no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—41no—
218C23×C13#11714yes—
219C23×C13C23×C411yescharacteristic
220C23×C13C2×#4112yes—
221C23×C13H(5,𝔽2)11yescharacteristic
222C23×C13H(5,𝔽2)12yes—
223C23×C13H(5,𝔽2)11yescharacteristic
224C23×C13H(5,𝔽2)12yes—
225C23×C13H(5,𝔽2)12yes—
226C23×C13H(5,𝔽2)12yes—
227C23×C132−1+412yes—
228D4×C13—416no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—416no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
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—
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—
277C23×D4C22×C1311yescharacteristic
278C24×C4C22×C1311yescharacteristic
279C22×C4⋊C4C22×C1312yes—
280C22×C22⋊C4C22×C1312yes—
281C22×C22⋊C4C22×C1312yes—
282C22×C22⋊C4C22×C1311yescharacteristic
283C22×C22⋊C4C22×C1312yes—
284C22×C22⋊C4C22×C1311yescharacteristic
285C22×C22⋊C4C22×C1311yescharacteristic
286C22×C22⋊C4C22×C1312yes—
287#386C4×C1318yescomplemented
288C2×#95C22×C1312yes—
289C2×#95C22×C1312yes—
290C2×#95C22×C1312yes—
291C2×#95C22×C1312yes—
292C2×#95C22×C1311yescharacteristic
293C2×#95C22×C1312yes—
294C2×#95C22×C1311yescharacteristic
295C2×#95C22×C1312yes—
296C2×#95C22×C1312yes—
297C2×#95C22×C1312yes—
298C2×#95C22×C1312yes—
299C22×C13—24no—
300C22×C13—28no—
301C22×C13—44no—
302C22×C13—44no—
303C22×C13—44no—
304C22×C13—44no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—44no—
308C22×C13—42no—
309C22×C13—44no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—44no—
313C22×C13—82no—
314C22×C13—82no—
315C22×C13—82no—
316C22×C13—82no—
317C22×C13C2×#11711yescharacteristic
318C22×C13#51811yescharacteristic
319C22×C13#51811yescharacteristic
320C22×C13#51812yes—
321C22×C13#52012yes—
322C22×C13#53812yes—
323C22×C13#53812yes—
324C22×C13#53812yes—
325C22×C13#53812yes—
326C22×C13#53912yes—
327C22×C13#53912yes—
328C22×C13#56012yes—
329C22×C13#56011yescharacteristic
330C22×C13#56012yes—
331C22×C13#56012yes—
332C22×C13#56011yescharacteristic
333C22×C13H(3,𝔽4)11yescharacteristic
334C22×C13#56212yes—
335C22×C13#56212yes—
336C22×C13#56212yes—
337C22×C13#56311yescharacteristic
338C4×C13—42no—
339C4×C13—44no—
340C4×C13—44no—
341C4×C13—82no—
342C4×C13—82no—
343C4×C13—82no—
344C4×C13—82no—
345C25C23×C1311yescharacteristic
346C25C23×C1311yescharacteristic
347C22×D4—24no—
348C22×D4—42no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4C2×C4×C1314yes—
352C23×C4—41no—
353C23×C4—41no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4C2×C4×C1314yes—
357C23×C4C23×C1312yes—
358C23×C4C23×C1312yes—
359C23×C4C23×C1312yes—
360C23×C4C23×C1312yes—
361C23×C4C23×C1312yes—
362C23×C4C23×C1312yes—
363C23×C4C23×C1311yescharacteristic
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4C2×C4×C1314yes—
384C2×C22⋊C4C2×C4×C1318yes—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—41no—
393#95—41no—
394#95—42no—
395#95C2×C4×C1318yes—
396C2×C13—44no—
397C2×C13—82no—
398C2×C13#231211yescharacteristic
399C2×C13#231812yes—
400C2×C13#237511yescharacteristic
401C2×C13#237611yescharacteristic
402C2×C13#237712yes—
403C2×C13#282412yes—
404C2×C13#282512yes—
405C2×C13#282612yes—
406C2×C13#282712yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—22no—
422C24C22×C4×C1312yes—
423C24C22×C4×C1312yes—
424C24C13×#4114yes—
425C24C24×C1311yescharacteristic
426C2×D4—28no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—48no—
430C2×D4—48no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
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×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—48no—
476C22×C4—44no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4C22×C4×C1312yes—
481C22×C4C22×C4×C1314yes—
482C22×C4C22×C4×C1314yes—
483C4⋊C4—48no—
484C22⋊C4—48no—
485C22⋊C4—44no—
486C22⋊C4—48no—
487C22⋊C4—48no—
488C22⋊C4—44no—
489C22⋊C4—48no—
490C22⋊C4—44no—
491C13#1466611yescharacteristic, direct product factor, Sylow
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—24no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—42no—
508C23—41no—
509C23—42no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23C13×#11714yes—
534C23C23×C4×C1311yescharacteristic
535C23C2×C13×#4112yes—
536C23C13×H(5,𝔽2)11yescharacteristic
537C23C13×H(5,𝔽2)12yes—
538C23C13×H(5,𝔽2)11yescharacteristic
539C23C13×H(5,𝔽2)12yes—
540C23C13×H(5,𝔽2)12yes—
541C23C13×H(5,𝔽2)12yes—
542C23C13×2−1+412yes—
543D4—416no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—416no—
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—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
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—
592C22—24no—
593C22—28no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—42no—
599C22—42no—
600C22—44no—
601C22—42no—
602C22—44no—
603C22—42no—
604C22—42no—
605C22—44no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22C2×C13×#11711yescharacteristic
611C22C13×#51811yescharacteristic
612C22C13×#51811yescharacteristic
613C22C13×#51812yes—
614C22C13×#52012yes—
615C22C13×#53812yes—
616C22C13×#53812yes—
617C22C13×#53812yes—
618C22C13×#53812yes—
619C22C13×#53912yes—
620C22C13×#53912yes—
621C22C13×#56012yes—
622C22C13×#56011yescharacteristic
623C22C13×#56012yes—
624C22C13×#56012yes—
625C22C13×#56011yescharacteristic
626C22C13×H(3,𝔽4)11yescharacteristic
627C22C13×#56212yes—
628C22C13×#56212yes—
629C22C13×#56212yes—
630C22C13×#56311yescharacteristic
631C4—42no—
632C4—44no—
633C4—44no—
634C4—82no—
635C4—82no—
636C4—82no—
637C4—82no—
638C2—44no—
639C2—82no—
640C2C13×#231211yescharacteristic
641C2C13×#231812yes—
642C2C13×#237511yescharacteristic
643C2C13×#237611yescharacteristic
644C2C13×#237712yes—
645C2C13×#282412yes—
646C2C13×#282512yes—
647C2C13×#282612yes—
648C2C13×#282712yes—
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×#1443C2semidirect
3. C13×#1442C2semidirect
4. C13×#1440C2semidirect
5. C13×#1439C2semidirect
6. C13×#1439C2semidirect
9. C13×C22⋊#95C2semidirect
20. C13×#386C4semidirect
83. #14666C13direct (N × H)
169. #1443C2×C13semidirect
170. #1442C2×C13semidirect
171. #1440C2×C13semidirect
172. #1439C2×C13semidirect
173. #1439C2×C13semidirect
176. C22⋊#95C2×C13semidirect
287. #386C4×C13semidirect
491. C13#14666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3862
C13×#14432
C13×#14422
C13×#14402
C13×#14392
C13×#14382
C13×C22⋊#952
#1466613