Finite Group Databasebeta

← C13×#18352 #15704691

Subgroups — C13×#18352 #15704691

Order 3328.

996 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic, complemented
2C13×#3193C212yesmaximal, complemented
3C13×#2635C211yesmaximal, characteristic
4C13×#1617C212yesmaximal, complemented
5C13×#1614C212yesmaximal, complemented
6C13×#1599C212yesmaximal, complemented
7C13×#1596C212yesmaximal, complemented
8C13×#1511C212yesmaximal, complemented
9C13×#1465C211yesmaximal, characteristic, complemented
10C13×#554—24no—
11C13×#554—22no—
12D4×Q8×C13—22no—
13C13×#544C2212yes—
14C13×#543—21no—
15C13×#543C2212yes—
16C13×#533—21no—
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8C2212yes—
19C2×C13×#121C2211yescharacteristic
20C13×#518—21no—
21C2×C4×D4×C13C2211yescharacteristic
22C13×#484C2214yes—
23C13×#480—22no—
24C13×#468—24no—
25C13×#450C2214yes—
26C13×#448—22no—
27C13×#407C2212yes—
28C13×#400C2211yescharacteristic
29C13×#399C2211yescharacteristic
30C13×#394—21no—
31C13×#394C2211yescharacteristic
32C13×#392—21no—
33C13×#392C2211yescharacteristic
34C13×#388—21no—
35C13×#386—21no—
36C13×#381C2211yescharacteristic
37C13×#328C2214yes—
38C13×#328C2214yes—
39C13×#324C2212yes—
40C13×#323C2212yes—
41C22×Q8×C13—21no—
42C22×Q8×C13D412yescomplemented
43C22×D4×C13—21no—
44C22×D4×C13—21no—
45C22×D4×C13D411yescharacteristic
46C22×D4×C13C2311yescharacteristic
47C23×C4×C13D411yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C2×C13×SD16—24no—
50C2×C13×M16—22no—
51C13×C4⋊Q8—21no—
52C13×C4⋊Q8—21no—
53C13×C4⋊Q8—24no—
54C13×#125—22no—
55C13×#125—24no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—22no—
58C13×C22⋊Q8—24no—
59C13×C22⋊Q8—24no—
60C13×C22⋊Q8—24no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—24no—
66C13×C22⋊Q8D414yescomplemented
67C13×C22⋊Q8C2314yes—
68C13×#121—22no—
69C13×#121—22no—
70C4×Q8×C13—22no—
71C4×Q8×C13—22no—
72C4×D4×C13—24no—
73C4×D4×C13—24no—
74C4×D4×C13—22no—
75C4×D4×C13—22no—
76C13×#117—22no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4D412yescomplemented
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4D411yescharacteristic
93C2×C13×C22⋊C4C2311yescharacteristic
94C2×C42×C13D411yescharacteristic
95C13×#107—24no—
96C13×#103—24no—
97C13×#102—24no—
98C13×C22⋊C8—22no—
99C13×C22⋊C8C2314yes—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95C2311yescharacteristic
104C13×#95C2311yescharacteristic
105#18352C1311yesmaximal, characteristic, direct product factor, Sylow
106C24×C13—21no—
107C24×C13C2×D411yescharacteristic
108C24×C13C2×D411yescharacteristic
109C2×Q8×C13—22no—
110C2×Q8×C13—22no—
111C2×Q8×C13—22no—
112C2×Q8×C13—82no—
113C2×Q8×C13—82no—
114C2×Q8×C13C2×D414yes—
115C2×D4×C13—22no—
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—42no—
120C2×D4×C13—42no—
121C2×D4×C13—81no—
122C2×D4×C13—81no—
123C2×D4×C13—81no—
124C2×D4×C13—81no—
125C2×D4×C13—81no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—81no—
136C22×C4×C13—81no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2411yescharacteristic
144C13×SD16—84no—
145C13×M16—82no—
146C2×C8×C13—24no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—81no—
159C13×C4⋊C4C2×D414yes—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—24no—
164C13×C22⋊C4—22no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—81no—
