Finite Group Databasebeta

← C13×#18996 #15705335

Subgroups — C13×#18996 #15705335

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3529C211yesmaximal, characteristic
2C13×#3239C212yesmaximal, complemented
3C13×#3152C211yesmaximal, characteristic, complemented
4C13×#1661C214yesmaximal, complemented
5C13×#1660C212yesmaximal, complemented
6C13×#1659C212yesmaximal, complemented
7C13×#1536C211yesmaximal, characteristic, complemented
8C13×#1529C212yesmaximal, complemented
9C2×C13×#137—21no—
10C2×C13×#137—21no—
11C13×#563—21no—
12C13×#563C2211yescharacteristic
13C13×#562—22no—
14C13×#562C2212yes—
15C13×H(3,𝔽4)C2211yescharacteristic
16C13×#560—21no—
17C13×#560—22no—
18C13×#532—21no—
19C13×#532C2211yescharacteristic
20C2×C13×C4⋊Q8C2211yescharacteristic, complemented
21C13×#529—22no—
22C13×#529C2212yes—
23C13×#525—21no—
24C13×#525—22no—
25C13×#501C2214yescomplemented
26C13×#497C2212yes—
27C13×#497C2212yescomplemented
28C13×#494—21no—
29C13×#492—21no—
30C13×#489C2214yes—
31C13×#484—22no—
32C13×#481—22no—
33C13×#475—22no—
34C13×#474—22no—
35C13×#432C2212yescomplemented
36C4×C13×M16C2211yescharacteristic, complemented
37C13×#330C2214yescomplemented
38C13×#329C2214yes—
39C13×#329C2212yes—
40C13×#329C2212yescomplemented
41C2×C13×#41—21no—
42C2×C13×#41D411yescharacteristic
43C2×C13×#41D411yescharacteristic
44C22×Q8×C13—21no—
45C23×C4×C13—21no—
46C13×#137—44no—
47C13×#137—44no—
48C2×C13×Q16—22no—
49C2×C13×Q16—22no—
50C2×C13×SD16—22no—
51C2×C13×SD16—22no—
52C2×C13×M16—21no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8D411yescharacteristic
57C13×C4⋊Q8C2312yes—
58C13×#127—21no—
59C13×#127D411yescharacteristic
60C13×#126—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#125—22no—
64C13×#125C2312yes—
65C13×#124—21no—
66C13×#124—22no—
67C13×#124—21no—
68C13×#124C2312yes—
69C13×#124C2311yescharacteristic
70C13×#124C2311yescharacteristic
71C13×#123—22no—
72C13×#123—21no—
73C13×#123—22no—
74C13×#123—21no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8D412yes—
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#121—22no—
87C13×#121—22no—
88C13×#121—22no—
89C13×#121—22no—
90C13×#121D412yes—
91C13×#120—21no—
92C13×#120—22no—
93C13×#120—21no—
94C13×#120—22no—
95C4×Q8×C13D412yes—
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C4×D4×C13—22no—
100C4×D4×C13D412yes—
101C13×#117—21no—
102C13×#117—22no—
103C2×C13×C4⋊C4—22no—
104C2×C42×C13—21no—
105C2×C42×C13C2311yescharacteristic
106C13×#107—24no—
107C13×#106—24no—
108C13×C4⋊C8—22no—
109C13×#103—24no—
110C13×#102—24no—
111C13×C22⋊C8—22no—
112C13×#97C2314yes—
113C13×#97C2312yes—
114C4×C8×C13—21no—
115#18996C1311yesmaximal, characteristic, direct product factor, Sylow
116C24×C13—21no—
117C13×#41—42no—
118C13×#41—42no—
119C13×#41—82no—
120C2×Q8×C13—21no—
121C2×Q8×C13—22no—
122C2×Q8×C13—42no—
123C2×Q8×C13—42no—
124C2×Q8×C13—41no—
125C2×Q8×C13C2×D412yes—
126C2×Q8×C13C2×D411yescharacteristic
127C2×Q8×C13C2×D411yescharacteristic
128C2×D4×C13—22no—
129C2×D4×C13—22no—
130C2×D4×C13—21no—
131C2×D4×C13—22no—
132C2×D4×C13—22no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—22no—
136C2×D4×C13C2×D412yes—
137C2×D4×C13C2×D411yescharacteristic
138C2×D4×C13C2×D411yescharacteristic
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—41no—
146C22×C4×C13—82no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D412yes—
149C13×Q16—44no—
150C13×Q16—44no—
151C13×SD16—44no—
152C13×SD16—44no—
153C13×M16—24no—
154C2×C8×C13—22no—
155C2×C8×C13—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
