Finite Group Databasebeta

← C13×#24556 #15710895

Subgroups — C13×#24556 #15710895

Order 3328.

1156 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#484C211yesmaximal, characteristic, complemented
2C2×C13×#407C211yesmaximal, characteristic
3C13×#2848C211yesmaximal, characteristic
4C2×C13×#380C211yesmaximal, characteristic
5C13×#2075C212yesmaximal, complemented
6C13×#2035C212yesmaximal, complemented
7C13×#1894C212yesmaximal, complemented
8C13×#1872C211yesmaximal, characteristic, complemented
9C13×#1853C211yesmaximal, characteristic, complemented
10C13×#1824C211yesmaximal, characteristic, complemented
11C13×#1809C212yesmaximal, complemented
12C24×C4×C13C2211yescharacteristic
13C22×C13×M16C2212yes—
14C2×C13×C22⋊Q8C2211yescharacteristic
15C2×C13×C22⋊Q8C2211yescharacteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4—21no—
20C13×#484—24no—
21C2×C13×#107C2212yescomplemented
22C2×C13×#106C2212yescomplemented
23C2×C13×#103C2212yescomplemented
24C2×C13×#103C2212yescomplemented
25C13×#407—24no—
26C2×C13×C22⋊C8C2212yes—
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C13×C22⋊C8C2211yescharacteristic
29C13×#385—21no—
30C13×#385—21no—
31C13×#385—21no—
32C13×#380—21no—
33C13×#380—21no—
34C13×#380C2212yes—
35C13×#380C2212yes—
36C13×#380C2211yescharacteristic
37C13×#380C2211yescharacteristic
38C13×#380C2211yescharacteristic
39C13×#379—21no—
40C2×C13×#95—21no—
41C13×#340C2212yescomplemented
42C13×#340C2212yescomplemented
43C13×#340C2212yescomplemented
44C13×#340C2212yescomplemented
45C25×C13D411yescharacteristic
46C22×Q8×C13C2311yescharacteristic
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—24no—
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13—42no—
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C2×C13×M16—24no—
60C2×C13×M16—24no—
61C2×C13×M16—42no—
62C22×C8×C13C2312yes—
63C22×C8×C13C2312yes—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—24no—
67C13×C22⋊Q8—42no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—42no—
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2312yes—
78C2×C13×C4⋊C4C2312yes—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—44no—
90C13×#107—24no—
91C13×#106—42no—
92C13×#103—24no—
93C13×#103—42no—
94C13×C22⋊C8—22no—
95C13×C22⋊C8—24no—
96C13×C22⋊C8D414yes—
97C13×#95—22no—
98C13×#95—22no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102#24556C1311yesmaximal, characteristic, direct product factor, Sylow
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—41no—
109C24×C13—41no—
110C24×C13C2×D411yescharacteristic
111C24×C13C2×D411yescharacteristic
112C24×C13C2×D411yescharacteristic
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—22no—
116C2×Q8×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—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13—48no—
142C22×C4×C13—48no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13#4112yes—
154C22×C4×C13#4114yes—
155C22×C4×C13C2411yescharacteristic
156C13×M16—48no—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
159C2×C8×C13—22no—
160C2×C8×C13—22no—
161C2×C8×C13—22no—
162C2×C8×C13C2×D414yes—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—44no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—42no—
181C13×C22⋊C4—42no—
182C13×C22⋊C4—44no—
183C13×C22⋊C4—42no—
184C2×#484C2×C1311yescharacteristic, complemented
185C2×#407C2×C1311yescharacteristic
186#2848C2×C1311yescharacteristic
187C2×#380C2×C1311yescharacteristic
188#2075C2×C1312yescomplemented
189#2035C2×C1312yescomplemented
190#1894C2×C1312yescomplemented
191#1872C2×C1311yescharacteristic, complemented
192#1853C2×C1311yescharacteristic, complemented
193#1824C2×C1311yescharacteristic, complemented
