Finite Group Databasebeta

← C13×#15417 #15701756

Subgroups — C13×#15417 #15701756

Order 3328.

1730 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C212yesmaximal, complemented
2C2×C13×#388C212yesmaximal, complemented
3C2×C13×#388C212yesmaximal, complemented
4C13×#1444C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1439C212yesmaximal, complemented
7C13×#1438C211yesmaximal, characteristic
8C13×#1438C212yesmaximal
9C13×#1436C212yesmaximal, complemented
10C23×D4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
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×C13C2212yes—
22C13×#396—28no—
23C13×#388—28no—
24C13×#388—28no—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2212yes—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C25×C13C2312yes—
35C22×D4×C13—24no—
36C22×D4×C13—22no—
37C22×D4×C13—42no—
38C22×D4×C13—41no—
39C22×D4×C13—41no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C2×C13×C4⋊C4—24no—
49C2×C13×C4⋊C4—24no—
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—41no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C4⋊C4—41no—
57C2×C13×C4⋊C4—42no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—24no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—24no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—24no—
68C2×C13×C22⋊C4—24no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—42no—
73C2×C13×C22⋊C4—42no—
74C2×C13×C22⋊C4—42no—
75C2×C13×C22⋊C4—42no—
76C2×C42×C13—24no—
77C2×C42×C13—24no—
78C2×C42×C13—42no—
79C13×#95—24no—
80C13×#95—24no—
81C13×#95—24no—
82C13×#95—22no—
83C13×#95—42no—
84C13×#95—41no—
85C13×#95—41no—
86C13×#95D414yescomplemented
87C13×#95D418yescomplemented
88#15417C1311yesmaximal, 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×C13#4114yes—
104C24×C13C2411yescharacteristic
105C2×D4×C13—48no—
106C2×D4×C13—44no—
107C2×D4×C13—44no—
108C2×D4×C13—48no—
109C2×D4×C13—44no—
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—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
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—21no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
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—21no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13C2×D414yes—
153C22×C4×C13C2×D414yes—
154C22×C4×C13C2×D414yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D414yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4114yes—
160C13×C4⋊C4—44no—
161C13×C4⋊C4—48no—
162C13×C4⋊C4—44no—
163C13×C4⋊C4—48no—
164C13×C22⋊C4—216no—
165C13×C22⋊C4—216no—
166C13×C22⋊C4—48no—
167C13×C22⋊C4—48no—
168C13×C22⋊C4—48no—
169C13×C22⋊C4—48no—
170C42×C13—48no—
171C2×#396C2×C1312yescomplemented
172C2×#388C2×C1312yescomplemented
173C2×#388C2×C1312yescomplemented
174#1444C2×C1311yescharacteristic, complemented
175#1442C2×C1311yescharacteristic, complemented
176#1439C2×C1312yescomplemented
177#1438C2×C1311yescharacteristic
178#1438C2×C1312yes—
179#1436C2×C1312yescomplemented
180C23×C13—24no—
181C23×C13—24no—
182C23×C13—24no—
183C23×C13—24no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
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×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13C22×D411yescharacteristic
216C23×C13C22×D412yes—
217C23×C13C2×#4112yes—
218C23×C13C2×#4111yescharacteristic
219C23×C13C2×#4112yes—
220C23×C13C2×#4111yescharacteristic
221C23×C13H(5,𝔽2)11yescharacteristic
222C23×C13H(5,𝔽2)12yes—
223C23×C13H(5,𝔽2)11yescharacteristic
224C23×C132−1+411yescharacteristic
225C23×C132−1+411yescharacteristic
226D4×C13—416no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
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—41no—
262C2×C4×C13—42no—
263C2×C4×C13—41no—
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—41no—
271C2×C4×C13—41no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C23×D4C22×C1311yescharacteristic
278C22×C4⋊C4C22×C1311yescharacteristic
279C22×C4⋊C4C22×C1312yes—
280C22×C4⋊C4C22×C1312yes—
281C22×C4⋊C4C22×C1311yescharacteristic
282C22×C22⋊C4C22×C1312yes—
283C22×C22⋊C4C22×C1312yes—
284C22×C22⋊C4C22×C1312yes—
285C22×C22⋊C4C22×C1312yes—
286C22×C22⋊C4C22×C1312yes—
287C22×C22⋊C4C22×C1312yes—
288C22×C42C22×C1312yes—
289#396—28no—
290#388—28no—
291#388—28no—
292C2×#95C22×C1312yes—
293C2×#95C22×C1312yes—
294C2×#95C22×C1311yescharacteristic
295C2×#95C22×C1312yes—
296C2×#95C22×C1311yescharacteristic
297C2×#95C22×C1312yes—
298C2×#95C22×C1311yescharacteristic
299C2×#95C22×C1312yes—
300C2×#95C22×C1311yescharacteristic
301C22×C13—44no—
302C22×C13—44no—
303C22×C13—44no—
304C22×C13—44no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—82no—
309C22×C13—82no—
310C22×C13—82no—
311C22×C13—82no—
312C22×C13—82no—
313C22×C13—82no—
314C22×C13—82no—
315C22×C13—82no—
316C22×C13#52512yes—
317C22×C13#52512yes—
318C22×C13#53212yes—
319C22×C13#53712yes—
320C22×C13#53711yescharacteristic
321C22×C13#53812yes—
