Finite Group Databasebeta

← C13×#8423 #15694762

Subgroups — C13×#8423 #15694762

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3511C211yesmaximal, characteristic
2C13×#1981C211yesmaximal, characteristic, complemented
3C13×#1806C211yesmaximal, characteristic, complemented
4C13×#1548C211yesmaximal, characteristic, complemented
5C13×#1547C211yesmaximal, characteristic, complemented
6C13×#1502C211yesmaximal, characteristic, complemented
7C13×#1477C211yesmaximal, characteristic, complemented
8C13×#556—21no—
9C13×#555C412yescomplemented
10C13×#554C412yescomplemented
11C13×#553—22no—
12C13×#548—22no—
13C13×#547—21no—
14C13×#542—22no—
15C13×#537—21no—
16C13×#533—21no—
17C13×#532—21no—
18C13×#532C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#520—21no—
21C4×C13×#41C2211yescharacteristic
22C13×#431C2211yescharacteristic
23C13×#423C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#104—21no—
26C2×C13×#103—22no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#339—21no—
29C13×#333—22no—
30C13×#332—21no—
31C13×#331—21no—
32C13×#327—22no—
33C13×Q8⋊C8—21no—
34C13×D4⋊C8—21no—
35C2×C13×#41—22no—
36C2×C13×#41—21no—
37C2×C13×#41D411yescharacteristic
38C22×Q8×C13D412yes—
39C2×C13×M16—21no—
40C22×C8×C13—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8C2×C412yes—
44C13×C4⋊Q8D412yes—
45C13×C4⋊Q8D411yescharacteristic
46C13×#127D411yescharacteristic
47C13×#126—24no—
48C13×#125—22no—
49C13×#124—22no—
50C13×#124—24no—
51C13×#124—21no—
52C13×#123—24no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—24no—
57C13×#121—22no—
58C13×#121—24no—
59C13×#121—22no—
60C13×#121—22no—
61C13×#121—21no—
62C13×#121D412yes—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13C2×C411yescharacteristic
66C4×Q8×C13D411yescharacteristic
67C4×D4×C13—22no—
68C4×D4×C13—24no—
69C4×D4×C13—22no—
70C4×D4×C13—21no—
71C4×D4×C13—21no—
72C4×D4×C13—21no—
73C4×D4×C13C2×C411yescharacteristic
74C4×D4×C13C2×C412yes—
75C4×D4×C13D411yescharacteristic
76C13×#117—22no—
77C13×#117—22no—
78C13×#117—21no—
79C13×#117D411yescharacteristic
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C13×C4⋊C8—21no—
88C13×C4⋊C8—21no—
89C13×C4⋊C8—21no—
90C13×C4⋊C8—21no—
91C13×C4⋊C8—21no—
92C13×#104—42no—
93C13×#103—44no—
94C13×C22⋊C8—21no—
95C4×C8×C13—21no—
96C13×#95—21no—
97#8423C1311yesmaximal, characteristic, direct product factor, Sylow
98C13×#41—21no—
99C13×#41—21no—
100C13×#41—21no—
101C13×#41—21no—
102C13×#41—41no—
103C13×#41—41no—
104C13×#41—41no—
105C13×#41—41no—
106C13×#41—82no—
107C13×#41—82no—
108C2×Q8×C13—21no—
109C2×Q8×C13—22no—
110C2×Q8×C13—42no—
111C2×Q8×C13—42no—
112C2×Q8×C13C22⋊C411yescharacteristic
113C2×Q8×C13C22⋊C414yes—
114C2×D4×C13—21no—
115C2×D4×C13—22no—
116C2×D4×C13—24no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13C22⋊C411yescharacteristic
120C2×D4×C13C22⋊C412yes—
121C22×C4×C13—24no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—41no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C13×M16—41no—
132C13×M16—41no—
133C2×C8×C13—42no—
134C2×C8×C13—41no—
135C2×C8×C13—41no—
136C2×C8×C13—41no—
137C13×C4⋊C4—24no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—22no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4C22⋊C411yescharacteristic
149C13×C4⋊C4C22⋊C411yescharacteristic
150C13×C4⋊C4C22⋊C412yes—
151C13×C22⋊C4—24no—
152C13×C22⋊C4—24no—
153C13×C22⋊C4—24no—
154C13×C22⋊C4—21no—
155C13×C22⋊C4—21no—
156C13×C22⋊C4—22no—
157C13×C22⋊C4—21no—
158C13×C22⋊C4—22no—
159C42×C13—24no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—41no—
164C42×C13—41no—
165C42×C13C22×C411yescharacteristic
166C42×C13C2×D411yescharacteristic