169C13×C22⋊C4—81no—
170C13×C22⋊C4—81no—
171C13×C22⋊C4—81no—
172C42×C13—24no—
173C42×C13—21no—
174C42×C13—21no—
175#3501C2×C1311yescharacteristic, complemented
176#3193C2×C1312yescomplemented
177#2635C2×C1311yescharacteristic
178#1617C2×C1312yescomplemented
179#1614C2×C1312yescomplemented
180#1599C2×C1312yescomplemented
181#1596C2×C1312yescomplemented
182#1511C2×C1312yescomplemented
183#1465C2×C1311yescharacteristic, complemented
184C23×C13—21no—
185C23×C13—21no—
186C23×C13—21no—
187C23×C13—21no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13#12012yes—
200C23×C13#13712yes—
201C23×C13C22×D411yescharacteristic
202Q8×C13—44no—
203Q8×C13—44no—
204Q8×C13—82no—
205Q8×C13—82no—
206D4×C13—28no—
207D4×C13—44no—
208D4×C13—84no—
209D4×C13—84no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—21no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—81no—
233C2×C4×C13—82no—
234C2×C4×C13—82no—
235C2×C4×C13—82no—
236C2×C4×C13—82no—
237C2×C4×C13#12011yescharacteristic
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13#13712yes—
240C2×C4×C13C22×D412yes—
241C8×C13—44no—
242#554—24no—
243#554—22no—
244D4×Q8—22no—
245#544C22×C1312yes—
246#543—21no—
247#543C22×C1312yes—
248#533—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C22×C1312yes—
251C2×#121C22×C1311yescharacteristic
252#518—21no—
253C2×C4×D4C22×C1311yescharacteristic
254#484C22×C1314yes—
255#480—22no—
256#468—24no—
257#450C22×C1314yes—
258#448—22no—
259#407C22×C1312yes—
260#400C22×C1311yescharacteristic
261#399C22×C1311yescharacteristic
262#394—21no—
263#394C22×C1311yescharacteristic
264#392—21no—
265#392C22×C1311yescharacteristic
266#388—21no—
267#386—21no—
268#381C22×C1311yescharacteristic
269#328C22×C1314yes—
270#328C22×C1314yes—
271#324C22×C1312yes—
272#323C22×C1312yes—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—22no—
276C22×C13—22no—
277C22×C13—22no—
278C22×C13—22no—
279C22×C13—42no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13—81no—
283C22×C13—81no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13C2×#12011yescharacteristic
293C22×C13C2×#13711yescharacteristic
294C22×C13C2×#13711yescharacteristic
295C4×C13—22no—
296C4×C13—22no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—41no—
300C4×C13—44no—
301C4×C13—41no—
302C4×C13—44no—
303C4×C13—81no—
304C4×C13—81no—
305C4×C13—81no—
306C22×Q8—21no—
307C22×Q8D4×C1312yescomplemented
308C22×D4—21no—
309C22×D4—21no—
310C22×D4D4×C1311yescharacteristic
311C22×D4C23×C1311yescharacteristic
312C23×C4D4×C1311yescharacteristic
313C23×C4C23×C1311yescharacteristic
314C2×SD16—24no—
315C2×M16—22no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—24no—
319#125—22no—
320#125—24no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331C22⋊Q8D4×C1314yescomplemented
332C22⋊Q8C23×C1314yes—
333#121—22no—
334#121—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×D4—24no—
338C4×D4—24no—
339C4×D4—22no—
340C4×D4—22no—
341#117—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4D4×C1312yescomplemented
347C2×C4⋊C4C23×C1311yescharacteristic
348C2×C4⋊C4C23×C1311yescharacteristic
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4D4×C1311yescharacteristic
358C2×C22⋊C4C23×C1311yescharacteristic
359C2×C42D4×C1311yescharacteristic