322C22×C13#53811yescharacteristic
323C22×C13#53911yescharacteristic
324C22×C13#54212yes—
325C22×C13D4212yes—
326C22×C13D4211yescharacteristic
327C22×C13#54612yes—
328C22×C13#54711yescharacteristic
329C22×C13#54812yes—
330C22×C13#55011yescharacteristic
331C22×C13#55112yes—
332C22×C13#55111yescharacteristic
333C22×C13#55212yes—
334C22×C13#55312yes—
335C22×C13#55511yescharacteristic
336C22×C13#55611yescharacteristic
337C22×C13#56011yescharacteristic
338C22×C13#56311yescharacteristic
339C4×C13—44no—
340C4×C13—42no—
341C4×C13—44no—
342C4×C13—44no—
343C4×C13—44no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—44no—
347C25C23×C1312yes—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—42no—
351C22×D4—41no—
352C22×D4—41no—
353C23×C4C23×C1311yescharacteristic
354C23×C4C23×C1312yes—
355C23×C4C23×C1312yes—
356C23×C4C23×C1312yes—
357C23×C4C23×C1312yes—
358C23×C4C23×C1312yes—
359C23×C4C23×C1311yescharacteristic
360C23×C4C23×C1311yescharacteristic
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—41no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—42no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—22no—
396#95—42no—
397#95—41no—
398#95—41no—
399#95D4×C1314yescomplemented
400#95D4×C1318yescomplemented
401C2×C13—84no—
402C2×C13#245612yes—
403C2×C13#246112yes—
404C2×C13#246311yescharacteristic
405C2×C13#255511yescharacteristic
406C2×C13#260112yes—
407C2×C13#260911yescharacteristic
408C2×C13#267511yescharacteristic
409C2×C13#270212yes—
410C2×C13#272711yescharacteristic
411C2×C13#273511yescharacteristic
412C2×C13#279511yescharacteristic
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24C13×#4114yes—
428C24C24×C1311yescharacteristic
429C2×D4—48no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—48no—
433C2×D4—44no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
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—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
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—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4C2×D4×C1314yes—
477C22×C4C2×D4×C1314yes—
478C22×C4C2×D4×C1314yes—
479C22×C4C2×D4×C1312yes—
480C22×C4C2×D4×C1314yes—
481C22×C4C13×#4112yes—
482C22×C4C13×#4112yes—
483C22×C4C13×#4114yes—
484C4⋊C4—44no—
485C4⋊C4—48no—
486C4⋊C4—44no—
487C4⋊C4—48no—
488C22⋊C4—216no—
489C22⋊C4—216no—
490C22⋊C4—48no—
491C22⋊C4—48no—
492C22⋊C4—48no—
493C22⋊C4—48no—
494C42—48no—
495C13#1541711yescharacteristic, direct product factor, Sylow
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
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—
531C23C22×D4×C1311yescharacteristic
532C23C22×D4×C1312yes—
533C23C2×C13×#4112yes—
534C23C2×C13×#4111yescharacteristic
535C23C2×C13×#4112yes—
536C23C2×C13×#4111yescharacteristic
537C23C13×H(5,𝔽2)11yescharacteristic
538C23C13×H(5,𝔽2)12yes—
539C23C13×H(5,𝔽2)11yescharacteristic
540C23C13×2−1+411yescharacteristic
541C23C13×2−1+411yescharacteristic
542D4—416no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
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—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22—82no—
606C22—82no—
607C22—82no—
608C22C13×#52512yes—
609C22C13×#52512yes—
610C22C13×#53212yes—
611C22C13×#53712yes—
612C22C13×#53711yescharacteristic
613C22C13×#53811yescharacteristic
614C22C13×#53812yes—
615C22C13×#53911yescharacteristic
616C22C13×#54212yes—
617C22D42×C1311yescharacteristic
618C22D42×C1312yes—
619C22C13×#54612yes—
620C22C13×#54711yescharacteristic
621C22C13×#54812yes—
622C22C13×#55011yescharacteristic
623C22C13×#55112yes—
624C22C13×#55111yescharacteristic
625C22C13×#55212yes—
626C22C13×#55312yes—
627C22C13×#55511yescharacteristic
628C22C13×#55611yescharacteristic
629C22C13×#56011yescharacteristic
630C22C13×#56311yescharacteristic
631C4—44no—
632C4—44no—
633C4—42no—
634C4—44no—
635C4—44no—
636C4—44no—
637C4—42no—
638C4—42no—
639C2—84no—
640C2C13×#245612yes—
641C2C13×#246112yes—
642C2C13×#246311yescharacteristic
643C2C13×#255511yescharacteristic
644C2C13×#260112yes—
645C2C13×#260911yescharacteristic
646C2C13×#267511yescharacteristic
647C2C13×#270212yes—
648C2C13×#272711yescharacteristic
649C2C13×#273511yescharacteristic
650C2C13×#279511yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#396C2semidirect
2. C2×C13×#388C2semidirect
3. C2×C13×#388C2semidirect
4. C13×#1444C2semidirect
5. C13×#1442C2semidirect
6. C13×#1439C2semidirect
9. C13×#1436C2semidirect
86. C13×#95D4semidirect
87. C13×#95D4semidirect
88. #15417C13direct (N × H)
171. C2×#396C2×C13semidirect
172. C2×#388C2×C13semidirect
173. C2×#388C2×C13semidirect
174. #1444C2×C13semidirect
175. #1442C2×C13semidirect
176. #1439C2×C13semidirect
179. #1436C2×C13semidirect
399. #95D4×C13semidirect
400. #95D4×C13semidirect
495. C13#15417direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3962
C2×C13×#3882
C13×#14442
C13×#14422
C13×#14392
C13×#14382
C13×#14362
#1541713