Finite Group Databasebeta

← C13×#18995 #15705334

Subgroups — C13×#18995 #15705334

Order 3328.

1024 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3529C211yesmaximal, characteristic, complemented
2C13×#3217C212yesmaximal, complemented
3C13×#3151C211yesmaximal, characteristic, complemented
4C13×#1657C212yesmaximal, complemented
5C13×#1656C214yesmaximal, complemented
6C13×#1655C212yesmaximal, complemented
7C13×#1536C211yesmaximal, characteristic, complemented
8C13×#1529C212yesmaximal, complemented
9C2×C13×AGL(1,ℤ/8)—21no—
10C2×C13×AGL(1,ℤ/8)—21no—
11C13×#563—21no—
12C13×#563C2211yescharacteristic, complemented
13C13×#562—22no—
14C13×#562C2212yescomplemented
15C13×H(3,𝔽4)C2211yescharacteristic, complemented
16C13×#560—21no—
17C13×#560—22no—
18C13×#532—21no—
19C13×#532C2211yescharacteristic
20C2×C13×#127C2211yescharacteristic, complemented
21C13×#529—22no—
22C13×#529C2212yes—
23C13×#525—21no—
24C13×#525—22no—
25C13×#496C2212yes—
26C13×#496C2214yes—
27C13×#496C2212yescomplemented
28C13×#493—21no—
29C13×#492—21no—
30C13×#490C2214yescomplemented
31C13×#460—22no—
32C13×#459—22no—
33C13×#450—22no—
34C13×#447—22no—
35C13×#432C2212yescomplemented
36C4×C13×M16C2211yescharacteristic, complemented
37C13×#330C2214yescomplemented
38C13×#329C2214yescomplemented
39C13×#329C2212yescomplemented
40C13×#329C2212yescomplemented
41C2×C13×#41—21no—
42C2×C13×#41D411yescharacteristic
43C2×C13×#41D411yescharacteristic
44C22×D4×C13—21no—
45C22×D4×C13—22no—
46C23×C4×C13—21no—
47C13×AGL(1,ℤ/8)—44no—
48C13×AGL(1,ℤ/8)—44no—
49C2×C13×SD16—22no—
50C2×C13×SD16—22no—
51C2×C13×SD16—24no—
52C2×C13×D8—22no—
53C2×C13×D8—22no—
54C2×C13×D8—24no—
55C2×C13×M16—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8D411yescharacteristic
58C13×#127—21no—
59C13×#127—22no—
60C13×#127—21no—
61C13×#127D411yescharacteristic
62C13×#127C2312yes—
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—22no—
66C13×#125—22no—
67C13×#125C2312yes—
68C13×#124—21no—
69C13×#124—22no—
70C13×#124—21no—
71C13×#124C2312yes—
72C13×#124C2311yescharacteristic
73C13×#124C2311yescharacteristic
74C13×#123—22no—
75C13×#123—21no—
76C13×#123—22no—
77C13×#123—21no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8D412yes—
86C13×#121—22no—
87C13×#121—22no—
88C13×#121—22no—
89C13×#121—22no—
90C13×#121—22no—
91C13×#121—22no—
92C13×#121—22no—
93C13×#121D412yes—
94C13×#120—21no—
95C13×#120—22no—
96C13×#120—21no—
97C13×#120—22no—
98C4×Q8×C13D412yes—
99C4×D4×C13—22no—
100C4×D4×C13—22no—
101C4×D4×C13—22no—
102C4×D4×C13—22no—
103C4×D4×C13D412yes—
104C13×#117—21no—
105C13×#117—22no—
106C2×C42×C13—21no—
107C2×C42×C13C2311yescharacteristic
108C13×C4⋊C8—22no—
109C13×#102—24no—
110C13×#102—24no—
111C13×C22⋊C8—22no—
112C13×#97C2314yes—
113C13×#97C2312yes—
114C4×C8×C13—21no—
115#18995C1311yesmaximal, characteristic, direct product factor, Sylow
116C24×C13—21no—
117C24×C13—41no—
118C13×#41—42no—
119C13×#41—42no—
120C13×#41—82no—
121C2×Q8×C13—21no—
122C2×Q8×C13C2×D412yes—
123C2×Q8×C13C2×D411yescharacteristic
124C2×Q8×C13C2×D411yescharacteristic
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—21no—
128C2×D4×C13—22no—
129C2×D4×C13—22no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—22no—
133C2×D4×C13—24no—
134C2×D4×C13—22no—
135C2×D4×C13—42no—
136C2×D4×C13—42no—
137C2×D4×C13—42no—
138C2×D4×C13—41no—
139C2×D4×C13—84no—
140C2×D4×C13C2×D412yes—
141C2×D4×C13C2×D411yescharacteristic
142C2×D4×C13C2×D411yescharacteristic
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—82no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C13×SD16—44no—
153C13×SD16—44no—
154C13×SD16—84no—
155C13×D8—44no—
156C13×D8—44no—
157C13×D8—84no—
158C13×M16—24no—
159C2×C8×C13—22no—
160C2×C8×C13—24no—
