Finite Group Databasebeta

← C13×#15465 #15701804

Subgroups — C13×#15465 #15701804

Order 3328.

1738 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×C13×#400C211yesmaximal, characteristic, complemented
3C2×C13×#397C211yesmaximal, characteristic
4C2×C13×#391C211yesmaximal, characteristic, complemented
5C13×#1446C211yesmaximal, characteristic, complemented
6C13×#1442C212yesmaximal, complemented
7C13×#1442C212yesmaximal, complemented
8C13×#1440C212yesmaximal
9C13×#1437C211yesmaximal, characteristic
10C13×#1436C211yesmaximal, characteristic, complemented
11C13×C22⋊#95C212yesmaximal
12C23×Q8×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C2×C13×C22⋊Q8—24no—
15C2×C13×C22⋊Q8—24no—
16C2×C13×C22⋊Q8—24no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2212yes—
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2212yes—
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C13×#400—24no—
27C13×#397—24no—
28C13×#391—24no—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C25×C13C2311yescharacteristic
42C22×Q8×C13—22no—
43C22×Q8×C13—22no—
44C22×Q8×C13—24no—
45C22×Q8×C13—42no—
46C22×Q8×C13D414yes—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—24no—
51C23×C4×C13—42no—
52C23×C4×C13C2312yes—
53C23×C4×C13C2312yes—
54C23×C4×C13C2312yes—
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C13×C22⋊Q8—232no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4D414yes—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—24no—
81C2×C13×C22⋊C4—24no—
82C2×C13×C22⋊C4—24no—
83C2×C13×C22⋊C4—24no—
84C2×C13×C22⋊C4—24no—
85C2×C13×C22⋊C4—42no—
86C2×C13×C22⋊C4D414yes—
87C2×C42×C13—22no—
88C2×C42×C13—42no—
89C13×#95—24no—
90C13×#95—24no—
91C13×#95—22no—
92C13×#95—24no—
93C13×#95—22no—
94C13×#95—24no—
95C13×#95—24no—
96C13×#95—24no—
97C13×#95—24no—
98C13×#95—24no—
99C13×#95—42no—
100C13×#95—42no—
101#15465C1311yesmaximal, characteristic, direct product factor, Sylow
102C24×C13—21no—
103C24×C13—21no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—22no—
109C24×C13C2×D412yes—
110C24×C13#4114yes—
111C24×C13C2411yescharacteristic
112C2×Q8×C13—28no—
113C2×Q8×C13—28no—
114C2×Q8×C13—44no—
115C2×Q8×C13—48no—
116C2×Q8×C13—48no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—28no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
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×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—48no—
167C22×C4×C13—48no—
168C22×C4×C13—44no—
169C22×C4×C13—44no—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2×D412yes—
178C22×C4×C13#4114yes—
179C22×C4×C13#4114yes—
180C13×C4⋊C4—28no—
181C13×C4⋊C4—28no—
182C13×C4⋊C4—28no—
183C13×C4⋊C4—44no—
184C13×C22⋊C4—28no—
185C13×C22⋊C4—28no—
186C13×C22⋊C4—48no—
187C13×C22⋊C4—48no—
188C42×C13—44no—
189C22×C22⋊Q8C2×C1311yescharacteristic
190C2×#400C2×C1311yescharacteristic, complemented
191C2×#397C2×C1311yescharacteristic
192C2×#391C2×C1311yescharacteristic, complemented
193#1446C2×C1311yescharacteristic, complemented
194#1442C2×C1312yescomplemented
195#1442C2×C1312yescomplemented
196#1440C2×C1312yes—
197#1437C2×C1311yescharacteristic
198#1436C2×C1311yescharacteristic, complemented
199C22⋊#95C2×C1312yes—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—22no—
203C23×C13—24no—
204C23×C13—24no—
205C23×C13—24no—
206C23×C13—24no—