360#107—24no—
361#103—24no—
362#102—24no—
363C22⋊C8—22no—
364C22⋊C8C23×C1314yes—
365#95—21no—
366#95—21no—
367#95—21no—
368#95C23×C1311yescharacteristic
369#95C23×C1311yescharacteristic
370C2×C13—21no—
371C2×C13—21no—
372C2×C13—42no—
373C2×C13—42no—
374C2×C13—161no—
375C2×C13#300411yescharacteristic
376C2×C13#302111yescharacteristic
377C2×C13#302611yescharacteristic
378C24—21no—
379C24C2×D4×C1311yescharacteristic
380C24C2×D4×C1311yescharacteristic
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—82no—
385C2×Q8—82no—
386C2×Q8C2×D4×C1314yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—81no—
394C2×D4—81no—
395C2×D4—81no—
396C2×D4—81no—
397C2×D4—81no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—81no—
408C22×C4—81no—
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1311yescharacteristic
413C22×C4C2×D4×C1312yes—
414C22×C4C2×D4×C1312yes—
415C22×C4C24×C1311yescharacteristic
416SD16—84no—
417M16—82no—
418C2×C8—24no—
419C4⋊C4—22no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—81no—
431C4⋊C4C2×D4×C1314yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—22no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—42no—
440C22⋊C4—81no—
441C22⋊C4—81no—
442C22⋊C4—81no—
443C22⋊C4—81no—
444C42—24no—
445C42—21no—
446C42—21no—
447C13#1835211yescharacteristic, direct product factor, Sylow
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23C13×#12012yes—
464C23C13×#13712yes—
465C23C22×D4×C1311yescharacteristic
466Q8—44no—
467Q8—44no—
468Q8—82no—
469Q8—82no—
470D4—28no—
471D4—44no—
472D4—84no—
473D4—84no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—81no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4C13×#12011yescharacteristic
502C2×C4C13×#12011yescharacteristic
503C2×C4C13×#13712yes—
504C2×C4C22×D4×C1312yes—
505C8—44no—
506C22—21no—
507C22—21no—
508C22—22no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—42no—
513C22—41no—
514C22—41no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22C2×C13×#12011yescharacteristic
526C22C2×C13×#13711yescharacteristic
527C22C2×C13×#13711yescharacteristic
528C4—22no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—44no—
534C4—41no—
535C4—44no—
536C4—81no—
537C4—81no—
538C4—81no—
539C2—21no—
540C2—21no—
541C2—42no—
542C2—42no—
543C2—161no—
544C2C13×#300411yescharacteristic
545C2C13×#302111yescharacteristic
546C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#2635C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C13×#3501C2semidirect
2. C13×#3193C2semidirect
4. C13×#1617C2semidirect
5. C13×#1614C2semidirect
6. C13×#1599C2semidirect
7. C13×#1596C2semidirect
8. C13×#1511C2semidirect
9. C13×#1465C2semidirect
42. C22×Q8×C13D4semidirect
66. C13×C22⋊Q8D4semidirect
81. C2×C13×C4⋊C4D4semidirect
105. #18352C13direct (N × H)
175. #3501C2×C13semidirect
176. #3193C2×C13semidirect
178. #1617C2×C13semidirect
179. #1614C2×C13semidirect
180. #1599C2×C13semidirect
181. #1596C2×C13semidirect
182. #1511C2×C13semidirect
183. #1465C2×C13semidirect
307. C22×Q8D4×C13semidirect
331. C22⋊Q8D4×C13semidirect
346. C2×C4⋊C4D4×C13semidirect
447. C13#18352direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35012
C13×#31932
C13×#26352
C13×#16172
C13×#16142
C13×#15992
C13×#15962
C13×#15112
C13×#14652
#1835213