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—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4C2×D412yes—
170C13×C4⋊C4C2×D412yes—
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
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—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—22no—
187C42×C13C2×D411yescharacteristic
188C42×C13C2×D412yes—
189C42×C13C2411yescharacteristic
190#3529C2×C1311yescharacteristic, complemented
191#3217C2×C1312yescomplemented
192#3151C2×C1311yescharacteristic, complemented
193#1657C2×C1312yescomplemented
194#1656C2×C1314yescomplemented
195#1655C2×C1312yescomplemented
196#1536C2×C1311yescharacteristic, complemented
197#1529C2×C1312yescomplemented
198C23×C13—21no—
199C23×C13—22no—
200C23×C13—21no—
201C23×C13—42no—
202C23×C13—82no—
203C23×C13—84no—
204C23×C13—81no—
205C23×C13—82no—
206C23×C13#12011yescharacteristic
207Q8×C13—41no—
208Q8×C13—41no—
209Q8×C13—42no—
210Q8×C13—81no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—42no—
214D4×C13—42no—
215D4×C13—42no—
216D4×C13—44no—
217D4×C13—44no—
218D4×C13—82no—
219D4×C13—84no—
220D4×C13—82no—
221D4×C13—81no—
222D4×C13—81no—
223D4×C13—82no—
224D4×C13—82no—
225D4×C13—82no—
226D4×C13—81no—
227D4×C13—82no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—44no—
237C2×C4×C13—42no—
238C2×C4×C13—82no—
239C2×C4×C13—82no—
240C2×C4×C13—81no—
241C2×C4×C13#12012yes—
242C2×C4×C13#12011yescharacteristic
243C2×C4×C13C22×D412yes—
244C2×C4×C13C22×D411yescharacteristic
245C8×C13—24no—
246C8×C13—44no—
247C2×AGL(1,ℤ/8)—21no—
248C2×AGL(1,ℤ/8)—21no—
249#563—21no—
250#563C22×C1311yescharacteristic, complemented
251#562—22no—
252#562C22×C1312yescomplemented
253H(3,𝔽4)C22×C1311yescharacteristic, complemented
254#560—21no—
255#560—22no—
256#532—21no—
257#532C22×C1311yescharacteristic
258C2×#127C22×C1311yescharacteristic, complemented
259#529—22no—
260#529C22×C1312yes—
261#525—21no—
262#525—22no—
263#496C22×C1312yes—
264#496C22×C1314yes—
265#496C22×C1312yescomplemented
266#493—21no—
267#492—21no—
268#490C22×C1314yescomplemented
269#460—22no—
270#459—22no—
271#450—22no—
272#447—22no—
273#432C22×C1312yescomplemented
274C4×M16C22×C1311yescharacteristic, complemented
275#330C22×C1314yescomplemented
276#329C22×C1312yescomplemented
277#329C22×C1312yescomplemented
278#329C22×C1314yescomplemented
279C22×C13—21no—
280C22×C13—22no—
281C22×C13—41no—
282C22×C13—42no—
283C22×C13—41no—
284C22×C13—42no—
285C22×C13—42no—
286C22×C13—42no—
287C22×C13—42no—
288C22×C13—84no—
289C22×C13—82no—
290C22×C13—84no—
291C22×C13—164no—
292C22×C13C2×#12011yescharacteristic
293C4×C13—21no—
294C4×C13—22no—
295C4×C13—22no—
296C4×C13—41no—
297C4×C13—42no—
298C4×C13—41no—
299C4×C13—42no—
300C4×C13—42no—
301C4×C13#45312yes—
302C2×#41—21no—
303C2×#41D4×C1311yescharacteristic
304C2×#41D4×C1311yescharacteristic
305C22×D4—21no—
306C22×D4—22no—
307C23×C4—21no—
308AGL(1,ℤ/8)—44no—
309AGL(1,ℤ/8)—44no—
310C2×SD16—22no—
311C2×SD16—22no—
312C2×SD16—24no—
313C2×D8—22no—
314C2×D8—22no—
315C2×D8—24no—
316C2×M16—21no—
317C4⋊Q8—21no—
318C4⋊Q8D4×C1311yescharacteristic
319#127—21no—
320#127—22no—
321#127—21no—
322#127D4×C1311yescharacteristic
323#127C23×C1312yes—
324#126—22no—
325#126—22no—
326#126—22no—
327#125—22no—
328#125C23×C1312yes—
329#124—21no—
330#124—22no—
331#124—21no—
332#124C23×C1312yes—
333#124C23×C1311yescharacteristic
334#124C23×C1311yescharacteristic
335#123—22no—
336#123—21no—
337#123—22no—
338#123—21no—
339#123—22no—
340#123—22no—
341#123—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8D4×C1312yes—
347#121—22no—
348#121—22no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121—22no—
354#121D4×C1312yes—
355#120—21no—
356#120—22no—
357#120—21no—
358#120—22no—