207C23×C13—24no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13#12414yes—
221C23×C13C22×D411yescharacteristic
222C23×C13C22×D411yescharacteristic
223C23×C13C22×D411yescharacteristic
224C23×C13C2×#4112yes—
225C23×C13C2×#4112yes—
226C23×C13C2×#4112yes—
227C23×C13H(5,𝔽2)12yes—
228C23×C132−1+412yes—
229C23×C132−1+412yes—
230Q8×C13—416no—
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—24no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—416no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—42no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
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×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#12014yes—
289C2×C4×C13#12314yes—
290C23×Q8C22×C1311yescharacteristic
291C24×C4C22×C1311yescharacteristic
292C2×C22⋊Q8—24no—
293C2×C22⋊Q8—24no—
294C2×C22⋊Q8—24no—
295C22×C4⋊C4C22×C1311yescharacteristic
296C22×C4⋊C4C22×C1311yescharacteristic
297C22×C4⋊C4C22×C1311yescharacteristic
298C22×C4⋊C4C22×C1311yescharacteristic
299C22×C22⋊C4C22×C1312yes—
300C22×C22⋊C4C22×C1311yescharacteristic
301C22×C22⋊C4C22×C1312yes—
302C22×C22⋊C4C22×C1311yescharacteristic
303C22×C42C22×C1311yescharacteristic
304#400—24no—
305#397—24no—
306#391—24no—
307C2×#95C22×C1311yescharacteristic
308C2×#95C22×C1312yes—
309C2×#95C22×C1312yes—
310C2×#95C22×C1311yescharacteristic
311C2×#95C22×C1312yes—
312C2×#95C22×C1312yes—
313C2×#95C22×C1312yes—
314C2×#95C22×C1312yes—
315C2×#95C22×C1312yes—
316C2×#95C22×C1312yes—
317C2×#95C22×C1312yes—
318C2×#95C22×C1312yes—
319C22×C13—24no—
320C22×C13—28no—
321C22×C13—44no—
322C22×C13—42no—
323C22×C13—44no—
324C22×C13—42no—
325C22×C13—44no—
326C22×C13—44no—
327C22×C13—44no—
328C22×C13C2×#12011yescharacteristic
329C22×C13C2×#12311yescharacteristic
330C22×C13C2×#12411yescharacteristic
331C22×C13#52912yes—
332C22×C13#53211yescharacteristic
333C22×C13#53411yescharacteristic
334C22×C13#53611yescharacteristic
335C22×C13#53611yescharacteristic
336C22×C13#53912yes—
337C22×C13#53912yes—
338C22×C13#54112yes—
339C22×C13#54612yes—
340C22×C13#54612yes—
341C22×C13#54712yes—
342C22×C13#54812yes—
343C22×C13#54812yes—
344C22×C13#54812yes—
345C22×C13#55112yes—
346C22×C13#55212yes—
347C22×C13#55612yes—
348C22×C13#56312yes—
349C4×C13—24no—
350C4×C13—24no—
351C4×C13—42no—
352C4×C13—42no—
353C4×C13—42no—
354C4×C13—42no—
355C4×C13—44no—
356C4×C13—82no—
357C4×C13—82no—
358C4×C13—82no—
359C25C23×C1311yescharacteristic
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—24no—
363C22×Q8—42no—
364C22×Q8D4×C1314yes—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—42no—
370C23×C4C23×C1312yes—
371C23×C4C23×C1312yes—
372C23×C4C23×C1312yes—
373C23×C4C23×C1311yescharacteristic
374C23×C4C23×C1311yescharacteristic
375C23×C4C23×C1311yescharacteristic
376C23×C4C23×C1311yescharacteristic
377C23×C4C23×C1312yes—
378C23×C4C23×C1311yescharacteristic
379C23×C4C23×C1311yescharacteristic
380C22⋊Q8—232no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4D4×C1314yes—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4D4×C1314yes—
405C2×C42—22no—
406C2×C42—42no—
407#95—24no—
408#95—24no—
409#95—22no—
410#95—24no—
411#95—22no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—42no—
418#95—42no—
419C2×C13—44no—
420C2×C13#240511yescharacteristic
421C2×C13#242112yes—
422C2×C13#243211yescharacteristic
423C2×C13#243611yescharacteristic
