Finite Group Databasebeta

← C13×#23986 #15710325

Subgroups — C13×#23986 #15710325

Order 3328.

1426 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3491C211yesmaximal, characteristic, complemented
2C13×#2849C212yesmaximal, complemented
3C13×#2280C211yesmaximal, characteristic, complemented
4C13×#2030C211yesmaximal, characteristic, complemented
5C13×#2029C211yesmaximal, characteristic, complemented
6C13×#2022C211yesmaximal, characteristic, complemented
7C13×#2021C211yesmaximal, characteristic
8C13×#1899C212yesmaximal, complemented
9C13×#1890C212yesmaximal, complemented
10C13×#1889C212yesmaximal, complemented
11C13×#1820C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C13×#552—24no—
14C13×#551—24no—
15C13×#543C2211yescharacteristic
16C13×#539—22no—
17C13×#534C2211yescharacteristic
18C13×#529—22no—
19C2×C13×#123C2212yes—
20C2×C13×#123C2212yes—
21C2×C13×#120C2212yes—
22C13×#518C2212yes—
23C2×C13×#117C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C2×C13×#99C2212yes—
26C2×C13×#99C2212yes—
27C13×#386—24no—
28C13×#385—24no—
29C13×#381C2211yescharacteristic
30C13×#381C2211yescharacteristic
31C13×#381C2212yes—
32C13×#381C2212yes—
33C13×#380—22no—
34C13×#379C2211yescharacteristic
35C13×#379C2211yescharacteristic
36C13×#379C2212yes—
37C4×C13×C22⋊C4—22no—
38C13×#342C2211yescharacteristic
39C13×#342C2211yescharacteristic
40C13×#342C2212yes—
41C13×#342C2212yes—
42C13×#342C2212yes—
43C25×C13C2311yescharacteristic
44C22×D4×C13—22no—
45C22×D4×C13C2312yes—
46C23×C4×C13—22no—
47C23×C4×C13—21no—
48C23×C4×C13—21no—
49C23×C4×C13—22no—
50C23×C4×C13—24no—
51C23×C4×C13—42no—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C13×#126—24no—
55C13×#126—24no—
56C13×#125—22no—
57C13×#125—24no—
58C13×#124—22no—
59C13×#123—24no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—24no—
63C13×#123—22no—
64C13×#123—24no—
65C13×#123—42no—
66C13×C22⋊Q8—24no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—24no—
69C13×#121—22no—
70C13×#120—22no—
71C13×#120—24no—
72C13×#120—42no—
73C4×Q8×C13—22no—
74C4×D4×C13—22no—
75C4×D4×C13—24no—
76C4×D4×C13—24no—
77C13×#117—24no—
78C13×#117—24no—
79C13×#117—22no—
80C13×#117—42no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4D412yescomplemented
84C2×C13×C4⋊C4D414yescomplemented
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—24no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4D414yescomplemented
92C2×C13×C22⋊C4C2311yescharacteristic
93C2×C13×C22⋊C4C2311yescharacteristic
94C2×C13×C22⋊C4C2312yes—
95C2×C13×C22⋊C4C2312yes—
96C2×C13×C22⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4C2311yescharacteristic
98C2×C13×C22⋊C4C2312yes—
99C2×C42×C13—21no—
100C2×C42×C13D412yescomplemented
101C13×#99—42no—
102C13×#99—42no—
103C13×#95—22no—
104C13×#95—22no—
105C13×#95—24no—
106C13×#95—24no—
107#23986C1311yesmaximal, characteristic, direct product factor, Sylow
108C24×C13—21no—
109C24×C13—22no—
110C24×C13—21no—
111C24×C13—22no—
112C24×C13—44no—
113C24×C13C2×D412yes—
114C24×C13#4112yes—
115C24×C13C2411yescharacteristic
116C2×Q8×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—44no—
125C2×D4×C13—48no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—22no—
129C22×C4×C13—24no—
130C22×C4×C13—24no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—48no—
141C22×C4×C13—48no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D414yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D414yes—
153C22×C4×C13#4112yes—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—44no—
162C13×C4⋊C4—42no—
163C13×C22⋊C4—24no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—24no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—44no—
178C13×C22⋊C4—44no—
179C13×C22⋊C4—44no—
180C13×C22⋊C4—44no—
181C13×C22⋊C4—48no—
