Finite Group Databasebeta

← C13×#18362 #15704701

Subgroups — C13×#18362 #15704701

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3491C211yesmaximal, characteristic
2C13×#3239C212yesmaximal, complemented
3C13×#2628C211yesmaximal, characteristic, complemented
4C13×#1615C214yesmaximal, complemented
5C13×#1614C212yesmaximal, complemented
6C13×#1613C212yesmaximal
7C13×#1512C212yesmaximal, complemented
8C13×#1464C211yesmaximal, characteristic, complemented
9C13×#552—22no—
10C13×#552—22no—
11C13×#551—22no—
12C13×#551—22no—
13C13×#543C2211yescharacteristic
14C13×#539—21no—
15C13×#539C2212yes—
16C13×#534C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic, complemented
18C13×#529—21no—
19C13×#529C2212yes—
20C2×C13×#123—21no—
21C13×#518—21no—
22C2×C13×#117C2211yescharacteristic
23C13×#501—22no—
24C13×#489—22no—
25C13×#484C2214yescomplemented
26C13×#481C2214yes—
27C13×#475—22no—
28C13×#474—22no—
29C13×#432C2212yescomplemented
30C13×#400C2212yescomplemented
31C13×#399C2212yes—
32C13×#395—21no—
33C13×#393—21no—
34C13×#389—21no—
35C13×#382C2211yescharacteristic, complemented
36C13×#380—21no—
37C13×#328C2214yescomplemented
38C13×#327C2214yes—
39C13×#324C2212yescomplemented
40C13×#323C2212yes—
41C22×Q8×C13—21no—
42C22×D4×C13—21no—
43C23×C4×C13D411yescharacteristic
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8—22no—
46C13×#126—22no—
47C13×#126—22no—
48C13×#126—22no—
49C13×#126—22no—
50C13×#125—21no—
51C13×#125—22no—
52C13×#125—22no—
53C13×#125D412yes—
54C13×#124—21no—
55C13×#124D412yes—
56C13×#123—22no—
57C13×#123—22no—
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—21no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8C2312yes—
69C13×#121—21no—
70C13×#121C2312yes—
71C13×#120—22no—
72C4×Q8×C13—21no—
73C4×Q8×C13D412yes—
74C4×D4×C13—22no—
75C4×D4×C13—22no—
76C4×D4×C13—21no—
77C4×D4×C13—22no—
78C4×D4×C13—22no—
79C4×D4×C13D412yes—
80C13×#117—22no—
81C13×#117—22no—
82C13×#117—22no—
83C13×#117—22no—
84C13×#117—22no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4D411yescharacteristic
91C2×C13×C4⋊C4C2312yes—
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C13×C22⋊C4C2311yescharacteristic
100C2×C42×C13D411yescharacteristic
101C2×C42×C13C2311yescharacteristic
102C13×#107—24no—
103C13×#106—24no—
104C13×C4⋊C8—22no—
105C13×#103—24no—
106C13×#102—24no—
107C13×C22⋊C8C2314yes—
108C13×#97—22no—
109C13×#95—22no—
110C13×#95—21no—
111C13×#95—22no—
112C13×#95C2312yes—
113#18362C1311yesmaximal, characteristic, direct product factor, Sylow
114C24×C13—21no—
115C24×C13C2×D411yescharacteristic
116C2×Q8×C13—21no—
117C2×Q8×C13—42no—
118C2×Q8×C13—82no—
119C2×Q8×C13C2×D412yes—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—21no—
123C2×D4×C13—42no—
124C2×D4×C13—42no—
125C2×D4×C13C2×D412yes—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—41no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2411yescharacteristic
143C2×C8×C13—24no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4—41no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—82no—
161C13×C4⋊C4C2×D412yes—
162C13×C4⋊C4C2×D412yes—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—82no—
176C42×C13—22no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—22no—
180C42×C13C2×D412yes—
181C42×C13C2×D412yes—
182#3491C2×C1311yescharacteristic
183#3239C2×C1312yescomplemented
184#2628C2×C1311yescharacteristic, complemented
185#1615C2×C1314yescomplemented
186#1614C2×C1312yescomplemented
187#1613C2×C1312yes—
188#1512C2×C1312yescomplemented
189#1464C2×C1311yescharacteristic, complemented
190C23×C13—21no—
191C23×C13—21no—
192C23×C13—22no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—42no—
196C23×C13—81no—
197C23×C13—81no—
198C23×C13#13712yes—
199C23×C13C22×D411yescharacteristic
200Q8×C13—42no—
201Q8×C13—84no—
202Q8×C13—81no—
203D4×C13—42no—
204D4×C13—44no—
205D4×C13—42no—
206D4×C13—42no—
207D4×C13—81no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—82no—
232C2×C4×C13—81no—
233C2×C4×C13—82no—
234C2×C4×C13—81no—
235C2×C4×C13#12011yescharacteristic
236C2×C4×C13#12011yescharacteristic
237C2×C4×C13#12012yes—
238C2×C4×C13C22×D412yes—
239C8×C13—44no—
240#552—22no—
241#552—22no—
242#551—22no—
243#551—22no—
244#543C22×C1311yescharacteristic
245#539—21no—
246#539C22×C1312yes—
247#534C22×C1311yescharacteristic
248C2×C4⋊Q8C22×C1311yescharacteristic, complemented
249#529—21no—
250#529C22×C1312yes—
251C2×#123—21no—
252#518—21no—
253C2×#117C22×C1311yescharacteristic
254#501—22no—
255#489—22no—
256#484C22×C1314yescomplemented
257#481C22×C1314yes—
258#475—22no—
259#474—22no—
260#432C22×C1312yescomplemented
261#400C22×C1312yescomplemented
262#399C22×C1312yes—
263#395—21no—
264#393—21no—
265#389—21no—
266#382C22×C1311yescharacteristic, complemented
267#380—21no—
268#328C22×C1314yescomplemented
269#327C22×C1314yes—
270#324C22×C1312yescomplemented
