Finite Group Databasebeta

← C13×#18357 #15704696

Subgroups — C13×#18357 #15704696

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3491C211yesmaximal, characteristic
2C13×#3218C212yesmaximal, complemented
3C13×#2628C211yesmaximal, characteristic, complemented
4C13×#1603C214yesmaximal, complemented
5C13×#1602C212yesmaximal, complemented
6C13×#1601C212yesmaximal
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×#497—22no—
24C13×#491—22no—
25C13×#462—22no—
26C13×#461—22no—
27C13×#451C2214yescomplemented
28C13×#448C2214yes—
29C13×#432C2212yescomplemented
30C13×#400—21no—
31C13×#399—21no—
32C13×#395C2212yescomplemented
33C13×#393C2212yes—
34C13×#389—21no—
35C13×#382C2211yescharacteristic, complemented
36C13×#380—21no—
37C13×#328C2214yescomplemented
38C13×#327C2214yes—
39C13×#324C2212yescomplemented
40C13×#323C2212yes—
41C22×Q8×C13C2312yes—
42C22×D4×C13—21no—
43C23×C4×C13D411yescharacteristic
44C2×C13×Q16—24no—
45C2×C13×SD16—24no—
46C13×C4⋊Q8—22no—
47C13×C4⋊Q8—22no—
48C13×#126—22no—
49C13×#126—22no—
50C13×#126—22no—
51C13×#126—22no—
52C13×#125—21no—
53C13×#125—22no—
54C13×#125—22no—
55C13×#125D412yes—
56C13×#124—21no—
57C13×#124D412yes—
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—22no—
70C13×C22⋊Q8C2312yes—
71C13×#121—21no—
72C13×#121C2312yes—
73C13×#120—22no—
74C4×Q8×C13—21no—
75C4×Q8×C13D412yes—
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C4×D4×C13—21no—
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C4×D4×C13D412yes—
82C13×#117—22no—
83C13×#117—22no—
84C13×#117—22no—
85C13×#117—22no—
86C13×#117—22no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C13×C22⋊C4C2311yescharacteristic
102C2×C42×C13D411yescharacteristic
103C2×C42×C13C2311yescharacteristic
104C13×C4⋊C8—22no—
105C13×#103—24no—
106C13×#103—24no—
107C13×C22⋊C8C2314yes—
108C13×#97—22no—
109C13×#95—22no—
110C13×#95—21no—
111C13×#95—22no—
112C13×#95C2312yes—
113#18357C1311yesmaximal, characteristic, direct product factor, Sylow
114C24×C13—21no—
115C24×C13C2×D411yescharacteristic
116C2×Q8×C13—21no—
117C2×Q8×C13—24no—
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
143C13×Q16—84no—
144C13×SD16—84no—
145C2×C8×C13—24no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—42no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—82no—
163C13×C4⋊C4C2×D412yes—
164C13×C4⋊C4C2×D412yes—
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—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—82no—
178C42×C13—22no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—22no—
182C42×C13C2×D412yes—
183C42×C13C2×D412yes—
184#3491C2×C1311yescharacteristic
185#3218C2×C1312yescomplemented
186#2628C2×C1311yescharacteristic, complemented
187#1603C2×C1314yescomplemented
188#1602C2×C1312yescomplemented
189#1601C2×C1312yes—
190#1512C2×C1312yescomplemented
191#1464C2×C1311yescharacteristic, complemented
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—22no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—42no—
198C23×C13—81no—
199C23×C13—81no—
200C23×C13#13712yes—
201C23×C13C22×D411yescharacteristic
202Q8×C13—42no—
203Q8×C13—44no—
204Q8×C13—44no—
205Q8×C13—81no—
206D4×C13—42no—
207D4×C13—44no—
208D4×C13—42no—
209D4×C13—42no—
210D4×C13—81no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—82no—
235C2×C4×C13—81no—
236C2×C4×C13—82no—
237C2×C4×C13—81no—
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13#12011yescharacteristic
240C2×C4×C13#12012yes—
241C2×C4×C13C22×D412yes—
242C8×C13—44no—
243#552—22no—
244#552—22no—
245#551—22no—
246#551—22no—
247#543C22×C1311yescharacteristic
248#539—21no—
249#539C22×C1312yes—
250#534C22×C1311yescharacteristic
251C2×C4⋊Q8C22×C1311yescharacteristic, complemented
252#529—21no—
253#529C22×C1312yes—
254C2×#123—21no—
255#518—21no—
256C2×#117C22×C1311yescharacteristic
257#497—22no—
258#491—22no—
259#462—22no—
260#461—22no—
261#451C22×C1314yescomplemented
262#448C22×C1314yes—
263#432C22×C1312yescomplemented
264#400—21no—
265#399—21no—
266#395C22×C1312yescomplemented
267#393C22×C1312yes—
268#389—21no—
269#382C22×C1311yescharacteristic, complemented
270#380—21no—
271#328C22×C1314yescomplemented
272#327C22×C1314yes—
273#324C22×C1312yescomplemented
274#323C22×C1312yes—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—22no—
278C22×C13—42no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—81no—
285C22×C13—162no—
286C22×C13C2×#12011yescharacteristic
