Finite Group Databasebeta

← C13×#8502 #15694841

Subgroups — C13×#8502 #15694841

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3547C211yesmaximal, characteristic
2C13×#1553C211yesmaximal, characteristic, complemented
3C13×#1535C211yesmaximal, characteristic, complemented
4C13×#1521C211yesmaximal, characteristic, complemented
5C13×#1515C211yesmaximal, characteristic, complemented
6C13×#1514C211yesmaximal, characteristic, complemented
7C13×#1497C211yesmaximal, characteristic, complemented
8C13×#562—22no—
9C13×#555—21no—
10C13×#555C411yescharacteristic, complemented
11C13×#554C411yescharacteristic, complemented
12C13×#553—21no—
13C13×#552—21no—
14D4×Q8×C13C411yescharacteristic, complemented
15C13×#548—21no—
16C13×#547C411yescharacteristic, complemented
17C13×#544—21no—
18C13×#542—22no—
19C13×#540—21no—
20C13×#537—21no—
21C13×#536—21no—
22C13×#533C2211yescharacteristic
23C13×#532C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C13×#432C2211yescharacteristic
26C13×#432C2211yescharacteristic
27C13×#431C2211yescharacteristic
28C13×#383C2211yescharacteristic
29C13×#332—21no—
30C13×#331—21no—
31C13×#330—21no—
32C13×#329—21no—
33C13×#328—22no—
34C13×#328—21no—
35C13×#327—21no—
36C13×#327—21no—
37C13×#327—21no—
38C13×Q8⋊C8—22no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C22×Q8×C13—21no—
42C13×C4⋊Q8—22no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8C2×C411yescharacteristic
45C13×C4⋊Q8C2×C411yescharacteristic
46C13×C4⋊Q8D411yescharacteristic
47C13×#127D411yescharacteristic
48C13×#126—22no—
49C13×#126—21no—
50C13×#125—22no—
51C13×#125—21no—
52C13×#125—21no—
53C13×#125D411yescharacteristic
54C13×#124—22no—
55C13×#124—22no—
56C13×#124—22no—
57C13×#124—21no—
58C13×#124D411yescharacteristic
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—21no—
63C13×#123—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—21no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—21no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8D411yescharacteristic
73C13×C22⋊Q8D412yes—
74C13×#121—22no—
75C13×#121—22no—
76C13×#121—22no—
77C13×#121—22no—
78C13×#121—21no—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—21no—
82C13×#121D411yescharacteristic
83C13×#121D411yescharacteristic
84C13×#121D411yescharacteristic
85C4×Q8×C13—21no—
86C4×Q8×C13C2×C411yescharacteristic
87C4×Q8×C13D412yes—
88C4×D4×C13—22no—
89C4×D4×C13—21no—
90C4×D4×C13—21no—
91C4×D4×C13—21no—
92C4×D4×C13—21no—
93C4×D4×C13C2×C411yescharacteristic
94C4×D4×C13C2×C411yescharacteristic
95C4×D4×C13C2×C411yescharacteristic
96C13×#117—22no—
97C13×#117—21no—
98C13×#117—21no—
99C13×#117—21no—
100C13×#117—21no—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—21no—
103C2×C42×C13C2311yescharacteristic
104C13×C4⋊C8—21no—
105C13×C4⋊C8—21no—
106C13×C4⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8—21no—
109C13×C22⋊C8—21no—
110C13×#97—21no—
111C13×#97—21no—
112C4×C8×C13—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116#8502C1311yesmaximal, characteristic, direct product factor, Sylow
117C13×#41—82no—
118C13×#41—82no—
119C2×Q8×C13—22no—
120C2×Q8×C13—21no—
121C2×Q8×C13—21no—
122C2×Q8×C13—82no—
123C2×Q8×C13C22⋊C411yescharacteristic
124C2×Q8×C13C22⋊C412yes—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13C22⋊C411yescharacteristic
133C2×D4×C13C22⋊C411yescharacteristic
134C2×D4×C13C22⋊C411yescharacteristic
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—41no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C2×C8×C13—41no—