167C42×C13C2×D411yescharacteristic
168C42×C13C2×D411yescharacteristic
169#3511C2×C1311yescharacteristic
170#1981C2×C1311yescharacteristic, complemented
171#1806C2×C1311yescharacteristic, complemented
172#1548C2×C1311yescharacteristic, complemented
173#1547C2×C1311yescharacteristic, complemented
174#1502C2×C1311yescharacteristic, complemented
175#1477C2×C1311yescharacteristic, complemented
176C23×C13—21no—
177C23×C13—22no—
178C23×C13#12011yescharacteristic
179Q8×C13—21no—
180Q8×C13—21no—
181Q8×C13—44no—
182Q8×C13—41no—
183Q8×C13—41no—
184Q8×C13—42no—
185Q8×C13—42no—
186D4×C13—21no—
187D4×C13—21no—
188D4×C13—42no—
189D4×C13—41no—
190D4×C13—42no—
191D4×C13—41no—
192D4×C13—42no—
193D4×C13—41no—
194D4×C13—41no—
195D4×C13—41no—
196D4×C13—41no—
197D4×C13—84no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—22no—
203C2×C4×C13—21no—
204C2×C4×C13—24no—
205C2×C4×C13—41no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—82no—
215C2×C4×C13—84no—
216C2×C4×C13—81no—
217C2×C4×C13—81no—
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C2×C22⋊C411yescharacteristic
220C2×C4×C13C2×C22⋊C411yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13#12011yescharacteristic
224C2×C4×C13#13511yescharacteristic
225C2×C4×C13#13511yescharacteristic
226C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
227C2×C4×C13#13711yescharacteristic
228C8×C13—81no—
229C8×C13—81no—
230C8×C13—81no—
231#556—21no—
232#555C4×C1312yescomplemented
233#554C4×C1312yescomplemented
234#553—22no—
235#548—22no—
236#547—21no—
237#542—22no—
238#537—21no—
239#533—21no—
240#532—21no—
241#532C22×C1311yescharacteristic
242C2×C4⋊Q8C22×C1311yescharacteristic
243#520—21no—
244C4×#41C22×C1311yescharacteristic
245#431C22×C1311yescharacteristic
246#423C22×C1311yescharacteristic
247C2×C4⋊C8C22×C1311yescharacteristic
248C2×#104—21no—
249C2×#103—22no—
250C4×C4⋊C4C22×C1311yescharacteristic
251#339—21no—
252#333—22no—
253#332—21no—
254#331—21no—
255#327—22no—
256Q8⋊C8—21no—
257D4⋊C8—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—41no—
261C22×C13—42no—
262C22×C13—41no—
263C22×C13—42no—
264C22×C13—41no—
265C22×C13—42no—
266C22×C13#37911yescharacteristic
267C22×C13#44911yescharacteristic
268C22×C13#45211yescharacteristic
269C4×C13—21no—
270C4×C13—21no—
271C4×C13—21no—
272C4×C13—41no—
273C4×C13—44no—
274C4×C13—41no—
275C4×C13—41no—
276C4×C13—42no—
277C4×C13—82no—
278C4×C13#41611yescharacteristic
279C4×C13#41711yescharacteristic
280C4×C13#44911yescharacteristic
281C4×C13#45211yescharacteristic
282C4×C13#45311yescharacteristic
283C4×C13#45511yescharacteristic
284C2×#41—22no—
285C2×#41—21no—
286C2×#41D4×C1311yescharacteristic
287C22×Q8D4×C1312yes—
288C2×M16—21no—
289C22×C8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C2×C4×C1312yes—
293C4⋊Q8D4×C1312yes—
294C4⋊Q8D4×C1311yescharacteristic
295#127D4×C1311yescharacteristic
296#126—24no—
297#125—22no—
298#124—22no—
299#124—24no—
300#124—21no—
301#123—24no—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306#121—22no—
307#121—24no—
308#121—22no—
309#121—22no—
310#121—21no—
311#121D4×C1312yes—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8C2×C4×C1311yescharacteristic
315C4×Q8D4×C1311yescharacteristic
316C4×D4—22no—
317C4×D4—24no—
318C4×D4—22no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4C2×C4×C1311yescharacteristic
323C4×D4C2×C4×C1312yes—
324C4×D4D4×C1311yescharacteristic
325#117—22no—
326#117—22no—
327#117—21no—
328#117D4×C1311yescharacteristic
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42C23×C1311yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341#104—42no—
342#103—44no—
343C22⋊C8—21no—
344C4×C8—21no—
