Finite Group Databasebeta

← C13×#18360 #15704699

Subgroups — C13×#18360 #15704699

Order 3328.

928 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3507C211yesmaximal, characteristic, complemented
2C13×#3215C211yesmaximal, characteristic, complemented
3C13×#3213C211yesmaximal, characteristic
4C13×#2632C211yesmaximal, characteristic, complemented
5C13×#1603C214yesmaximal, complemented
6C13×#1597C214yesmaximal, complemented
7C13×#1515C211yesmaximal, characteristic, complemented
8C13×#1514C211yesmaximal, characteristic, complemented
9C13×#1467C211yesmaximal, characteristic, complemented
10C13×#559—21no—
11C13×#557—21no—
12C13×#556—21no—
13C13×#556—22no—
14C13×#554—21no—
15C13×#552—22no—
16C13×#539C2214yes—
17C13×#536—21no—
18C13×#533C2211yescharacteristic
19C13×#532C2211yescharacteristic
20C13×#529—22no—
21C2×C13×#124C2211yescharacteristic
22C13×#520—21no—
23C2×C4×Q8×C13C2211yescharacteristic
24C13×#497—21no—
25C13×#496—21no—
26C13×#489—21no—
27C13×#489—21no—
28C13×#464—22no—
29C13×#463—22no—
30C13×#451C2212yes—
31C13×#450C2212yes—
32C13×#448C2212yes—
33C13×#447C2212yes—
34C13×#432C2211yescharacteristic
35C13×#432C2211yescharacteristic
36C13×#399—21no—
37C13×#395C2212yes—
38C13×#394C2212yes—
39C13×#393—21no—
40C13×#388—22no—
41C13×#383C2211yescharacteristic
42C13×#328C2214yes—
43C13×#327C2214yes—
44C13×#324C2214yes—
45C2×C13×#41—21no—
46C22×Q8×C13D411yescharacteristic
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13C2311yescharacteristic
49C2×C13×Q16—22no—
50C2×C13×SD16—22no—
51C2×C13×SD16—22no—
52C2×C13×D8—22no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8D411yescharacteristic
55C13×C4⋊Q8D411yescharacteristic
56C13×C4⋊Q8D411yescharacteristic
57C13×#127D411yescharacteristic
58C13×#126—24no—
59C13×#126—24no—
60C13×#125—22no—
61C13×#125—24no—
62C13×#125—21no—
63C13×#124—22no—
64C13×#124—22no—
65C13×#124—21no—
66C13×#124—21no—
67C13×#124—21no—
68C13×#124—21no—
69C13×#124—21no—
70C13×#123—24no—
71C13×#123—24no—
72C13×C22⋊Q8—22no—
73C13×C22⋊Q8—22no—
74C13×C22⋊Q8—24no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8C2312yes—
77C13×#121—21no—
78C13×#121C2312yes—
79C4×Q8×C13—22no—
80C4×Q8×C13—22no—
81C4×Q8×C13—21no—
82C4×Q8×C13—21no—
83C4×Q8×C13—21no—
84C4×Q8×C13—21no—
85C4×Q8×C13—21no—
86C4×Q8×C13D412yes—
87C4×D4×C13—22no—
88C4×D4×C13—22no—
89C4×D4×C13—24no—
90C4×D4×C13—21no—
91C4×D4×C13D412yes—
92C13×#117—22no—
93C13×#117—24no—
94C13×#117—21no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4D411yescharacteristic
98C2×C13×C4⋊C4C2312yes—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—21no—
102C2×C13×C22⋊C4—22no—
103C2×C42×C13D412yes—
104C2×C42×C13C2311yescharacteristic
105C13×C4⋊C8—21no—
106C13×C4⋊C8—21no—
107C13×#103—22no—
108C13×#103—22no—
109C13×#102—22no—
110C13×#102—22no—
111C13×C22⋊C8C2312yes—
112C13×C22⋊C8C2312yes—
113C13×#97—21no—
114C13×#97—21no—
115C13×#95—21no—
116C13×#95—21no—
117C13×#95—22no—
118C13×#95C2312yes—
119#18360C1311yesmaximal, characteristic, direct product factor, Sylow
120C24×C13—21no—
121C13×#41—44no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—42no—
129C2×Q8×C13—81no—
130C2×Q8×C13C2×D412yes—
131C2×D4×C13—22no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—81no—
137C2×D4×C13C2×D412yes—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C13×Q16—82no—
148C13×SD16—82no—