146C2×C8×C13—41no—
147C2×C8×C13—41no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4C22⋊C411yescharacteristic
163C13×C4⋊C4C22⋊C411yescharacteristic
164C13×C4⋊C4C22⋊C411yescharacteristic
165C13×C4⋊C4C22⋊C411yescharacteristic
166C13×C4⋊C4C22⋊C412yes—
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—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C42×C13—22no—
183C42×C13—21no—
184C42×C13—22no—
185C42×C13C22×C411yescharacteristic
186C42×C13C2×D411yescharacteristic
187C42×C13C2×D411yescharacteristic
188C42×C13C2×D411yescharacteristic
189#3547C2×C1311yescharacteristic
190#1553C2×C1311yescharacteristic, complemented
191#1535C2×C1311yescharacteristic, complemented
192#1521C2×C1311yescharacteristic, complemented
193#1515C2×C1311yescharacteristic, complemented
194#1514C2×C1311yescharacteristic, complemented
195#1497C2×C1311yescharacteristic, complemented
196C23×C13—21no—
197C23×C13—21no—
198C23×C13—21no—
199C23×C13#12011yescharacteristic
200Q8×C13—42no—
201Q8×C13—41no—
202Q8×C13—42no—
203Q8×C13—81no—
204Q8×C13—82no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—41no—
208D4×C13—81no—
209D4×C13—81no—
210D4×C13—81no—
211D4×C13—81no—
212D4×C13—81no—
213D4×C13—82no—
214D4×C13—82no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—21no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—82no—
229C2×C4×C13—82no—
230C2×C4×C13—82no—
231C2×C4×C13—81no—
232C2×C4×C13—81no—
233C2×C4×C13—81no—
234C2×C4×C13C2×C22⋊C411yescharacteristic
235C2×C4×C13C2×C22⋊C411yescharacteristic
236C2×C4×C13C2×C22⋊C411yescharacteristic
237C2×C4×C13#12011yescharacteristic
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13#12011yescharacteristic
240C8×C13—81no—
241C8×C13—81no—
242C8×C13—81no—
243#562—22no—
244#555—21no—
245#555C4×C1311yescharacteristic, complemented
246#554C4×C1311yescharacteristic, complemented
247#553—21no—
248#552—21no—
249D4×Q8C4×C1311yescharacteristic, complemented
250#548—21no—
251#547C4×C1311yescharacteristic, complemented
252#544—21no—
253#542—22no—
254#540—21no—
255#537—21no—
256#536—21no—
257#533C22×C1311yescharacteristic
258#532C22×C1311yescharacteristic
259#529C22×C1311yescharacteristic
260#432C22×C1311yescharacteristic
261#432C22×C1311yescharacteristic
262#431C22×C1311yescharacteristic
263#383C22×C1311yescharacteristic
264#332—21no—
265#331—21no—
266#330—21no—
267#329—21no—
268#328—22no—
269#328—21no—
270#327—21no—
271#327—21no—
272#327—21no—
273Q8⋊C8—22no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13—41no—
283C22×C13—41no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13#37911yescharacteristic
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—41no—
294C4×C13—42no—
295C4×C13—41no—
296C4×C13—41no—
297C4×C13—42no—
298C4×C13—41no—
299C4×C13—41no—
300C4×C13—161no—
301C2×#41—21no—
302C2×#41—21no—
303C22×Q8—21no—
304C4⋊Q8—22no—
305C4⋊Q8—21no—
306C4⋊Q8C2×C4×C1311yescharacteristic
307C4⋊Q8C2×C4×C1311yescharacteristic
308C4⋊Q8D4×C1311yescharacteristic
309#127D4×C1311yescharacteristic
310#126—22no—
311#126—21no—
312#125—22no—
313#125—21no—
314#125—21no—
315#125D4×C1311yescharacteristic
316#124—22no—
317#124—22no—
318#124—22no—
319#124—21no—
320#124D4×C1311yescharacteristic
321#123—22no—
322#123—22no—
323#123—22no—
324#123—21no—
325#123—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—21no—
329C22⋊Q8—22no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—22no—
334C22⋊Q8D4×C1311yescharacteristic
335C22⋊Q8D4×C1312yes—
336#121—22no—
337#121—22no—
338#121—22no—