345#95—21no—
346C2×C13—21no—
347C2×C13—21no—
348C2×C13—81no—
349C2×C13—82no—
350C2×C13#178811yescharacteristic
351C2×C13#179211yescharacteristic
352C2×C13#179611yescharacteristic
353#41—21no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—41no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—82no—
362#41—82no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8C13×C22⋊C411yescharacteristic
368C2×Q8C13×C22⋊C414yes—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4C13×C22⋊C411yescharacteristic
375C2×D4C13×C22⋊C412yes—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—41no—
383C22×C4C2×D4×C1311yescharacteristic
384C22×C4C2×D4×C1311yescharacteristic
385C22×C4C2×D4×C1311yescharacteristic
386M16—41no—
387M16—41no—
388C2×C8—42no—
389C2×C8—41no—
390C2×C8—41no—
391C2×C8—41no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—41no—
403C4⋊C4C13×C22⋊C411yescharacteristic
404C4⋊C4C13×C22⋊C411yescharacteristic
405C4⋊C4C13×C22⋊C412yes—
406C22⋊C4—24no—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—22no—
412C22⋊C4—21no—
413C22⋊C4—22no—
414C42—24no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—41no—
419C42—41no—
420C42C22×C4×C1311yescharacteristic
421C42C2×D4×C1311yescharacteristic
422C42C2×D4×C1311yescharacteristic
423C42C2×D4×C1311yescharacteristic
424C13#842311yescharacteristic, direct product factor, Sylow
425C23—21no—
426C23—22no—
427C23C13×#12011yescharacteristic
428Q8—21no—
429Q8—21no—
430Q8—44no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—42no—
435D4—21no—
436D4—21no—
437D4—42no—
438D4—41no—
439D4—42no—
440D4—41no—
441D4—42no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—84no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—82no—
464C2×C4—84no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4C2×C13×C22⋊C411yescharacteristic
468C2×C4C2×C13×C22⋊C411yescharacteristic
469C2×C4C2×C13×C22⋊C411yescharacteristic
470C2×C4C13×#12011yescharacteristic
471C2×C4C13×#12011yescharacteristic
472C2×C4C13×#12011yescharacteristic
473C2×C4C13×#13511yescharacteristic
474C2×C4C13×#13511yescharacteristic
475C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
476C2×C4C13×#13711yescharacteristic
477C8—81no—
478C8—81no—
479C8—81no—
480C22—21no—
481C22—21no—
482C22—41no—
483C22—42no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—42no—
488C22C13×#37911yescharacteristic
489C22C13×#44911yescharacteristic
490C22C13×#45211yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—42no—
496C4—41no—
497C4—44no—
498C4—41no—
499C4—82no—
500C4C13×#41611yescharacteristic
501C4C13×#41711yescharacteristic
502C4C13×#44911yescharacteristic
503C4C13×#45211yescharacteristic
504C4C13×#45311yescharacteristic
505C4C13×#45511yescharacteristic
506C2—21no—
507C2—21no—
508C2—81no—
509C2—82no—
510C2C13×#178811yescharacteristic
511C2C13×#179211yescharacteristic
512C2C13×#179611yescharacteristic
subgroupG/H
center, socleC22×C13#379
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3511C2
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×#1981C2semidirect
3. C13×#1806C2semidirect
4. C13×#1548C2semidirect
5. C13×#1547C2semidirect
6. C13×#1502C2semidirect
7. C13×#1477C2semidirect
9. C13×#555C4semidirect
10. C13×#554C4semidirect
97. #8423C13direct (N × H)
170. #1981C2×C13semidirect
171. #1806C2×C13semidirect
172. #1548C2×C13semidirect
173. #1547C2×C13semidirect
174. #1502C2×C13semidirect
175. #1477C2×C13semidirect
232. #555C4×C13semidirect
233. #554C4×C13semidirect
424. C13#8423direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35112
C13×#19812
C13×#18062
C13×#15482
C13×#15472
C13×#15022
C13×#14772
#842313