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—24no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4C2×D412yes—
167C13×C4⋊C4C2×D412yes—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
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—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—22no—
184C42×C13C2×D411yescharacteristic
185C42×C13C2×D412yes—
186C42×C13C2411yescharacteristic
187#3529C2×C1311yescharacteristic
188#3239C2×C1312yescomplemented
189#3152C2×C1311yescharacteristic, complemented
190#1661C2×C1314yescomplemented
191#1660C2×C1312yescomplemented
192#1659C2×C1312yescomplemented
193#1536C2×C1311yescharacteristic, complemented
194#1529C2×C1312yescomplemented
195C23×C13—21no—
196C23×C13—22no—
197C23×C13—21no—
198C23×C13—81no—
199C23×C13—82no—
200C23×C13#12011yescharacteristic
201Q8×C13—41no—
202Q8×C13—41no—
203Q8×C13—42no—
204Q8×C13—42no—
205Q8×C13—42no—
206Q8×C13—81no—
207Q8×C13—82no—
208D4×C13—41no—
209D4×C13—41no—
210D4×C13—42no—
211D4×C13—82no—
212D4×C13—82no—
213D4×C13—81no—
214D4×C13—81no—
215D4×C13—82no—
216D4×C13—82no—
217D4×C13—82no—
218D4×C13—81no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—44no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—82no—
231C2×C4×C13—82no—
232C2×C4×C13—81no—
233C2×C4×C13—82no—
234C2×C4×C13#12012yes—
235C2×C4×C13#12011yescharacteristic
236C2×C4×C13C22×D412yes—
237C2×C4×C13C22×D411yescharacteristic
238C8×C13—24no—
239C8×C13—44no—
240C2×#137—21no—
241C2×#137—21no—
242#563—21no—
243#563C22×C1311yescharacteristic
244#562—22no—
245#562C22×C1312yes—
246H(3,𝔽4)C22×C1311yescharacteristic
247#560—21no—
248#560—22no—
249#532—21no—
250#532C22×C1311yescharacteristic
251C2×C4⋊Q8C22×C1311yescharacteristic, complemented
252#529—22no—
253#529C22×C1312yes—
254#525—21no—
255#525—22no—
256#501C22×C1314yescomplemented
257#497C22×C1312yes—
258#497C22×C1312yescomplemented
259#494—21no—
260#492—21no—
261#489C22×C1314yes—
262#484—22no—
263#481—22no—
264#475—22no—
265#474—22no—
266#432C22×C1312yescomplemented
267C4×M16C22×C1311yescharacteristic, complemented
268#330C22×C1314yescomplemented
269#329C22×C1312yes—
270#329C22×C1314yes—
271#329C22×C1312yescomplemented
272C22×C13—21no—
273C22×C13—22no—
274C22×C13—41no—
275C22×C13—42no—
276C22×C13—41no—
277C22×C13—42no—
278C22×C13—42no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—84no—
282C22×C13C2×#12011yescharacteristic
283C4×C13—21no—
284C4×C13—22no—
285C4×C13—22no—
286C4×C13—41no—
287C4×C13—42no—
288C4×C13—41no—
289C4×C13—42no—
290C4×C13—42no—
291C4×C13—82no—
292C4×C13#45312yes—
293C2×#41—21no—
294C2×#41D4×C1311yescharacteristic
295C2×#41D4×C1311yescharacteristic
296C22×Q8—21no—
297C23×C4—21no—
298#137—44no—
299#137—44no—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×SD16—22no—
303C2×SD16—22no—
304C2×M16—21no—
305C4⋊Q8—21no—
306C4⋊Q8—22no—
307C4⋊Q8—21no—
308C4⋊Q8D4×C1311yescharacteristic
309C4⋊Q8C23×C1312yes—
310#127—21no—
311#127D4×C1311yescharacteristic
312#126—22no—
313#126—22no—
314#126—22no—
315#125—22no—
316#125C23×C1312yes—
317#124—21no—
318#124—22no—
319#124—21no—
320#124C23×C1312yes—
321#124C23×C1311yescharacteristic
322#124C23×C1311yescharacteristic
323#123—22no—
324#123—21no—
325#123—22no—
326#123—21no—
327#123—22no—
328#123—22no—
329#123—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8D4×C1312yes—
335#121—22no—
336#121—22no—
337#121—22no—
338#121—22no—
339#121—22no—
340#121—22no—
341#121—22no—
342#121D4×C1312yes—
343#120—21no—
344#120—22no—
345#120—21no—
346#120—22no—