194#1809C2×C1312yescomplemented
195C23×C13—21no—
196C23×C13—21no—
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—28no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—44no—
213C23×C13—44no—
214C23×C13—44no—
215C23×C13—44no—
216C23×C13—44no—
217C23×C13—44no—
218C23×C13#12112yes—
219C23×C13#12312yes—
220C23×C13AGL(1,ℤ/8)12yes—
221C23×C13#13712yes—
222C23×C13#13712yes—
223C23×C13C22×D411yescharacteristic
224Q8×C13—42no—
225Q8×C13—42no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—44no—
238C2×C4×C13—44no—
239C2×C4×C13—44no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—42no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—42no—
260C2×C4×C13—84no—
261C2×C4×C13—84no—
262C2×C4×C13#12112yes—
263C2×C4×C13#12312yes—
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C2×#4112yes—
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13H(5,𝔽2)12yes—
268C8×C13—24no—
269C8×C13—42no—
270C24×C4C22×C1311yescharacteristic
271C22×M16C22×C1312yes—
272C2×C22⋊Q8C22×C1311yescharacteristic
273C2×C22⋊Q8C22×C1311yescharacteristic
274C2×C22⋊Q8C22×C1311yescharacteristic
275C22×C4⋊C4C22×C1311yescharacteristic
276C22×C4⋊C4C22×C1311yescharacteristic
277C22×C22⋊C4—21no—
278#484—24no—
279C2×#107C22×C1312yescomplemented
280C2×#106C22×C1312yescomplemented
281C2×#103C22×C1312yescomplemented
282C2×#103C22×C1312yescomplemented
283#407—24no—
284C2×C22⋊C8C22×C1312yes—
285C2×C22⋊C8C22×C1311yescharacteristic
286C2×C22⋊C8C22×C1311yescharacteristic
287#385—21no—
288#385—21no—
289#385—21no—
290#380—21no—
291#380—21no—
292#380C22×C1311yescharacteristic
293#380C22×C1312yes—
294#380C22×C1311yescharacteristic
295#380C22×C1312yes—
296#380C22×C1311yescharacteristic
297#379—21no—
298C2×#95—21no—
299#340C22×C1312yescomplemented
300#340C22×C1312yescomplemented
301#340C22×C1312yescomplemented
302#340C22×C1312yescomplemented
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—22no—
310C22×C13—22no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—22no—
315C22×C13—416no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13#47014yes—
325C22×C13C2×#12111yescharacteristic
326C22×C13C2×#12311yescharacteristic
327C22×C13#53411yescharacteristic
328C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C13C2×#13711yescharacteristic
330C22×C13C2×#13711yescharacteristic
331C22×C13#57511yescharacteristic
332C4×C13—22no—
333C4×C13—22no—
334C4×C13—41no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—82no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13—82no—
341C4×C13#54612yes—
342C4×C13#55112yes—
343C25D4×C1311yescharacteristic
344C22×Q8C23×C1311yescharacteristic
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—24no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—42no—
351C23×C4D4×C1311yescharacteristic
352C23×C4D4×C1311yescharacteristic
353C23×C4D4×C1311yescharacteristic
354C23×C4C23×C1311yescharacteristic
355C23×C4C23×C1311yescharacteristic
356C23×C4C23×C1311yescharacteristic
357C2×M16—24no—
358C2×M16—24no—
359C2×M16—42no—
360C22×C8C23×C1312yes—
361C22×C8C23×C1312yes—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—24no—
365C22⋊Q8—42no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4C23×C1312yes—
375C2×C4⋊C4C23×C1312yes—
376C2×C4⋊C4C23×C1311yescharacteristic
377C2×C4⋊C4C23×C1311yescharacteristic
378C2×C4⋊C4C23×C1311yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—44no—
388#107—24no—
389#106—42no—
390#103—24no—
391#103—42no—
392C22⋊C8—22no—
393C22⋊C8—24no—
394C22⋊C8D4×C1314yes—
395#95—22no—
396#95—22no—
397#95—21no—
398#95—21no—
399#95—21no—
400C2×C13—24no—
401C2×C13—42no—
402C2×C13—42no—
403C2×C13#241211yescharacteristic
404C2×C13C2×#47011yescharacteristic
405C2×C13#305511yescharacteristic
