Finite Group Databasebeta

← C13×#18430 #15704769

Subgroups — C13×#18430 #15704769

Order 3328.

996 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic, complemented
3C13×#3205C211yesmaximal, characteristic, complemented
4C13×#2641C211yesmaximal, characteristic, complemented
5C13×#1598C214yesmaximal, complemented
6C13×#1597C214yesmaximal, complemented
7C13×#1505C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1470C211yesmaximal, characteristic, complemented
10C13×#563—21no—
11C13×#562—21no—
12C13×#554—21no—
13C13×#553—21no—
14C13×#553—21no—
15C13×#547—22no—
16C13×#547—21no—
17C13×#544—21no—
18C13×#540—21no—
19C13×#539—22no—
20C13×#539C2212yes—
21C13×#537C2212yes—
22C13×#532C2211yescharacteristic
23C2×C13×#127C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#496—21no—
27C13×#493—21no—
28C13×#490—21no—
29C13×#486—21no—
30C13×#460—21no—
31C13×#459—22no—
32C13×#459—21no—
33C13×#450C2212yes—
34C13×#447C2214yes—
35C13×#447C2212yes—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#394—22no—
39C13×#394C2214yes—
40C13×#390—21no—
41C13×#390—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#327C2212yes—
45C13×#327C2214yes—
46C13×#324C2214yes—
47C2×C13×#41—21no—
48C2×C13×#41—22no—
49C22×D4×C13—21no—
50C22×D4×C13—21no—
51C22×D4×C13C2312yes—
52C2×C13×SD16—22no—
53C2×C13×D8—24no—
54C2×C13×D8—22no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8D411yescharacteristic
58C13×#127—21no—
59C13×#127—21no—
60C13×#127—21no—
61C13×#127—21no—
62C13×#127D411yescharacteristic
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—21no—
66C13×#125—21no—
67C13×#125—22no—
68C13×#125—21no—
69C13×#125—21no—
70C13×#125—21no—
71C13×#125—21no—
72C13×#125D411yescharacteristic
73C13×#124—21no—
74C13×#124D411yescharacteristic
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—21no—
81C13×#123—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8C2311yescharacteristic
89C13×#121—21no—
90C13×#121—22no—
91C13×#121—21no—
92C13×#121—22no—
93C13×#121—22no—
94C13×#121—21no—
95C13×#121—22no—
96C13×#121C2311yescharacteristic
97C13×#121C2312yes—
98C4×Q8×C13D411yescharacteristic
99C4×D4×C13—22no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13—22no—
104C4×D4×C13—21no—
105C4×D4×C13D411yescharacteristic
106C4×D4×C13D412yes—
107C13×#117—21no—
108C13×#117—21no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D412yes—
114C2×C13×C4⋊C4C2312yes—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4—24no—
117C2×C42×C13—21no—
118C2×C42×C13C2311yescharacteristic
119C13×C4⋊C8—21no—
120C13×C4⋊C8—21no—
121C13×#102—24no—
122C13×#102—22no—
123C13×#102—22no—
124C13×C22⋊C8C2312yes—
125C13×C22⋊C8C2312yes—
126C13×#97—21no—
127C4×C8×C13—21no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18430C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—22no—
132C13×#41—82no—
133C13×#41—84no—
134C2×Q8×C13—22no—
135C2×Q8×C13—21no—
136C2×Q8×C13C2×D411yescharacteristic
137C2×D4×C13—21no—
138C2×D4×C13—22no—
139C2×D4×C13—22no—
140C2×D4×C13—22no—
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—44no—
146C2×D4×C13—41no—
147C2×D4×C13—41no—
148C2×D4×C13—41no—
149C2×D4×C13—41no—
150C2×D4×C13—82no—
151C2×D4×C13—82no—
152C2×D4×C13C2×D411yescharacteristic
153C2×D4×C13C2×D412yes—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—21no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2411yescharacteristic
165C13×SD16—82no—
166C13×D8—84no—
167C13×D8—82no—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4C2×D412yes—
188C13×C4⋊C4C2×D411yescharacteristic
189C13×C4⋊C4C2×D411yescharacteristic
