Finite Group Databasebeta

← C13×#18336 #15704675

Subgroups — C13×#18336 #15704675

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3459C211yesmaximal, characteristic
2C13×#3218C212yesmaximal, complemented
3C13×#2563C211yesmaximal, characteristic, complemented
4C13×#1606C214yesmaximal, complemented
5C13×#1602C212yesmaximal, complemented
6C13×#1601C212yesmaximal, 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×C4×D4×C13—21no—
22C2×C4×D4×C13C2211yescharacteristic
23C13×#497—22no—
24C13×#491—22no—
25C13×#462—22no—
26C13×#461—22no—
27C13×#451C2214yescomplemented
28C13×#448C2214yes—
29C13×#432C2212yescomplemented
30C13×#393C2212yes—
31C13×#393C2212yescomplemented
32C13×#390—21no—
33C13×#382—21no—
34C13×#380—21no—
35C13×#380—21no—
36C4×C13×C4⋊C4C2211yescharacteristic, complemented
37C13×#328C2214yescomplemented
38C13×#327C2214yes—
39C13×#323C2212yes—
40C13×#323C2212yescomplemented
41C2×C13×#41—21no—
42C22×Q8×C13C2312yes—
43C22×D4×C13—21no—
44C22×D4×C13D411yescharacteristic
45C23×C4×C13—21no—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C2×C13×Q16—24no—
49C2×C13×SD16—24no—
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8—22no—
52C13×#126—22no—
53C13×#126—22no—
54C13×#126—22no—
55C13×#125—22no—
56C13×#125D412yes—
57C13×#124—22no—
58C13×#124D412yes—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×C22⋊Q8—21no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—22no—
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—21no—
95C2×C13×C4⋊C4D411yescharacteristic
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4C2311yescharacteristic
101C2×C13×C22⋊C4C2311yescharacteristic
102C2×C42×C13—21no—
103C2×C42×C13—21no—
104C2×C42×C13C2311yescharacteristic
105C13×C4⋊C8—22no—
106C13×#103—24no—
107C13×#103—24no—
108C13×C22⋊C8C2314yes—
109C13×#97—22no—
110C13×#95—22no—
111C13×#95—22no—
112C13×#95C2312yes—
113#18336C1311yesmaximal, characteristic, direct product factor, Sylow
114C24×C13—21no—
115C24×C13C2×D411yescharacteristic
116C24×C13C2×D411yescharacteristic
117C13×#41—82no—
118C2×Q8×C13—21no—
119C2×Q8×C13—24no—
120C2×Q8×C13—82no—
121C2×Q8×C13C2×D412yes—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—21no—
127C2×D4×C13—22no—
128C2×D4×C13—22no—
129C2×D4×C13—41no—
130C2×D4×C13—42no—
131C2×D4×C13—42no—
132C2×D4×C13C2×D412yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—82no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C13×Q16—84no—
153C13×SD16—84no—
154C2×C8×C13—24no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—41no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4C2×D412yes—
169C13×C4⋊C4C2×D412yes—
170C13×C22⋊C4—22no—
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—22no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—22no—
182C13×C22⋊C4—82no—
183C13×C22⋊C4—82no—
184C42×C13—22no—
185C42×C13—22no—
186C42×C13—42no—
187C42×C13C2×D412yes—
188C42×C13C2×D412yes—
189#3459C2×C1311yescharacteristic
190#3218C2×C1312yescomplemented
191#2563C2×C1311yescharacteristic, complemented
192#1606C2×C1314yescomplemented
193#1602C2×C1312yescomplemented
194#1601C2×C1312yescomplemented
195#1509C2×C1312yescomplemented
196#1466C2×C1311yescharacteristic, complemented
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—22no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—42no—
208C23×C13—81no—
209C23×C13—81no—
210C23×C13#13712yes—
211C23×C13C22×D411yescharacteristic
212Q8×C13—42no—
213Q8×C13—44no—
214Q8×C13—44no—
215Q8×C13—81no—
216D4×C13—44no—
217D4×C13—42no—
218D4×C13—44no—
219D4×C13—42no—
220D4×C13—42no—
221D4×C13—82no—
222D4×C13—81no—
223D4×C13—82no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—22no—
232C2×C4×C13—41no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—44no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—81no—
246C2×C4×C13—81no—
247C2×C4×C13—81no—
248C2×C4×C13—82no—
249C2×C4×C13—81no—
250C2×C4×C13#12012yes—
251C2×C4×C13#12011yescharacteristic
252C2×C4×C13#12011yescharacteristic
253C2×C4×C13C22×D412yes—
254C8×C13—44no—
255#543C22×C1311yescharacteristic
256#539—22no—
257#539—21no—
258#538—22no—
259#538C22×C1312yes—
260#534—21no—
261#534C22×C1311yescharacteristic
262C2×C4⋊Q8C22×C1311yescharacteristic, complemented
263#529—22no—
264#529C22×C1312yes—
265#525—21no—
266#525—22no—
267C2×C4×D4—21no—
268C2×C4×D4C22×C1311yescharacteristic
269#497—22no—
270#491—22no—
271#462—22no—
272#461—22no—
273#451C22×C1314yescomplemented
274#448C22×C1314yes—
275#432C22×C1312yescomplemented
276#393C22×C1312yes—
277#393C22×C1312yescomplemented
278#390—21no—
279#382—21no—
280#380—21no—
281#380—21no—
282C4×C4⋊C4C22×C1311yescharacteristic, complemented
283#328C22×C1314yescomplemented
284#327C22×C1314yes—
285#323C22×C1312yes—
286#323C22×C1312yescomplemented
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—22no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13—42no—