347C4×Q8D4×C1312yes—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4D4×C1312yes—
353#117—21no—
354#117—22no—
355C2×C4⋊C4—22no—
356C2×C42—21no—
357C2×C42C23×C1311yescharacteristic
358#107—24no—
359#106—24no—
360C4⋊C8—22no—
361#103—24no—
362#102—24no—
363C22⋊C8—22no—
364#97C23×C1314yes—
365#97C23×C1312yes—
366C4×C8—21no—
367C2×C13—41no—
368C2×C13—81no—
369C2×C13—81no—
370C2×C13—82no—
371C2×C13C2×#45311yescharacteristic
372C2×C13#302212yes—
373C24—21no—
374#41—42no—
375#41—42no—
376#41—82no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—42no—
380C2×Q8—42no—
381C2×Q8—41no—
382C2×Q8C2×D4×C1312yes—
383C2×Q8C2×D4×C1311yescharacteristic
384C2×Q8C2×D4×C1311yescharacteristic
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4C2×D4×C1312yes—
394C2×D4C2×D4×C1311yescharacteristic
395C2×D4C2×D4×C1311yescharacteristic
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—41no—
403C22×C4—82no—
404C22×C4C2×D4×C1311yescharacteristic
405C22×C4C2×D4×C1312yes—
406Q16—44no—
407Q16—44no—
408SD16—44no—
409SD16—44no—
410M16—24no—
411C2×C8—22no—
412C2×C8—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—24no—
422C4⋊C4—42no—
423C4⋊C4C2×D4×C1312yes—
424C4⋊C4C2×D4×C1312yes—
425C22⋊C4—21no—
426C22⋊C4—21no—
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—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C42—21no—
439C42—21no—
440C42—22no—
441C42C2×D4×C1311yescharacteristic
442C42C2×D4×C1312yes—
443C42C24×C1311yescharacteristic
444C13#1899611yescharacteristic, direct product factor, Sylow
445C23—21no—
446C23—22no—
447C23—21no—
448C23—81no—
449C23—82no—
450C23C13×#12011yescharacteristic
451Q8—41no—
452Q8—41no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456Q8—81no—
457Q8—82no—
458D4—41no—
459D4—41no—
460D4—42no—
461D4—82no—
462D4—82no—
463D4—81no—
464D4—81no—
465D4—82no—
466D4—82no—
467D4—82no—
468D4—81no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—81no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4C13×#12012yes—
485C2×C4C13×#12011yescharacteristic
486C2×C4C22×D4×C1312yes—
487C2×C4C22×D4×C1311yescharacteristic
488C8—24no—
489C8—44no—
490C22—21no—
491C22—22no—
492C22—41no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—84no—
500C22C2×C13×#12011yescharacteristic
501C4—21no—
502C4—22no—
503C4—22no—
504C4—41no—
505C4—42no—
506C4—41no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4C13×#45312yes—
511C2—41no—
512C2—81no—
513C2—82no—
514C2—81no—
515C2C2×C13×#45311yescharacteristic
516C2C13×#302212yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3529C2
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
2. C13×#3239C2semidirect
3. C13×#3152C2semidirect
4. C13×#1661C2semidirect
5. C13×#1660C2semidirect
6. C13×#1659C2semidirect
7. C13×#1536C2semidirect
8. C13×#1529C2semidirect
20. C2×C13×C4⋊Q8C22semidirect
25. C13×#501C22semidirect
27. C13×#497C22semidirect
35. C13×#432C22semidirect
36. C4×C13×M16C22semidirect
37. C13×#330C22semidirect
40. C13×#329C22semidirect
115. #18996C13direct (N × H)
188. #3239C2×C13semidirect
189. #3152C2×C13semidirect
190. #1661C2×C13semidirect
191. #1660C2×C13semidirect
192. #1659C2×C13semidirect
193. #1536C2×C13semidirect
194. #1529C2×C13semidirect
251. C2×C4⋊Q8C22×C13semidirect
256. #501C22×C13semidirect
258. #497C22×C13semidirect
266. #432C22×C13semidirect
267. C4×M16C22×C13semidirect
268. #330C22×C13semidirect
271. #329C22×C13semidirect
444. C13#18996direct (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×#32392
C13×#31522
C13×#16612
C13×#16602
C13×#16592
C13×#15362
C13×#15292
#1899613