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—21no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—84no—
203C13×C22⋊C4—84no—
204C42×C13—22no—
205C42×C13—21no—
206C42×C13—42no—
207C42×C13C2×D411yescharacteristic
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2×D411yescharacteristic
211#3559C2×C1311yescharacteristic, complemented
212#3217C2×C1311yescharacteristic, complemented
213#3205C2×C1311yescharacteristic, complemented
214#2641C2×C1311yescharacteristic, complemented
215#1598C2×C1314yescomplemented
216#1597C2×C1314yescomplemented
217#1505C2×C1311yescharacteristic, complemented
218#1500C2×C1311yescharacteristic, complemented
219#1470C2×C1311yescharacteristic, complemented
220C23×C13—21no—
221C23×C13—22no—
222C23×C13—44no—
223C23×C13—44no—
224C23×C13—42no—
225C23×C13—44no—
226C23×C13C22×D411yescharacteristic
227Q8×C13—41no—
228Q8×C13—81no—
229Q8×C13—82no—
230D4×C13—42no—
231D4×C13—41no—
232D4×C13—44no—
233D4×C13—42no—
234D4×C13—42no—
235D4×C13—44no—
236D4×C13—42no—
237D4×C13—42no—
238D4×C13—81no—
239D4×C13—82no—
240D4×C13—82no—
241D4×C13—82no—
242D4×C13—82no—
243D4×C13—82no—
244D4×C13—82no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—24no—
254C2×C4×C13—41no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—82no—
261C2×C4×C13—82no—
262C2×C4×C13—82no—
263C2×C4×C13—82no—
264C2×C4×C13#12011yescharacteristic
265C2×C4×C13#12011yescharacteristic
266C2×C4×C13#12011yescharacteristic
267C2×C4×C13#12011yescharacteristic
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C8×C13—42no—
271C8×C13—42no—
272#563—21no—
273#562—21no—
274#554—21no—
275#553—21no—
276#553—21no—
277#547—22no—
278#547—21no—
279#544—21no—
280#540—21no—
281#539—22no—
282#539C22×C1312yes—
283#537C22×C1312yes—
284#532C22×C1311yescharacteristic
285C2×#127C22×C1311yescharacteristic
286#529C22×C1311yescharacteristic
287C2×#125C22×C1311yescharacteristic
288#496—21no—
289#493—21no—
290#490—21no—
291#486—21no—
292#460—21no—
293#459—22no—
294#459—21no—
295#450C22×C1312yes—
296#447C22×C1314yes—
297#447C22×C1312yes—
298#432C22×C1311yescharacteristic
299#431C22×C1311yescharacteristic
300#394—22no—
301#394C22×C1314yes—
302#390—21no—
303#390—21no—
304#376C22×C1311yescharacteristic
305#328C22×C1312yes—
306#327C22×C1314yes—
307#327C22×C1312yes—
308#324C22×C1314yes—
309C22×C13—21no—
310C22×C13—21no—
311C22×C13—42no—
312C22×C13—41no—
313C22×C13—41no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—41no—
317C22×C13—88no—
318C22×C13—82no—
319C22×C13—82no—
320C22×C13—82no—
321C22×C13C2×#12011yescharacteristic
322C22×C13#57612yes—
323C4×C13—21no—
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—42no—
329C4×C13—42no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—42no—
333C4×C13—41no—
334C4×C13—82no—
335C4×C13#45412yes—
336C2×#41—21no—
337C2×#41—22no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4C23×C1312yes—
341C2×SD16—22no—
342C2×D8—24no—
343C2×D8—22no—
344C4⋊Q8—21no—
345C4⋊Q8—22no—
346C4⋊Q8D4×C1311yescharacteristic
347#127—21no—
348#127—21no—
349#127—21no—
350#127—21no—
351#127D4×C1311yescharacteristic
352#126—22no—
353#126—22no—
354#126—21no—
355#125—21no—
356#125—22no—
357#125—21no—
358#125—21no—
359#125—21no—
360#125—21no—
361#125D4×C1311yescharacteristic
362#124—21no—
363#124D4×C1311yescharacteristic
364#123—22no—
365#123—22no—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—21no—
370#123—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8C23×C1311yescharacteristic
378#121—21no—
379#121—22no—
380#121—21no—
381#121—22no—
382#121—22no—
383#121—21no—
384#121—22no—
385#121C23×C1311yescharacteristic
386#121C23×C1312yes—