182C42×C13—24no—
183C42×C13—22no—
184C42×C13—22no—
185C42×C13—42no—
186#3491C2×C1311yescharacteristic, complemented
187#2849C2×C1312yescomplemented
188#2280C2×C1311yescharacteristic, complemented
189#2030C2×C1311yescharacteristic, complemented
190#2029C2×C1311yescharacteristic, complemented
191#2022C2×C1311yescharacteristic, complemented
192#2021C2×C1311yescharacteristic
193#1899C2×C1312yescomplemented
194#1890C2×C1312yescomplemented
195#1889C2×C1312yescomplemented
196#1820C2×C1311yescharacteristic, complemented
197C23×C13—24no—
198C23×C13—28no—
199C23×C13—22no—
200C23×C13—24no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—44no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—44no—
208C23×C13—48no—
209C23×C13—44no—
210C23×C13—44no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—42no—
214C23×C13C22×D411yescharacteristic
215C23×C13C22×D412yes—
216C23×C13C2×#4111yescharacteristic
217C23×C13C2×#4111yescharacteristic
218C23×C13H(5,𝔽2)12yes—
219Q8×C13—82no—
220D4×C13—42no—
221D4×C13—42no—
222D4×C13—42no—
223D4×C13—42no—
224D4×C13—82no—
225D4×C13—88no—
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—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—22no—
240C2×C4×C13—48no—
241C2×C4×C13—48no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—44no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—44no—
251C2×C4×C13—44no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—84no—
257C2×C4×C13#12012yes—
258C2×C4×C13#12012yes—
259C24×C4C22×C1311yescharacteristic
260#552—24no—
261#551—24no—
262#543C22×C1311yescharacteristic
263#539—22no—
264#534C22×C1311yescharacteristic
265#529—22no—
266C2×#123C22×C1312yes—
267C2×#123C22×C1312yes—
268C2×#120C22×C1312yes—
269#518C22×C1312yes—
270C2×#117C22×C1311yescharacteristic
271C2×#117C22×C1311yescharacteristic
272C2×#99C22×C1312yes—
273C2×#99C22×C1312yes—
274#386—24no—
275#385—24no—
276#381C22×C1312yes—
277#381C22×C1312yes—
278#381C22×C1311yescharacteristic
279#381C22×C1311yescharacteristic
280#380—22no—
281#379C22×C1312yes—
282#379C22×C1311yescharacteristic
283#379C22×C1311yescharacteristic
284C4×C22⋊C4—22no—
285#342C22×C1312yes—
286#342C22×C1311yescharacteristic
287#342C22×C1311yescharacteristic
288#342C22×C1312yes—
289#342C22×C1312yes—
290C22×C13—22no—
291C22×C13—24no—
292C22×C13—28no—
293C22×C13—24no—
294C22×C13—41no—
295C22×C13—41no—
296C22×C13—42no—
297C22×C13—44no—
298C22×C13—44no—
299C22×C13—48no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—44no—
303C22×C13—42no—
304C22×C13—44no—
305C22×C13—82no—
306C22×C13—82no—
307C22×C13C2×#12011yescharacteristic
308C22×C13#52511yescharacteristic
309C22×C13#53511yescharacteristic
310C22×C13#54612yes—
311C22×C13#54612yes—
312C4×C13—22no—
313C4×C13—22no—
314C4×C13—42no—
315C4×C13—42no—
316C4×C13—42no—
317C4×C13—44no—
318C4×C13—42no—
319C4×C13—81no—
320C4×C13—81no—
321C4×C13—82no—
322C4×C13—82no—
323C25C23×C1311yescharacteristic
324C22×D4—22no—
325C22×D4C23×C1312yes—
326C23×C4—22no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—22no—
330C23×C4—24no—
331C23×C4—42no—
332C23×C4C23×C1311yescharacteristic
333C23×C4C23×C1311yescharacteristic
334#126—24no—
335#126—24no—
336#125—22no—
337#125—24no—
338#124—22no—
339#123—24no—
340#123—22no—
341#123—22no—
342#123—24no—
343#123—22no—
344#123—24no—
345#123—42no—
346C22⋊Q8—24no—
347C22⋊Q8—22no—
348C22⋊Q8—24no—
349#121—22no—
350#120—22no—
351#120—24no—
352#120—42no—
353C4×Q8—22no—
354C4×D4—22no—
355C4×D4—24no—
356C4×D4—24no—
357#117—24no—
358#117—24no—
359#117—22no—
360#117—42no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4D4×C1312yescomplemented
364C2×C4⋊C4D4×C1314yescomplemented
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4D4×C1314yescomplemented
372C2×C22⋊C4C23×C1311yescharacteristic