149C13×SD16—82no—
150C13×D8—82no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—82no—
167C13×C4⋊C4C2×D412yes—
168C13×C4⋊C4C2×D412yes—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—24no—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—44no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4—41no—
178C13×C22⋊C4—41no—
179C13×C22⋊C4—41no—
180C13×C22⋊C4—82no—
181C42×C13—24no—
182C42×C13—22no—
183C42×C13—22no—
184C42×C13—22no—
185C42×C13C2×D411yescharacteristic
186C42×C13C2×D411yescharacteristic
187C42×C13C2×D411yescharacteristic
188C42×C13C2×D411yescharacteristic
189#3507C2×C1311yescharacteristic, complemented
190#3215C2×C1311yescharacteristic, complemented
191#3213C2×C1311yescharacteristic
192#2632C2×C1311yescharacteristic, complemented
193#1603C2×C1314yescomplemented
194#1597C2×C1314yescomplemented
195#1515C2×C1311yescharacteristic, complemented
196#1514C2×C1311yescharacteristic, complemented
197#1467C2×C1311yescharacteristic, complemented
198C23×C13—22no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—41no—
202C23×C13—42no—
203C23×C13C22×D411yescharacteristic
204Q8×C13—42no—
205Q8×C13—42no—
206Q8×C13—42no—
207Q8×C13—42no—
208Q8×C13—42no—
209Q8×C13—42no—
210Q8×C13—42no—
211D4×C13—42no—
212D4×C13—42no—
213D4×C13—42no—
214D4×C13—42no—
215D4×C13—42no—
216D4×C13—44no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—44no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—42no—
234C2×C4×C13—84no—
235C2×C4×C13#12011yescharacteristic
236C2×C4×C13#12011yescharacteristic
237C2×C4×C13#12011yescharacteristic
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C8×C13—42no—
242C8×C13—42no—
243#559—21no—
244#557—21no—
245#556—21no—
246#556—22no—
247#554—21no—
248#552—22no—
249#539C22×C1314yes—
250#536—21no—
251#533C22×C1311yescharacteristic
252#532C22×C1311yescharacteristic
253#529—22no—
254C2×#124C22×C1311yescharacteristic
255#520—21no—
256C2×C4×Q8C22×C1311yescharacteristic
257#497—21no—
258#496—21no—
259#489—21no—
260#489—21no—
261#464—22no—
262#463—22no—
263#451C22×C1312yes—
264#450C22×C1312yes—
265#448C22×C1312yes—
266#447C22×C1312yes—
267#432C22×C1311yescharacteristic
268#432C22×C1311yescharacteristic
269#399—21no—
270#395C22×C1312yes—
271#394C22×C1312yes—
272#393—21no—
273#388—22no—
274#383C22×C1311yescharacteristic
275#328C22×C1314yes—
276#327C22×C1314yes—
277#324C22×C1314yes—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—84no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13C2×#12011yescharacteristic
288C22×C13#57512yes—
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—42no—
296C4×C13—42no—
297C4×C13—42no—
298C4×C13—42no—
299C4×C13—42no—
300C4×C13—82no—
301C4×C13—81no—
302C2×#41—21no—
303C22×Q8D4×C1311yescharacteristic
304C22×Q8C23×C1311yescharacteristic
305C22×D4C23×C1311yescharacteristic
306C2×Q16—22no—
307C2×SD16—22no—
308C2×SD16—22no—
309C2×D8—22no—
310C4⋊Q8—22no—
311C4⋊Q8D4×C1311yescharacteristic
312C4⋊Q8D4×C1311yescharacteristic
313C4⋊Q8D4×C1311yescharacteristic
314#127D4×C1311yescharacteristic
315#126—24no—
316#126—24no—
317#125—22no—
318#125—24no—
319#125—21no—
320#124—22no—
321#124—22no—
322#124—21no—
323#124—21no—
324#124—21no—
325#124—21no—
326#124—21no—
327#123—24no—
328#123—24no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8—21no—
333C22⋊Q8C23×C1312yes—
334#121—21no—