296C22×C13—41no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13—41no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—84no—
303C22×C13C2×#12011yescharacteristic
304C22×C13C2×#13711yescharacteristic
305C22×C13#57511yescharacteristic
306C4×C13—22no—
307C4×C13—21no—
308C4×C13—22no—
309C4×C13—42no—
310C4×C13—41no—
311C4×C13—41no—
312C4×C13—42no—
313C4×C13—42no—
314C4×C13—82no—
315C4×C13—82no—
316C4×C13#45512yes—
317C2×#41—21no—
318C22×Q8C23×C1312yes—
319C22×D4—21no—
320C22×D4D4×C1311yescharacteristic
321C23×C4—21no—
322C23×C4D4×C1311yescharacteristic
323C23×C4D4×C1311yescharacteristic
324C2×Q16—24no—
325C2×SD16—24no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328#126—22no—
329#126—22no—
330#126—22no—
331#125—22no—
332#125D4×C1312yes—
333#124—22no—
334#124D4×C1312yes—
335#123—22no—
336#123—22no—
337#123—22no—
338#123—22no—
339#123—22no—
340#123—22no—
341C22⋊Q8—21no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—21no—
345C22⋊Q8—22no—
346C22⋊Q8C23×C1312yes—
347#121—22no—
348#121—21no—
349#121—22no—
350#121—22no—
351#121—21no—
352#121C23×C1312yes—
353#120—22no—
354#120—22no—
355#120—22no—
356C4×Q8D4×C1312yes—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4D4×C1312yes—
365#117—21no—
366#117—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4D4×C1311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4C23×C1311yescharacteristic
377C2×C22⋊C4C23×C1311yescharacteristic
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C23×C1311yescharacteristic
381C4⋊C8—22no—
382#103—24no—
383#103—24no—
384C22⋊C8C23×C1314yes—
385#97—22no—
386#95—22no—
387#95—22no—
388#95C23×C1312yes—
389C2×C13—21no—
390C2×C13—21no—
391C2×C13—42no—
392C2×C13—81no—
393C2×C13—82no—
394C2×C13#300711yescharacteristic
395C2×C13C2×#45511yescharacteristic
396C2×C13#302711yescharacteristic
397C24—21no—
398C24C2×D4×C1311yescharacteristic
399C24C2×D4×C1311yescharacteristic
400#41—82no—
401C2×Q8—21no—
402C2×Q8—24no—
403C2×Q8—82no—
404C2×Q8C2×D4×C1312yes—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4C2×D4×C1312yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—82no—
430C22×C4C2×D4×C1311yescharacteristic
431C22×C4C2×D4×C1311yescharacteristic
432C22×C4C2×D4×C1311yescharacteristic
433C22×C4C2×D4×C1311yescharacteristic
434C22×C4C24×C1311yescharacteristic
435Q16—84no—
436SD16—84no—
437C2×C8—24no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4C2×D4×C1312yes—
452C4⋊C4C2×D4×C1312yes—
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—82no—
466C22⋊C4—82no—
467C42—22no—
468C42—22no—
469C42—42no—
470C42C2×D4×C1312yes—
471C42C2×D4×C1312yes—
472C13#1833611yescharacteristic, direct product factor, Sylow
473C23—21no—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—21no—
478C23—21no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—81no—
485C23—81no—
486C23C13×#13712yes—
487C23C22×D4×C1311yescharacteristic
488Q8—42no—
489Q8—44no—
490Q8—44no—
491Q8—81no—
492D4—44no—
493D4—42no—
494D4—44no—
495D4—42no—
496D4—42no—
497D4—82no—
498D4—81no—
499D4—82no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—81no—
522C2×C4—81no—
523C2×C4—82no—
524C2×C4—81no—
525C2×C4—81no—
526C2×C4C13×#12012yes—
527C2×C4C13×#12011yescharacteristic
528C2×C4C13×#12011yescharacteristic
529C2×C4C22×D4×C1312yes—
530C8—44no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—42no—
540C22—41no—
541C22—42no—
542C22—42no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22C2×C13×#12011yescharacteristic
548C22C2×C13×#13711yescharacteristic
549C22C13×#57511yescharacteristic
550C4—22no—
551C4—21no—
552C4—22no—
553C4—42no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—82no—
559C4—82no—
560C4C13×#45512yes—
561C2—21no—
562C2—21no—
563C2—42no—
564C2—81no—
565C2—82no—
566C2C13×#300711yescharacteristic
567C2C2×C13×#45511yescharacteristic
568C2C13×#302711yescharacteristic
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×#3218C2semidirect
3. C13×#2563C2semidirect
4. C13×#1606C2semidirect
5. C13×#1602C2semidirect
6. C13×#1601C2semidirect
7. C13×#1509C2semidirect
8. C13×#1466C2semidirect
16. C2×C13×C4⋊Q8C22semidirect
27. C13×#451C22semidirect
29. C13×#432C22semidirect
31. C13×#393C22semidirect
36. C4×C13×C4⋊C4C22semidirect
37. C13×#328C22semidirect
40. C13×#323C22semidirect
113. #18336C13direct (N × H)
190. #3218C2×C13semidirect
191. #2563C2×C13semidirect
192. #1606C2×C13semidirect
193. #1602C2×C13semidirect
194. #1601C2×C13semidirect
195. #1509C2×C13semidirect
196. #1466C2×C13semidirect
262. C2×C4⋊Q8C22×C13semidirect
273. #451C22×C13semidirect
275. #432C22×C13semidirect
277. #393C22×C13semidirect
282. C4×C4⋊C4C22×C13semidirect
283. #328C22×C13semidirect
286. #323C22×C13semidirect
472. C13#18336direct (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×#32182
C13×#25632
C13×#16062
C13×#16022
C13×#16012
C13×#15092
C13×#14662
#1833613