373C2×C22⋊C4C23×C1311yescharacteristic
374C2×C22⋊C4C23×C1312yes—
375C2×C22⋊C4C23×C1312yes—
376C2×C22⋊C4C23×C1311yescharacteristic
377C2×C22⋊C4C23×C1311yescharacteristic
378C2×C22⋊C4C23×C1312yes—
379C2×C42—21no—
380C2×C42D4×C1312yescomplemented
381#99—42no—
382#99—42no—
383#95—22no—
384#95—22no—
385#95—24no—
386#95—24no—
387C2×C13—21no—
388C2×C13—22no—
389C2×C13—22no—
390C2×C13—21no—
391C2×C13—44no—
392C2×C13—82no—
393C2×C13#240411yescharacteristic
394C2×C13#302512yes—
395C24—21no—
396C24—22no—
397C24—21no—
398C24—22no—
399C24—44no—
400C24C2×D4×C1312yes—
401C24C13×#4112yes—
402C24C24×C1311yescharacteristic
403C2×Q8—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—44no—
412C2×D4—48no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—48no—
428C22×C4—48no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4C2×D4×C1312yes—
434C22×C4C2×D4×C1314yes—
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C2×D4×C1311yescharacteristic
437C22×C4C2×D4×C1312yes—
438C22×C4C2×D4×C1312yes—
439C22×C4C2×D4×C1314yes—
440C22×C4C13×#4112yes—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—44no—
449C4⋊C4—42no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—44no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—48no—
469C42—24no—
470C42—22no—
471C42—22no—
472C42—42no—
473C13#2398611yescharacteristic, direct product factor, Sylow
474C23—24no—
475C23—28no—
476C23—22no—
477C23—24no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—44no—
482C23—42no—
483C23—42no—
484C23—44no—
485C23—48no—
486C23—44no—
487C23—44no—
488C23—41no—
489C23—41no—
490C23—42no—
491C23C22×D4×C1311yescharacteristic
492C23C22×D4×C1312yes—
493C23C2×C13×#4111yescharacteristic
494C23C2×C13×#4111yescharacteristic
495C23C13×H(5,𝔽2)12yes—
496Q8—82no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—82no—
502D4—88no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—48no—
518C2×C4—48no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4C13×#12012yes—
535C2×C4C13×#12012yes—
536C22—22no—
537C22—24no—
538C22—28no—
539C22—24no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—44no—
544C22—44no—
545C22—48no—
546C22—42no—
547C22—44no—
548C22—42no—
549C22—44no—
550C22—42no—
551C22—82no—
552C22—82no—
553C22C2×C13×#12011yescharacteristic
554C22C13×#52511yescharacteristic
555C22C13×#53511yescharacteristic
556C22C13×#54612yes—
557C22C13×#54612yes—
558C4—22no—
559C4—22no—
560C4—42no—
561C4—44no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—81no—
566C4—81no—
567C4—82no—
568C4—82no—
569C2—21no—
570C2—22no—
571C2—22no—
572C2—21no—
573C2—44no—
574C2—82no—
575C2C13×#240411yescharacteristic
576C2C13×#302512yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#2021C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3491C2semidirect
2. C13×#2849C2semidirect
3. C13×#2280C2semidirect
4. C13×#2030C2semidirect
5. C13×#2029C2semidirect
6. C13×#2022C2semidirect
8. C13×#1899C2semidirect
9. C13×#1890C2semidirect
10. C13×#1889C2semidirect
11. C13×#1820C2semidirect
83. C2×C13×C4⋊C4D4semidirect
84. C2×C13×C4⋊C4D4semidirect
91. C2×C13×C22⋊C4D4semidirect
100. C2×C42×C13D4semidirect
107. #23986C13direct (N × H)
186. #3491C2×C13semidirect
187. #2849C2×C13semidirect
188. #2280C2×C13semidirect
189. #2030C2×C13semidirect
190. #2029C2×C13semidirect
191. #2022C2×C13semidirect
193. #1899C2×C13semidirect
194. #1890C2×C13semidirect
195. #1889C2×C13semidirect
196. #1820C2×C13semidirect
363. C2×C4⋊C4D4×C13semidirect
364. C2×C4⋊C4D4×C13semidirect
371. C2×C22⋊C4D4×C13semidirect
380. C2×C42D4×C13semidirect
473. C13#23986direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34912
C13×#28492
C13×#22802
C13×#20302
C13×#20292
C13×#20222
C13×#20212
C13×#18992
C13×#18902
C13×#18892
C13×#18202
#2398613