287C22×C13C2×#13711yescharacteristic
288C22×C13#57511yescharacteristic
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—22no—
292C4×C13—22no—
293C4×C13—41no—
294C4×C13—42no—
295C4×C13—41no—
296C4×C13—42no—
297C4×C13—41no—
298C4×C13—42no—
299C4×C13—82no—
300C4×C13—82no—
301C22×Q8C23×C1312yes—
302C22×D4—21no—
303C23×C4D4×C1311yescharacteristic
304C2×Q16—24no—
305C2×SD16—24no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308#126—22no—
309#126—22no—
310#126—22no—
311#126—22no—
312#125—21no—
313#125—22no—
314#125—22no—
315#125D4×C1312yes—
316#124—21no—
317#124D4×C1312yes—
318#123—22no—
319#123—22no—
320#123—22no—
321#123—22no—
322#123—22no—
323#123—22no—
324#123—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—21no—
329C22⋊Q8—22no—
330C22⋊Q8C23×C1312yes—
331#121—21no—
332#121C23×C1312yes—
333#120—22no—
334C4×Q8—21no—
335C4×Q8D4×C1312yes—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4D4×C1312yes—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4D4×C1311yescharacteristic
354C2×C4⋊C4C23×C1311yescharacteristic
355C2×C22⋊C4—22no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4D4×C1311yescharacteristic
361C2×C22⋊C4C23×C1311yescharacteristic
362C2×C42D4×C1311yescharacteristic
363C2×C42C23×C1311yescharacteristic
364C4⋊C8—22no—
365#103—24no—
366#103—24no—
367C22⋊C8C23×C1314yes—
368#97—22no—
369#95—22no—
370#95—21no—
371#95—22no—
372#95C23×C1312yes—
373C2×C13—21no—
374C2×C13—21no—
375C2×C13—42no—
376C2×C13—82no—
377C2×C13#300711yescharacteristic
378C2×C13#302211yescharacteristic
379C2×C13#302711yescharacteristic
380C24—21no—
381C24C2×D4×C1311yescharacteristic
382C2×Q8—21no—
383C2×Q8—24no—
384C2×Q8—82no—
385C2×Q8C2×D4×C1312yes—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4C2×D4×C1312yes—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—41no—
403C22×C4C2×D4×C1311yescharacteristic
404C22×C4C2×D4×C1311yescharacteristic
405C22×C4C2×D4×C1311yescharacteristic
406C22×C4C2×D4×C1311yescharacteristic
407C22×C4C2×D4×C1311yescharacteristic
408C22×C4C24×C1311yescharacteristic
409Q16—84no—
410SD16—84no—
411C2×C8—24no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—42no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—42no—
428C4⋊C4—82no—
429C4⋊C4C2×D4×C1312yes—
430C4⋊C4C2×D4×C1312yes—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—82no—
444C42—22no—
445C42—21no—
446C42—21no—
447C42—22no—
448C42C2×D4×C1312yes—
449C42C2×D4×C1312yes—
450C13#1835711yescharacteristic, direct product factor, Sylow
451C23—21no—
452C23—21no—
453C23—22no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—81no—
458C23—81no—
459C23C13×#13712yes—
460C23C22×D4×C1311yescharacteristic
461Q8—42no—
462Q8—44no—
463Q8—44no—
464Q8—81no—
465D4—42no—
466D4—44no—
467D4—42no—
468D4—42no—
469D4—81no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—82no—
494C2×C4—81no—
495C2×C4—82no—
496C2×C4—81no—
497C2×C4C13×#12011yescharacteristic
498C2×C4C13×#12011yescharacteristic
499C2×C4C13×#12012yes—
500C2×C4C22×D4×C1312yes—
501C8—44no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—162no—
513C22C2×C13×#12011yescharacteristic
514C22C2×C13×#13711yescharacteristic
515C22C13×#57511yescharacteristic
516C4—21no—
517C4—21no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—82no—
527C4—82no—
528C2—21no—
529C2—21no—
530C2—42no—
531C2—82no—
532C2C13×#300711yescharacteristic
533C2C13×#302211yescharacteristic
534C2C13×#302711yescharacteristic
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×#3218C2semidirect
3. C13×#2628C2semidirect
4. C13×#1603C2semidirect
5. C13×#1602C2semidirect
7. C13×#1512C2semidirect
8. C13×#1464C2semidirect
17. C2×C13×C4⋊Q8C22semidirect
27. C13×#451C22semidirect
29. C13×#432C22semidirect
32. C13×#395C22semidirect
35. C13×#382C22semidirect
37. C13×#328C22semidirect
39. C13×#324C22semidirect
113. #18357C13direct (N × H)
185. #3218C2×C13semidirect
186. #2628C2×C13semidirect
187. #1603C2×C13semidirect
188. #1602C2×C13semidirect
190. #1512C2×C13semidirect
191. #1464C2×C13semidirect
251. C2×C4⋊Q8C22×C13semidirect
261. #451C22×C13semidirect
263. #432C22×C13semidirect
266. #395C22×C13semidirect
269. #382C22×C13semidirect
271. #328C22×C13semidirect
273. #324C22×C13semidirect
450. C13#18357direct (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×#32182
C13×#26282
C13×#16032
C13×#16022
C13×#16012
C13×#15122
C13×#14642
#1835713