387C4×Q8D4×C1311yescharacteristic
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4D4×C1311yescharacteristic
395C4×D4D4×C1312yes—
396#117—21no—
397#117—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4D4×C1311yescharacteristic
401C2×C4⋊C4D4×C1312yes—
402C2×C4⋊C4D4×C1311yescharacteristic
403C2×C4⋊C4C23×C1312yes—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C42—21no—
407C2×C42C23×C1311yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410#102—24no—
411#102—22no—
412#102—22no—
413C22⋊C8C23×C1312yes—
414C22⋊C8C23×C1312yes—
415#97—21no—
416C4×C8—21no—
417#95—21no—
418#95C23×C1312yes—
419C2×C13—22no—
420C2×C13—81no—
421C2×C13—82no—
422C2×C13—162no—
423C2×C13#300811yescharacteristic
424C2×C13C2×#45411yescharacteristic
425C2×C13#302711yescharacteristic
426C24—22no—
427#41—82no—
428#41—84no—
429C2×Q8—22no—
430C2×Q8—21no—
431C2×Q8C2×D4×C1311yescharacteristic
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—44no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—82no—
446C2×D4—82no—
447C2×D4C2×D4×C1311yescharacteristic
448C2×D4C2×D4×C1312yes—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4C2×D4×C1312yes—
456C22×C4C2×D4×C1311yescharacteristic
457C22×C4C2×D4×C1311yescharacteristic
458C22×C4C2×D4×C1312yes—
459C22×C4C24×C1311yescharacteristic
460SD16—82no—
461D8—84no—
462D8—82no—
463C2×C8—22no—
464C2×C8—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4C2×D4×C1312yes—
483C4⋊C4C2×D4×C1311yescharacteristic
484C4⋊C4C2×D4×C1311yescharacteristic
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—84no—
498C22⋊C4—84no—
499C42—22no—
500C42—21no—
501C42—42no—
502C42C2×D4×C1311yescharacteristic
503C42C2×D4×C1311yescharacteristic
504C42C2×D4×C1311yescharacteristic
505C42C2×D4×C1311yescharacteristic
506C13#1843011yescharacteristic, direct product factor, Sylow
507C23—21no—
508C23—22no—
509C23—44no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23C22×D4×C1311yescharacteristic
514Q8—41no—
515Q8—81no—
516Q8—82no—
517D4—42no—
518D4—41no—
519D4—44no—
520D4—42no—
521D4—42no—
522D4—44no—
523D4—42no—
524D4—42no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—82no—
531D4—82no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4C13×#12011yescharacteristic
552C2×C4C13×#12011yescharacteristic
553C2×C4C13×#12011yescharacteristic
554C2×C4C13×#12011yescharacteristic
555C2×C4C22×D4×C1311yescharacteristic
556C2×C4C22×D4×C1311yescharacteristic
557C8—42no—
558C8—42no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—88no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22C2×C13×#12011yescharacteristic
572C22C13×#57612yes—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—82no—
585C4C13×#45412yes—
586C2—22no—
587C2—81no—
588C2—82no—
589C2—162no—
590C2C13×#300811yescharacteristic
591C2C2×C13×#45411yescharacteristic
592C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
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×#3559C2semidirect
2. C13×#3217C2semidirect
3. C13×#3205C2semidirect
4. C13×#2641C2semidirect
5. C13×#1598C2semidirect
6. C13×#1597C2semidirect
7. C13×#1505C2semidirect
8. C13×#1500C2semidirect
9. C13×#1470C2semidirect
130. #18430C13direct (N × H)
211. #3559C2×C13semidirect
212. #3217C2×C13semidirect
213. #3205C2×C13semidirect
214. #2641C2×C13semidirect
215. #1598C2×C13semidirect
216. #1597C2×C13semidirect
217. #1505C2×C13semidirect
218. #1500C2×C13semidirect
219. #1470C2×C13semidirect
506. C13#18430direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#32172
C13×#32052
C13×#26412
C13×#15982
C13×#15972
C13×#15052
C13×#15002
C13×#14702
#1843013