406C2×C13#309211yescharacteristic
407C2×C13#309511yescharacteristic
408C2×C13#319311yescharacteristic
409C2×C13#319611yescharacteristic
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—41no—
416C24—41no—
417C24C2×D4×C1311yescharacteristic
418C24C2×D4×C1311yescharacteristic
419C24C2×D4×C1311yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—22no—
423C2×Q8—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—48no—
449C22×C4—48no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4C2×D4×C1311yescharacteristic
457C22×C4C2×D4×C1311yescharacteristic
458C22×C4C2×D4×C1312yes—
459C22×C4C2×D4×C1311yescharacteristic
460C22×C4C13×#4112yes—
461C22×C4C13×#4114yes—
462C22×C4C24×C1311yescharacteristic
463M16—48no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8C2×D4×C1314yes—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C22⋊C4—44no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—44no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C13#2455611yescharacteristic, direct product factor, Sylow
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—28no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—44no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23C13×#12112yes—
516C23C13×#12312yes—
517C23C13×AGL(1,ℤ/8)12yes—
518C23C13×#13712yes—
519C23C13×#13712yes—
520C23C22×D4×C1311yescharacteristic
521Q8—42no—
522Q8—42no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4C13×#12112yes—
560C2×C4C13×#12312yes—
561C2×C4C22×D4×C1311yescharacteristic
562C2×C4C2×C13×#4112yes—
563C2×C4C2×C13×#4111yescharacteristic
564C2×C4C13×H(5,𝔽2)12yes—
565C8—24no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—416no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C13×#47014yes—
589C22C2×C13×#12111yescharacteristic
590C22C2×C13×#12311yescharacteristic
591C22C13×#53411yescharacteristic
592C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
593C22C2×C13×#13711yescharacteristic
594C22C2×C13×#13711yescharacteristic
595C22C13×#57511yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—81no—
600C4—82no—
601C4—81no—
602C4—81no—
603C4—82no—
604C4—81no—
605C4C13×#54612yes—
606C4C13×#55112yes—
607C2—24no—
608C2—42no—
609C2—42no—
610C2C13×#241211yescharacteristic
611C2C2×C13×#47011yescharacteristic
612C2C13×#305511yescharacteristic
613C2C13×#309211yescharacteristic
614C2C13×#309511yescharacteristic
615C2C13×#319311yescharacteristic
616C2C13×#319611yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC25×C13D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C24×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#484C2semidirect
5. C13×#2075C2semidirect
6. C13×#2035C2semidirect
7. C13×#1894C2semidirect
8. C13×#1872C2semidirect
9. C13×#1853C2semidirect
10. C13×#1824C2semidirect
11. C13×#1809C2semidirect
21. C2×C13×#107C22semidirect
22. C2×C13×#106C22semidirect
23. C2×C13×#103C22semidirect
24. C2×C13×#103C22semidirect
41. C13×#340C22semidirect
42. C13×#340C22semidirect
43. C13×#340C22semidirect
44. C13×#340C22semidirect
102. #24556C13direct (N × H)
184. C2×#484C2×C13semidirect
188. #2075C2×C13semidirect
189. #2035C2×C13semidirect
190. #1894C2×C13semidirect
191. #1872C2×C13semidirect
192. #1853C2×C13semidirect
193. #1824C2×C13semidirect
194. #1809C2×C13semidirect
279. C2×#107C22×C13semidirect
280. C2×#106C22×C13semidirect
281. C2×#103C22×C13semidirect
282. C2×#103C22×C13semidirect
299. #340C22×C13semidirect
300. #340C22×C13semidirect
301. #340C22×C13semidirect
302. #340C22×C13semidirect
491. C13#24556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4842
C2×C13×#4072
C13×#28482
C2×C13×#3802
C13×#20752
C13×#20352
C13×#18942
C13×#18722
C13×#18532
C13×#18242
C13×#18092
#2455613