Finite Group Databasebeta

← C13×#18343 #15704682

Subgroups — C13×#18343 #15704682

Order 3328.

1034 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3459C211yesmaximal, characteristic
2C13×#3239C212yesmaximal, complemented
3C13×#2542C211yesmaximal, characteristic, complemented
4C13×#1618C214yesmaximal, complemented
5C13×#1614C212yesmaximal, complemented
6C13×#1613C212yesmaximal, complemented
7C13×#1509C212yesmaximal, complemented
8C13×#1466C211yesmaximal, characteristic, complemented
9C13×#543C2211yescharacteristic
10C13×#539—22no—
11C13×#539—21no—
12C13×#538—22no—
13C13×#538C2212yes—
14C13×#534—21no—
15C13×#534C2211yescharacteristic
16C2×C13×C4⋊Q8C2211yescharacteristic, complemented
17C13×#529—22no—
18C13×#529C2212yes—
19C13×#525—21no—
20C13×#525—22no—
21C2×C13×C22⋊Q8—21no—
22C2×C13×C22⋊Q8—21no—
23C2×C4×D4×C13—21no—
24C2×C4×D4×C13C2211yescharacteristic
25C13×#501—22no—
26C13×#489—22no—
27C13×#484C2214yescomplemented
28C13×#481C2214yes—
29C13×#475—22no—
30C13×#474—22no—
31C13×#432C2212yescomplemented
32C13×#399C2212yes—
33C13×#399C2212yescomplemented
34C13×#390—21no—
35C13×#384—21no—
36C4×C13×C4⋊C4C2211yescharacteristic, complemented
37C13×#328C2214yescomplemented
38C13×#327C2214yes—
39C13×#323C2212yes—
40C13×#323C2212yescomplemented
41C2×C13×#41—21no—
42C22×Q8×C13—21no—
43C22×D4×C13—21no—
44C22×D4×C13D411yescharacteristic
45C23×C4×C13—21no—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C13×C4⋊Q8—22no—
49C13×C4⋊Q8—22no—
50C13×#126—22no—
51C13×#126—22no—
52C13×#126—22no—
53C13×#125—22no—
54C13×#125D412yes—
55C13×#124—22no—
56C13×#124D412yes—
57C13×#123—22no—
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—21no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—44no—
69C13×C22⋊Q8—44no—
70C13×C22⋊Q8C2312yes—
71C13×#121—22no—
72C13×#121—21no—
73C13×#121—22no—
74C13×#121—22no—
75C13×#121—21no—
76C13×#121C2312yes—
77C13×#120—22no—
78C13×#120—22no—
79C13×#120—22no—
80C4×Q8×C13D412yes—
81C4×D4×C13—22no—
82C4×D4×C13—22no—
83C4×D4×C13—22no—
84C4×D4×C13—22no—
85C4×D4×C13—22no—
86C4×D4×C13—22no—
87C4×D4×C13—22no—
88C4×D4×C13D412yes—
89C13×#117—21no—
90C13×#117—22no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4D411yescharacteristic
97C2×C13×C4⋊C4C2312yes—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4C2311yescharacteristic
103C2×C13×C22⋊C4C2311yescharacteristic
104C2×C42×C13—21no—
105C2×C42×C13—21no—
106C2×C42×C13C2311yescharacteristic
107C13×#107—24no—
108C13×#106—24no—
109C13×C4⋊C8—22no—
110C13×#103—24no—
111C13×#102—24no—
112C13×C22⋊C8C2314yes—
113C13×#97—22no—
114C13×#95C2312yes—
115#18343C1311yesmaximal, characteristic, direct product factor, Sylow
116C24×C13—21no—
117C24×C13C2×D411yescharacteristic
118C24×C13C2×D411yescharacteristic
119C13×#41—82no—
120C2×Q8×C13—21no—
121C2×Q8×C13—42no—
122C2×Q8×C13—42no—
123C2×Q8×C13—41no—
124C2×Q8×C13—41no—
125C2×Q8×C13C2×D412yes—
126C2×D4×C13—22no—
127C2×D4×C13—22no—
128C2×D4×C13—22no—
129C2×D4×C13—22no—
130C2×D4×C13—21no—
131C2×D4×C13—22no—
132C2×D4×C13—22no—
133C2×D4×C13—41no—
134C2×D4×C13—42no—
135C2×D4×C13—42no—
136C2×D4×C13C2×D412yes—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—82no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2411yescharacteristic
156C2×C8×C13—24no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—24no—
168C13×C4⋊C4—44no—
169C13×C4⋊C4—44no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4C2×D412yes—
172C13×C4⋊C4C2×D412yes—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—22no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—44no—