359C4×Q8D4×C1312yes—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4D4×C1312yes—
365#117—21no—
366#117—22no—
367C2×C42—21no—
368C2×C42C23×C1311yescharacteristic
369C4⋊C8—22no—
370#102—24no—
371#102—24no—
372C22⋊C8—22no—
373#97C23×C1314yes—
374#97C23×C1312yes—
375C4×C8—21no—
376C2×C13—41no—
377C2×C13—81no—
378C2×C13—81no—
379C2×C13—82no—
380C2×C13—162no—
381C2×C13C2×#45311yescharacteristic
382C2×C13#302112yes—
383C24—21no—
384C24—41no—
385#41—42no—
386#41—42no—
387#41—82no—
388C2×Q8—21no—
389C2×Q8C2×D4×C1312yes—
390C2×Q8C2×D4×C1311yescharacteristic
391C2×Q8C2×D4×C1311yescharacteristic
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—41no—
406C2×D4—84no—
407C2×D4C2×D4×C1312yes—
408C2×D4C2×D4×C1311yescharacteristic
409C2×D4C2×D4×C1311yescharacteristic
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—82no—
417C22×C4C2×D4×C1311yescharacteristic
418C22×C4C2×D4×C1312yes—
419SD16—44no—
420SD16—44no—
421SD16—84no—
422D8—44no—
423D8—44no—
424D8—84no—
425M16—24no—
426C2×C8—22no—
427C2×C8—24no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4C2×D4×C1312yes—
437C4⋊C4C2×D4×C1312yes—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C42—21no—
452C42—21no—
453C42—22no—
454C42C2×D4×C1311yescharacteristic
455C42C2×D4×C1312yes—
456C42C24×C1311yescharacteristic
457C13#1899511yescharacteristic, direct product factor, Sylow
458C23—21no—
459C23—22no—
460C23—21no—
461C23—42no—
462C23—82no—
463C23—84no—
464C23—81no—
465C23—82no—
466C23C13×#12011yescharacteristic
467Q8—41no—
468Q8—41no—
469Q8—42no—
470Q8—81no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—42no—
476D4—44no—
477D4—44no—
478D4—82no—
479D4—84no—
480D4—82no—
481D4—81no—
482D4—81no—
483D4—82no—
484D4—82no—
485D4—82no—
486D4—81no—
487D4—82no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—82no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4C13×#12012yes—
502C2×C4C13×#12011yescharacteristic
503C2×C4C22×D4×C1312yes—
504C2×C4C22×D4×C1311yescharacteristic
505C8—24no—
506C8—44no—
507C22—21no—
508C22—22no—
509C22—41no—
510C22—42no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—84no—
517C22—82no—
518C22—84no—
519C22—164no—
520C22C2×C13×#12011yescharacteristic
521C4—21no—
522C4—22no—
523C4—22no—
524C4—41no—
525C4—42no—
526C4—41no—
527C4—42no—
528C4—42no—
529C4C13×#45312yes—
530C2—41no—
531C2—81no—
532C2—82no—
533C2—81no—
534C2—162no—
535C2C2×C13×#45311yescharacteristic
536C2C13×#302112yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3529C2semidirect
2. C13×#3217C2semidirect
3. C13×#3151C2semidirect
4. C13×#1657C2semidirect
5. C13×#1656C2semidirect
6. C13×#1655C2semidirect
7. C13×#1536C2semidirect
8. C13×#1529C2semidirect
12. C13×#563C22semidirect
14. C13×#562C22semidirect
15. C13×H(3,𝔽4)C22semidirect
20. C2×C13×#127C22semidirect
27. C13×#496C22semidirect
30. C13×#490C22semidirect
35. C13×#432C22semidirect
36. C4×C13×M16C22semidirect
37. C13×#330C22semidirect
38. C13×#329C22semidirect
39. C13×#329C22semidirect
40. C13×#329C22semidirect
115. #18995C13direct (N × H)
190. #3529C2×C13semidirect
191. #3217C2×C13semidirect
192. #3151C2×C13semidirect
193. #1657C2×C13semidirect
194. #1656C2×C13semidirect
195. #1655C2×C13semidirect
196. #1536C2×C13semidirect
197. #1529C2×C13semidirect
250. #563C22×C13semidirect
252. #562C22×C13semidirect
253. H(3,𝔽4)C22×C13semidirect
258. C2×#127C22×C13semidirect
265. #496C22×C13semidirect
268. #490C22×C13semidirect
273. #432C22×C13semidirect
274. C4×M16C22×C13semidirect
275. #330C22×C13semidirect
276. #329C22×C13semidirect
277. #329C22×C13semidirect
278. #329C22×C13semidirect
457. C13#18995direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35292
C13×#32172
C13×#31512
C13×#16572
C13×#16562
C13×#16552
C13×#15362
C13×#15292
#1899513