Finite Group Databasebeta

← C13×#15342 #15701681

Subgroups — C13×#15342 #15701681

Order 3328.

1838 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C212yesmaximal, complemented
2C2×C13×#390C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#385C212yesmaximal, complemented
5C13×#1444C212yesmaximal, complemented
6C13×#1440C212yesmaximal, complemented
7C13×#1439C212yesmaximal, complemented
8C13×#1438C211yesmaximal, characteristic
9C13×#1434C212yesmaximal, complemented
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C13×#397—28no—
24C13×#390—24no—
25C13×#386—24no—
26C13×#385—28no—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C25×C13C2311yescharacteristic
36C25×C13C2311yescharacteristic
37C22×D4×C13—24no—
38C22×D4×C13—24no—
39C22×D4×C13—41no—
40C22×D4×C13—41no—
41C22×D4×C13D414yes—
42C23×C4×C13—22no—
43C23×C4×C13—24no—
44C23×C4×C13—42no—
45C23×C4×C13—41no—
46C23×C4×C13—41no—
47C23×C4×C13C2312yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2312yes—
52C23×C4×C13C2312yes—
53C23×C4×C13C2311yescharacteristic
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—42no—
59C2×C13×C4⋊C4—41no—
60C2×C13×C4⋊C4—41no—
61C2×C13×C4⋊C4—42no—
62C2×C13×C4⋊C4—42no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—24no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—41no—
77C2×C13×C22⋊C4—41no—
78C2×C13×C22⋊C4—42no—
79C2×C13×C22⋊C4—42no—
80C2×C13×C22⋊C4—42no—
81C2×C42×C13—22no—
82C2×C42×C13—24no—
83C13×#95—24no—
84C13×#95—24no—
85C13×#95—24no—
86C13×#95—24no—
87C13×#95—24no—
88C13×#95—24no—
89C13×#95—42no—
90C13×#95D418yescomplemented
91#15342C1311yesmaximal, characteristic, direct product factor, Sylow
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—21no—
105C24×C13—21no—
106C24×C13—22no—
107C24×C13C2×D412yes—
108C24×C13C2×D412yes—
109C24×C13#4114yes—
110C24×C13C2411yescharacteristic
111C2×D4×C13—28no—
112C2×D4×C13—28no—
113C2×D4×C13—44no—
114C2×D4×C13—48no—
115C2×D4×C13—48no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
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—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—44no—
158C22×C4×C13—48no—
159C22×C4×C13—48no—
160C22×C4×C13—44no—
161C22×C4×C13—44no—
162C22×C4×C13C2×D414yes—
163C22×C4×C13C2×D414yes—
164C22×C4×C13C2×D414yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13#4114yes—
167C22×C4×C13#4114yes—
168C13×C4⋊C4—48no—
169C13×C4⋊C4—44no—
170C13×C4⋊C4—48no—
171C13×C22⋊C4—216no—
172C13×C22⋊C4—44no—
173C13×C22⋊C4—44no—
174C13×C22⋊C4—48no—
175C13×C22⋊C4—48no—
176C13×C22⋊C4—48no—
177C13×C22⋊C4—44no—
178C42×C13—44no—
179C2×#397C2×C1312yescomplemented
180C2×#390C2×C1311yescharacteristic
181C2×#386C2×C1311yescharacteristic
182C2×#385C2×C1312yescomplemented
183#1444C2×C1312yescomplemented
184#1440C2×C1312yescomplemented
185#1439C2×C1312yescomplemented
186#1438C2×C1311yescharacteristic
187#1434C2×C1312yescomplemented
188C23×C13—22no—
189C23×C13—24no—
190C23×C13—22no—
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—24no—
196C23×C13—24no—
197C23×C13—24no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—41no—
208C23×C13—42no—
209C23×C13—41no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—41no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13—41no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13#12314yes—
230C23×C13C22×D411yescharacteristic
231C23×C13C22×D412yes—
232C23×C13C2×#4112yes—
233C23×C13C2×#4112yes—
234C23×C13C2×#4112yes—
235C23×C13H(5,𝔽2)11yescharacteristic
236C23×C13H(5,𝔽2)11yescharacteristic
237C23×C13H(5,𝔽2)12yes—
238C23×C132−1+412yes—
239D4×C13—416no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
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—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—416no—
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×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#12314yes—
288C23×D4C22×C1311yescharacteristic
289C24×C4C22×C1311yescharacteristic
290C22×C4⋊C4C22×C1312yes—
291C22×C4⋊C4C22×C1312yes—
292C22×C4⋊C4C22×C1311yescharacteristic
293C22×C22⋊C4C22×C1312yes—
294C22×C22⋊C4C22×C1311yescharacteristic
295C22×C22⋊C4C22×C1311yescharacteristic
296C22×C22⋊C4C22×C1312yes—
297C22×C22⋊C4C22×C1312yes—
298C22×C22⋊C4C22×C1311yescharacteristic
299C22×C22⋊C4C22×C1312yes—
300C22×C42C22×C1311yescharacteristic
301#397—28no—
302#390—24no—
303#386—24no—
304#385—28no—
305C2×#95C22×C1312yes—
306C2×#95C22×C1312yes—
307C2×#95C22×C1312yes—
308C2×#95C22×C1312yes—
309C2×#95C22×C1312yes—
310C2×#95C22×C1312yes—
311C2×#95C22×C1312yes—
312C2×#95C22×C1312yes—
313C22×C13—28no—
314C22×C13—24no—
315C22×C13—44no—
316C22×C13—42no—
317C22×C13—44no—
318C22×C13—44no—
319C22×C13—42no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—42no—
323C22×C13—44no—
324C22×C13—44no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—82no—
328C22×C13—82no—