186C13×C22⋊C4—44no—
187C42×C13—22no—
188C42×C13—22no—
189C42×C13—42no—
190C42×C13C2×D412yes—
191C42×C13C2×D412yes—
192#3459C2×C1311yescharacteristic
193#3239C2×C1312yescomplemented
194#2542C2×C1311yescharacteristic, complemented
195#1618C2×C1314yescomplemented
196#1614C2×C1312yescomplemented
197#1613C2×C1312yescomplemented
198#1509C2×C1312yescomplemented
199#1466C2×C1311yescharacteristic, complemented
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—22no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—42no—
211C23×C13—81no—
212C23×C13—81no—
213C23×C13#13712yes—
214C23×C13C22×D411yescharacteristic
215Q8×C13—42no—
216Q8×C13—82no—
217Q8×C13—81no—
218Q8×C13—82no—
219D4×C13—44no—
220D4×C13—42no—
221D4×C13—44no—
222D4×C13—42no—
223D4×C13—42no—
224D4×C13—82no—
225D4×C13—81no—
226D4×C13—82no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—44no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—81no—
249C2×C4×C13—81no—
250C2×C4×C13—81no—
251C2×C4×C13—82no—
252C2×C4×C13—81no—
253C2×C4×C13#12012yes—
254C2×C4×C13#12011yescharacteristic
255C2×C4×C13#12011yescharacteristic
256C2×C4×C13C22×D412yes—
257C8×C13—44no—
258#543C22×C1311yescharacteristic
259#539—22no—
260#539—21no—
261#538—22no—
262#538C22×C1312yes—
263#534—21no—
264#534C22×C1311yescharacteristic
265C2×C4⋊Q8C22×C1311yescharacteristic, complemented
266#529—22no—
267#529C22×C1312yes—
268#525—21no—
269#525—22no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—21no—
272C2×C4×D4—21no—
273C2×C4×D4C22×C1311yescharacteristic
274#501—22no—
275#489—22no—
276#484C22×C1314yescomplemented
277#481C22×C1314yes—
278#475—22no—
279#474—22no—
280#432C22×C1312yescomplemented
281#399C22×C1312yes—
282#399C22×C1312yescomplemented
283#390—21no—
284#384—21no—
285C4×C4⋊C4C22×C1311yescharacteristic, complemented
286#328C22×C1314yescomplemented
287#327C22×C1314yes—
288#323C22×C1312yes—
289#323C22×C1312yescomplemented
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—22no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—41no—
298C22×C13—42no—
299C22×C13—41no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13—81no—
304C22×C13—81no—
305C22×C13—84no—
306C22×C13C2×#12011yescharacteristic
307C22×C13C2×#13711yescharacteristic
308C22×C13#57511yescharacteristic
309C4×C13—22no—
310C4×C13—21no—
311C4×C13—22no—
312C4×C13—44no—
313C4×C13—42no—
314C4×C13—41no—
315C4×C13—41no—
316C4×C13—42no—
317C4×C13—42no—
318C4×C13—82no—
319C4×C13#45312yes—
320C2×#41—21no—
321C22×Q8—21no—
322C22×D4—21no—
323C22×D4D4×C1311yescharacteristic
324C23×C4—21no—
325C23×C4D4×C1311yescharacteristic
326C23×C4D4×C1311yescharacteristic
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329#126—22no—
330#126—22no—
331#126—22no—
332#125—22no—
333#125D4×C1312yes—
334#124—22no—
335#124D4×C1312yes—
336#123—22no—
337#123—22no—
338#123—22no—
339#123—22no—
340#123—22no—
341#123—22no—
342C22⋊Q8—21no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—21no—
346C22⋊Q8—22no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8C23×C1312yes—
350#121—22no—
351#121—21no—
352#121—22no—
353#121—22no—
354#121—21no—
355#121C23×C1312yes—
356#120—22no—
357#120—22no—
358#120—22no—
359C4×Q8D4×C1312yes—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4D4×C1312yes—
368#117—21no—
369#117—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C1311yescharacteristic
376C2×C4⋊C4C23×C1312yes—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4C23×C1311yescharacteristic