271#323C22×C1312yes—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—22no—
275C22×C13—42no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—42no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—81no—
282C22×C13—162no—
283C22×C13C2×#12011yescharacteristic
284C22×C13C2×#13711yescharacteristic
285C22×C13#57511yescharacteristic
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—22no—
289C4×C13—22no—
290C4×C13—41no—
291C4×C13—42no—
292C4×C13—41no—
293C4×C13—42no—
294C4×C13—41no—
295C4×C13—42no—
296C4×C13—82no—
297C4×C13—82no—
298C22×Q8—21no—
299C22×D4—21no—
300C23×C4D4×C1311yescharacteristic
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303#126—22no—
304#126—22no—
305#126—22no—
306#126—22no—
307#125—21no—
308#125—22no—
309#125—22no—
310#125D4×C1312yes—
311#124—21no—
312#124D4×C1312yes—
313#123—22no—
314#123—22no—
315#123—22no—
316#123—22no—
317#123—22no—
318#123—22no—
319#123—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—21no—
324C22⋊Q8—22no—
325C22⋊Q8C23×C1312yes—
326#121—21no—
327#121C23×C1312yes—
328#120—22no—
329C4×Q8—21no—
330C4×Q8D4×C1312yes—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—21no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4D4×C1312yes—
337#117—22no—
338#117—22no—
339#117—22no—
340#117—22no—
341#117—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4D4×C1311yescharacteristic
348C2×C4⋊C4C23×C1312yes—
349C2×C4⋊C4C23×C1311yescharacteristic
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4D4×C1311yescharacteristic
356C2×C22⋊C4C23×C1311yescharacteristic
357C2×C42D4×C1311yescharacteristic
358C2×C42C23×C1311yescharacteristic
359#107—24no—
360#106—24no—
361C4⋊C8—22no—
362#103—24no—
363#102—24no—
364C22⋊C8C23×C1314yes—
365#97—22no—
366#95—22no—
367#95—21no—
368#95—22no—
369#95C23×C1312yes—
370C2×C13—21no—
371C2×C13—21no—
372C2×C13—42no—
373C2×C13—82no—
374C2×C13#300711yescharacteristic
375C2×C13#302111yescharacteristic
376C2×C13#302811yescharacteristic
377C24—21no—
378C24C2×D4×C1311yescharacteristic
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8—82no—
382C2×Q8C2×D4×C1312yes—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4C2×D4×C1312yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4C2×D4×C1311yescharacteristic
401C22×C4C2×D4×C1311yescharacteristic
402C22×C4C2×D4×C1311yescharacteristic
403C22×C4C2×D4×C1311yescharacteristic
404C22×C4C2×D4×C1311yescharacteristic
405C22×C4C24×C1311yescharacteristic
406C2×C8—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—24no—
420C4⋊C4—42no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—82no—
424C4⋊C4C2×D4×C1312yes—
425C4⋊C4C2×D4×C1312yes—
426C22⋊C4—22no—
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—
438C22⋊C4—82no—
439C42—22no—
440C42—21no—
441C42—21no—
442C42—22no—
443C42C2×D4×C1312yes—
444C42C2×D4×C1312yes—
445C13#1836211yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—21no—
448C23—22no—
449C23—41no—
450C23—41no—
451C23—42no—
452C23—81no—
453C23—81no—
454C23C13×#13712yes—
455C23C22×D4×C1311yescharacteristic
456Q8—42no—
457Q8—84no—
458Q8—81no—
459D4—42no—
460D4—44no—
461D4—42no—
462D4—42no—
463D4—81no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—82no—
488C2×C4—81no—
489C2×C4—82no—
490C2×C4—81no—
491C2×C4C13×#12011yescharacteristic
492C2×C4C13×#12011yescharacteristic
493C2×C4C13×#12012yes—
494C2×C4C22×D4×C1312yes—
495C8—44no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—42no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—81no—
506C22—162no—
507C22C2×C13×#12011yescharacteristic
508C22C2×C13×#13711yescharacteristic
509C22C13×#57511yescharacteristic
510C4—21no—
511C4—21no—
512C4—22no—
513C4—22no—
514C4—41no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—82no—
521C4—82no—
522C2—21no—
523C2—21no—
524C2—42no—
525C2—82no—
526C2C13×#300711yescharacteristic
527C2C13×#302111yescharacteristic
528C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#534C22
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×#2628C2semidirect
4. C13×#1615C2semidirect
5. C13×#1614C2semidirect
7. C13×#1512C2semidirect
8. C13×#1464C2semidirect
17. C2×C13×C4⋊Q8C22semidirect
25. C13×#484C22semidirect
29. C13×#432C22semidirect
30. C13×#400C22semidirect
35. C13×#382C22semidirect
37. C13×#328C22semidirect
39. C13×#324C22semidirect
113. #18362C13direct (N × H)
183. #3239C2×C13semidirect
184. #2628C2×C13semidirect
185. #1615C2×C13semidirect
186. #1614C2×C13semidirect
188. #1512C2×C13semidirect
189. #1464C2×C13semidirect
248. C2×C4⋊Q8C22×C13semidirect
256. #484C22×C13semidirect
260. #432C22×C13semidirect
261. #400C22×C13semidirect
266. #382C22×C13semidirect
268. #328C22×C13semidirect
270. #324C22×C13semidirect
445. C13#18362direct (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×#32392
C13×#26282
C13×#16152
C13×#16142
C13×#16132
C13×#15122
C13×#14642
#1836213