339#121—22no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121D4×C1311yescharacteristic
345#121D4×C1311yescharacteristic
346#121D4×C1311yescharacteristic
347C4×Q8—21no—
348C4×Q8C2×C4×C1311yescharacteristic
349C4×Q8D4×C1312yes—
350C4×D4—22no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4C2×C4×C1311yescharacteristic
356C4×D4C2×C4×C1311yescharacteristic
357C4×D4C2×C4×C1311yescharacteristic
358#117—22no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C42C23×C1311yescharacteristic
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372#97—21no—
373#97—21no—
374C4×C8—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C2×C13—41no—
379C2×C13—81no—
380C2×C13—81no—
381C2×C13—81no—
382C2×C13#179411yescharacteristic
383C2×C13#179511yescharacteristic
384C2×C13#179611yescharacteristic
385#41—82no—
386#41—82no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—82no—
391C2×Q8C13×C22⋊C411yescharacteristic
392C2×Q8C13×C22⋊C412yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4C13×C22⋊C411yescharacteristic
401C2×D4C13×C22⋊C411yescharacteristic
402C2×D4C13×C22⋊C411yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1311yescharacteristic
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4C13×C22⋊C411yescharacteristic
431C4⋊C4C13×C22⋊C411yescharacteristic
432C4⋊C4C13×C22⋊C411yescharacteristic
433C4⋊C4C13×C22⋊C411yescharacteristic
434C4⋊C4C13×C22⋊C412yes—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C42—22no—
451C42—21no—
452C42—22no—
453C42C22×C4×C1311yescharacteristic
454C42C2×D4×C1311yescharacteristic
455C42C2×D4×C1311yescharacteristic
456C42C2×D4×C1311yescharacteristic
457C13#850211yescharacteristic, direct product factor, Sylow
458C23—21no—
459C23—21no—
460C23—21no—
461C23C13×#12011yescharacteristic
462Q8—41no—
463Q8—42no—
464Q8—42no—
465Q8—81no—
466Q8—82no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—81no—
471D4—81no—
472D4—81no—
473D4—81no—
474D4—81no—
475D4—82no—
476D4—82no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4C2×C13×C22⋊C411yescharacteristic
497C2×C4C2×C13×C22⋊C411yescharacteristic
498C2×C4C2×C13×C22⋊C411yescharacteristic
499C2×C4C13×#12011yescharacteristic
500C2×C4C13×#12011yescharacteristic
501C2×C4C13×#12011yescharacteristic
502C8—81no—
503C8—81no—
504C8—81no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22C13×#37911yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—41no—
525C4—42no—
526C4—41no—
527C4—41no—
528C4—42no—
529C4—41no—
530C4—41no—
531C4—161no—
532C2—41no—
533C2—81no—
534C2—81no—
535C2—81no—
536C2C13×#179411yescharacteristic
537C2C13×#179511yescharacteristic
538C2C13×#179611yescharacteristic
subgroupG/H
center, socleC22×C13#379
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3547C2
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×#1553C2semidirect
3. C13×#1535C2semidirect
4. C13×#1521C2semidirect
5. C13×#1515C2semidirect
6. C13×#1514C2semidirect
7. C13×#1497C2semidirect
10. C13×#555C4semidirect
11. C13×#554C4semidirect
14. D4×Q8×C13C4semidirect
16. C13×#547C4semidirect
116. #8502C13direct (N × H)
190. #1553C2×C13semidirect
191. #1535C2×C13semidirect
192. #1521C2×C13semidirect
193. #1515C2×C13semidirect
194. #1514C2×C13semidirect
195. #1497C2×C13semidirect
245. #555C4×C13semidirect
246. #554C4×C13semidirect
249. D4×Q8C4×C13semidirect
251. #547C4×C13semidirect
457. C13#8502direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35472
C13×#15532
C13×#15352
C13×#15212
C13×#15152
C13×#15142
C13×#14972
#850213