382C2×C22⋊C4C23×C1311yescharacteristic
383C2×C42—21no—
384C2×C42—21no—
385C2×C42C23×C1311yescharacteristic
386#107—24no—
387#106—24no—
388C4⋊C8—22no—
389#103—24no—
390#102—24no—
391C22⋊C8C23×C1314yes—
392#97—22no—
393#95C23×C1312yes—
394C2×C13—21no—
395C2×C13—21no—
396C2×C13—42no—
397C2×C13—81no—
398C2×C13—82no—
399C2×C13#300711yescharacteristic
400C2×C13C2×#45311yescharacteristic
401C2×C13#302811yescharacteristic
402C24—21no—
403C24C2×D4×C1311yescharacteristic
404C24C2×D4×C1311yescharacteristic
405#41—82no—
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8C2×D4×C1312yes—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—41no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4C2×D4×C1312yes—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—82no—
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1311yescharacteristic
439C22×C4C2×D4×C1311yescharacteristic
440C22×C4C2×D4×C1311yescharacteristic
441C22×C4C24×C1311yescharacteristic
442C2×C8—24no—
443C4⋊C4—22no—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—24no—
454C4⋊C4—44no—
455C4⋊C4—44no—
456C4⋊C4—42no—
457C4⋊C4C2×D4×C1312yes—
458C4⋊C4C2×D4×C1312yes—
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—44no—
472C22⋊C4—44no—
473C42—22no—
474C42—22no—
475C42—42no—
476C42C2×D4×C1312yes—
477C42C2×D4×C1312yes—
478C13#1834311yescharacteristic, direct product factor, Sylow
479C23—21no—
480C23—21no—
481C23—21no—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—42no—
490C23—81no—
491C23—81no—
492C23C13×#13712yes—
493C23C22×D4×C1311yescharacteristic
494Q8—42no—
495Q8—82no—
496Q8—81no—
497Q8—82no—
498D4—44no—
499D4—42no—
500D4—44no—
501D4—42no—
502D4—42no—
503D4—82no—
504D4—81no—
505D4—82no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—82no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4C13×#12012yes—
533C2×C4C13×#12011yescharacteristic
534C2×C4C13×#12011yescharacteristic
535C2×C4C22×D4×C1312yes—
536C8—44no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—42no—
546C22—41no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—84no—
553C22C2×C13×#12011yescharacteristic
554C22C2×C13×#13711yescharacteristic
555C22C13×#57511yescharacteristic
556C4—22no—
557C4—21no—
558C4—22no—
559C4—44no—
560C4—42no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—82no—
566C4C13×#45312yes—
567C2—21no—
568C2—21no—
569C2—42no—
570C2—81no—
571C2—82no—
572C2C13×#300711yescharacteristic
573C2C2×C13×#45311yescharacteristic
574C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3459C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3239C2semidirect
3. C13×#2542C2semidirect
4. C13×#1618C2semidirect
5. C13×#1614C2semidirect
6. C13×#1613C2semidirect
7. C13×#1509C2semidirect
8. C13×#1466C2semidirect
16. C2×C13×C4⋊Q8C22semidirect
27. C13×#484C22semidirect
31. C13×#432C22semidirect
33. C13×#399C22semidirect
36. C4×C13×C4⋊C4C22semidirect
37. C13×#328C22semidirect
40. C13×#323C22semidirect
115. #18343C13direct (N × H)
193. #3239C2×C13semidirect
194. #2542C2×C13semidirect
195. #1618C2×C13semidirect
196. #1614C2×C13semidirect
197. #1613C2×C13semidirect
198. #1509C2×C13semidirect
199. #1466C2×C13semidirect
265. C2×C4⋊Q8C22×C13semidirect
276. #484C22×C13semidirect
280. #432C22×C13semidirect
282. #399C22×C13semidirect
285. C4×C4⋊C4C22×C13semidirect
286. #328C22×C13semidirect
289. #323C22×C13semidirect
478. C13#18343direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34592
C13×#32392
C13×#25422
C13×#16182
C13×#16142
C13×#16132
C13×#15092
C13×#14662
#1834313