329C22×C13—82no—
330C22×C13—82no—
331C22×C13C2×#12311yescharacteristic
332C22×C13C2×#12311yescharacteristic
333C22×C13#52512yes—
334C22×C13#53212yes—
335C22×C13#53411yescharacteristic
336C22×C13#53512yes—
337C22×C13#53912yes—
338C22×C13#54212yes—
339C22×C13#54212yes—
340C22×C13D4212yes—
341C22×C13D4211yescharacteristic
342C22×C13#54712yes—
343C22×C13#54712yes—
344C22×C13#54812yes—
345C22×C13#55111yescharacteristic
346C22×C13#55112yes—
347C22×C13#55112yes—
348C22×C13#55312yes—
349C22×C13#55312yes—
350C22×C13#56011yescharacteristic
351C22×C13#56311yescharacteristic
352C4×C13—24no—
353C4×C13—44no—
354C4×C13—44no—
355C4×C13—44no—
356C4×C13—44no—
357C4×C13—82no—
358C4×C13—82no—
359C25C23×C1311yescharacteristic
360C25C23×C1311yescharacteristic
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4D4×C1314yes—
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—42no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4C23×C1312yes—
372C23×C4C23×C1312yes—
373C23×C4C23×C1312yes—
374C23×C4C23×C1312yes—
375C23×C4C23×C1312yes—
376C23×C4C23×C1312yes—
377C23×C4C23×C1311yescharacteristic
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C42—22no—
406C2×C42—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—42no—
414#95D4×C1318yescomplemented
415C2×C13—44no—
416C2×C13—82no—
417C2×C13#242212yes—
418C2×C13#244312yes—
419C2×C13#246112yes—
420C2×C13#248311yescharacteristic
421C2×C13#260312yes—
422C2×C13#266911yescharacteristic
423C2×C13#271711yescharacteristic
424C2×C13#272312yes—
425C2×C13#275712yes—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24C2×D4×C1312yes—
442C24C2×D4×C1312yes—
443C24C13×#4114yes—
444C24C24×C1311yescharacteristic
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—44no—
448C2×D4—48no—
449C2×D4—48no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
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—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—44no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4C2×D4×C1314yes—
497C22×C4C2×D4×C1314yes—
498C22×C4C2×D4×C1314yes—
499C22×C4C2×D4×C1312yes—
500C22×C4C13×#4114yes—
501C22×C4C13×#4114yes—
502C4⋊C4—48no—
503C4⋊C4—44no—
504C4⋊C4—48no—
505C22⋊C4—216no—
506C22⋊C4—44no—
507C22⋊C4—44no—
508C22⋊C4—48no—
509C22⋊C4—48no—
510C22⋊C4—48no—
511C22⋊C4—44no—
512C42—44no—
513C13#1534211yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—24no—
516C23—22no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—24no—
528C23—24no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—41no—
534C23—42no—
535C23—41no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—41no—
554C23—41no—
555C23C13×#12314yes—
556C23C22×D4×C1311yescharacteristic
557C23C22×D4×C1312yes—
558C23C2×C13×#4112yes—
559C23C2×C13×#4112yes—
560C23C2×C13×#4112yes—
561C23C13×H(5,𝔽2)11yescharacteristic
562C23C13×H(5,𝔽2)11yescharacteristic
563C23C13×H(5,𝔽2)12yes—
564C23C13×2−1+412yes—
565D4—416no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—416no—
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×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4C13×#12314yes—
614C22—28no—
615C22—24no—
616C22—44no—
617C22—44no—
618C22—42no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—44no—
623C22—42no—
624C22—44no—
625C22—44no—
626C22—42no—
627C22—42no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22C2×C13×#12311yescharacteristic
633C22C2×C13×#12311yescharacteristic
634C22C13×#52512yes—
635C22C13×#53212yes—
636C22C13×#53411yescharacteristic
637C22C13×#53512yes—
638C22C13×#53912yes—
639C22C13×#54212yes—
640C22C13×#54212yes—
641C22D42×C1312yes—
642C22D42×C1311yescharacteristic
643C22C13×#54712yes—
644C22C13×#54712yes—
645C22C13×#54812yes—
646C22C13×#55112yes—
647C22C13×#55111yescharacteristic
648C22C13×#55112yes—
649C22C13×#55312yes—
650C22C13×#55312yes—
651C22C13×#56011yescharacteristic
652C22C13×#56311yescharacteristic
653C4—24no—
654C4—44no—
655C4—44no—
656C4—44no—
657C4—44no—
658C4—82no—
659C4—82no—
660C2—44no—
661C2—82no—
662C2C13×#242212yes—
663C2C13×#244312yes—
664C2C13×#246112yes—
665C2C13×#248311yescharacteristic
666C2C13×#260312yes—
667C2C13×#266911yescharacteristic
668C2C13×#271711yescharacteristic
669C2C13×#272312yes—
670C2C13×#275712yes—
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×#397C2semidirect
4. C2×C13×#385C2semidirect
5. C13×#1444C2semidirect
6. C13×#1440C2semidirect
7. C13×#1439C2semidirect
9. C13×#1434C2semidirect
90. C13×#95D4semidirect
91. #15342C13direct (N × H)
179. C2×#397C2×C13semidirect
182. C2×#385C2×C13semidirect
183. #1444C2×C13semidirect
184. #1440C2×C13semidirect
185. #1439C2×C13semidirect
187. #1434C2×C13semidirect
414. #95D4×C13semidirect
513. C13#15342direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3902
C2×C13×#3862
C2×C13×#3852
C13×#14442
C13×#14402
C13×#14392
C13×#14382
C13×#14342
#1534213