335#121C23×C1312yes—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8D4×C1312yes—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—24no—
347C4×D4—21no—
348C4×D4D4×C1312yes—
349#117—22no—
350#117—24no—
351#117—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4D4×C1311yescharacteristic
355C2×C4⋊C4C23×C1312yes—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C42D4×C1312yes—
361C2×C42C23×C1311yescharacteristic
362C4⋊C8—21no—
363C4⋊C8—21no—
364#103—22no—
365#103—22no—
366#102—22no—
367#102—22no—
368C22⋊C8C23×C1312yes—
369C22⋊C8C23×C1312yes—
370#97—21no—
371#97—21no—
372#95—21no—
373#95—21no—
374#95—22no—
375#95C23×C1312yes—
376C2×C13—22no—
377C2×C13—82no—
378C2×C13—161no—
379C2×C13#300511yescharacteristic
380C2×C13#302011yescharacteristic
381C2×C13#302711yescharacteristic
382C24—21no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—42no—
391C2×Q8—81no—
392C2×Q8C2×D4×C1312yes—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—81no—
399C2×D4C2×D4×C1312yes—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4C2×D4×C1312yes—
405C22×C4C2×D4×C1311yescharacteristic
406C22×C4C2×D4×C1312yes—
407C22×C4C2×D4×C1311yescharacteristic
408C22×C4C24×C1311yescharacteristic
409Q16—82no—
410SD16—82no—
411SD16—82no—
412D8—82no—
413C2×C8—22no—
414C2×C8—22no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—82no—
429C4⋊C4C2×D4×C1312yes—
430C4⋊C4C2×D4×C1312yes—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—44no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—82no—
443C42—24no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42C2×D4×C1311yescharacteristic
448C42C2×D4×C1311yescharacteristic
449C42C2×D4×C1311yescharacteristic
450C42C2×D4×C1311yescharacteristic
451C13#1836011yescharacteristic, direct product factor, Sylow
452C23—22no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—42no—
457C23C22×D4×C1311yescharacteristic
458Q8—42no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—44no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4C13×#12011yescharacteristic
490C2×C4C13×#12011yescharacteristic
491C2×C4C13×#12011yescharacteristic
492C2×C4C13×#12011yescharacteristic
493C2×C4C22×D4×C1311yescharacteristic
494C2×C4C22×D4×C1311yescharacteristic
495C8—42no—
496C8—42no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—84no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C2×C13×#12011yescharacteristic
507C22C13×#57512yes—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—82no—
520C4—81no—
521C2—22no—
522C2—82no—
523C2—161no—
524C2C13×#300511yescharacteristic
525C2C13×#302011yescharacteristic
526C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3213C2
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
1. C13×#3507C2semidirect
2. C13×#3215C2semidirect
4. C13×#2632C2semidirect
5. C13×#1603C2semidirect
6. C13×#1597C2semidirect
7. C13×#1515C2semidirect
8. C13×#1514C2semidirect
9. C13×#1467C2semidirect
119. #18360C13direct (N × H)
189. #3507C2×C13semidirect
190. #3215C2×C13semidirect
192. #2632C2×C13semidirect
193. #1603C2×C13semidirect
194. #1597C2×C13semidirect
195. #1515C2×C13semidirect
196. #1514C2×C13semidirect
197. #1467C2×C13semidirect
451. C13#18360direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35072
C13×#32152
C13×#32132
C13×#26322
C13×#16032
C13×#15972
C13×#15152
C13×#15142
C13×#14672
#1836013