424C2×C13#248812yes—
425C2×C13#256012yes—
426C2×C13#268912yes—
427C2×C13#269012yes—
428C2×C13#272812yes—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24C2×D4×C1312yes—
437C24C13×#4114yes—
438C24C24×C1311yescharacteristic
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—44no—
442C2×Q8—48no—
443C2×Q8—48no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—28no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
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—22no—
479C22×C4—22no—
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—48no—
494C22×C4—48no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4C2×D4×C1312yes—
498C22×C4C2×D4×C1312yes—
499C22×C4C2×D4×C1312yes—
500C22×C4C2×D4×C1312yes—
501C22×C4C2×D4×C1312yes—
502C22×C4C2×D4×C1312yes—
503C22×C4C2×D4×C1312yes—
504C22×C4C2×D4×C1312yes—
505C22×C4C13×#4114yes—
506C22×C4C13×#4114yes—
507C4⋊C4—28no—
508C4⋊C4—28no—
509C4⋊C4—28no—
510C4⋊C4—44no—
511C22⋊C4—28no—
512C22⋊C4—28no—
513C22⋊C4—48no—
514C22⋊C4—48no—
515C42—44no—
516C13#1546511yescharacteristic, direct product factor, Sylow
517C23—22no—
518C23—24no—
519C23—22no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C13×#12414yes—
538C23C22×D4×C1311yescharacteristic
539C23C22×D4×C1311yescharacteristic
540C23C22×D4×C1311yescharacteristic
541C23C2×C13×#4112yes—
542C23C2×C13×#4112yes—
543C23C2×C13×#4112yes—
544C23C13×H(5,𝔽2)12yes—
545C23C13×2−1+412yes—
546C23C13×2−1+412yes—
547Q8—416no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—416no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
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—
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×C4C13×#12014yes—
606C2×C4C13×#12314yes—
607C22—24no—
608C22—28no—
609C22—44no—
610C22—42no—
611C22—44no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22C2×C13×#12011yescharacteristic
617C22C2×C13×#12311yescharacteristic
618C22C2×C13×#12411yescharacteristic
619C22C13×#52912yes—
620C22C13×#53211yescharacteristic
621C22C13×#53411yescharacteristic
622C22C13×#53611yescharacteristic
623C22C13×#53611yescharacteristic
624C22C13×#53912yes—
625C22C13×#53912yes—
626C22C13×#54112yes—
627C22C13×#54612yes—
628C22C13×#54612yes—
629C22C13×#54712yes—
630C22C13×#54812yes—
631C22C13×#54812yes—
632C22C13×#54812yes—
633C22C13×#55112yes—
634C22C13×#55212yes—
635C22C13×#55612yes—
636C22C13×#56312yes—
637C4—24no—
638C4—24no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—82no—
645C4—82no—
646C4—82no—
647C2—44no—
648C2C13×#240511yescharacteristic
649C2C13×#242112yes—
650C2C13×#243211yescharacteristic
651C2C13×#243611yescharacteristic
652C2C13×#248812yes—
653C2C13×#256012yes—
654C2C13×#268912yes—
655C2C13×#269012yes—
656C2C13×#272812yes—
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#400C2semidirect
4. C2×C13×#391C2semidirect
5. C13×#1446C2semidirect
6. C13×#1442C2semidirect
7. C13×#1442C2semidirect
10. C13×#1436C2semidirect
101. #15465C13direct (N × H)
190. C2×#400C2×C13semidirect
192. C2×#391C2×C13semidirect
193. #1446C2×C13semidirect
194. #1442C2×C13semidirect
195. #1442C2×C13semidirect
198. #1436C2×C13semidirect
516. C13#15465direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C2×C13×#4002
C2×C13×#3972
C2×C13×#3912
C13×#14462
C13×#14422
C13×#14402
C13×#14372
C13×#14362
C13×C22⋊#952
#1546513