Finite Group Databasebeta

← C13×#19032 #15705371

Subgroups — C13×#19032 #15705371

Order 3328.

896 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C13×#3165C211yesmaximal, characteristic, complemented
4C2×C13×#489C211yesmaximal, characteristic, complemented
5C13×#1664C214yesmaximal, complemented
6C13×#1661C214yesmaximal, complemented
7C13×#1531C211yesmaximal, characteristic, complemented
8C13×#1527C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C13×#563C2212yes—
11C13×#562C2212yes—
12C13×#556—21no—
13C13×#551—22no—
14D4×Q8×C13—21no—
15C13×#548—21no—
16C13×#546—21no—
17C13×#543—21no—
18C13×#542—21no—
19C13×#542—22no—
20C13×#538—21no—
21C13×#536—21no—
22C13×#533C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C13×#501C2214yescomplemented
27C13×#500—21no—
28C13×#498—21no—
29C13×#497C2212yescomplemented
30C13×#491C2212yescomplemented
31C13×#489—22no—
32C13×#489C2214yes—
33C13×#462—21no—
34C13×#461—21no—
35C13×#451—21no—
36C13×#448—21no—
37C13×#432C2211yescharacteristic
38C13×#428—22no—
39C2×C13×#103—21no—
40C2×C13×#102—21no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yescomplemented
44C13×#330C2214yescomplemented
45C13×#329C2214yes—
46C13×#329C2212yescomplemented
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13D411yescharacteristic
52C2×C13×Q16—22no—
53C2×C13×SD16—22no—
54C2×C13×M16—21no—
55C22×C8×C13—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—22no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8D411yescharacteristic
62C13×C4⋊Q8D411yescharacteristic
63C13×C4⋊Q8C2312yes—
64C13×#126—22no—
65C13×#126—22no—
66C13×#126—22no—
67C13×#126—21no—
68C13×#125C2311yescharacteristic
69C13×#125C2312yes—
70C13×#124—21no—
71C13×#124—22no—
72C13×#124—22no—
73C13×#124—21no—
74C13×#124—21no—
75C13×#124D412yes—
76C13×#124C2312yes—
77C13×#124C2311yescharacteristic
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—21no—
81C13×#123—22no—
82C13×#123—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8D411yescharacteristic
94C13×#121—21no—
95C13×#121—22no—
96C13×#121—22no—
97C13×#121D411yescharacteristic
98C13×#120—22no—
99C4×Q8×C13—21no—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×Q8×C13D411yescharacteristic
103C4×D4×C13—22no—
104C4×D4×C13—21no—
105C4×D4×C13—22no—
106C4×D4×C13—21no—
107C4×D4×C13D411yescharacteristic
108C13×#117—22no—
109C13×#117—21no—
110C13×#117D412yes—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C42×C13C2311yescharacteristic
117C13×#107—24no—
118C13×#106—24no—
119C13×C4⋊C8—21no—
120C13×#103—24no—
121C13×#103—22no—
122C13×#103—22no—
123C13×#102—24no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19032C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—21no—
132C13×#41—82no—
133C2×Q8×C13—22no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—22no—
138C2×Q8×C13—42no—
139C2×Q8×C13—41no—
140C2×Q8×C13—82no—
141C2×Q8×C13—82no—
142C2×Q8×C13C2×D412yes—
143C2×Q8×C13C2×D411yescharacteristic
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—42no—
149C2×D4×C13C2×D412yes—
150C2×D4×C13C2×D411yescharacteristic
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—41no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C13×Q16—82no—
161C13×SD16—82no—
162C13×M16—24no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C2×C8×C13—42no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4C2×D411yescharacteristic
184C13×C4⋊C4C2×D411yescharacteristic
185C13×C4⋊C4C2×D412yes—
186C13×C4⋊C4C2×D412yes—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—21no—
201C13×C22⋊C4—21no—
202C42×C13—22no—
203C42×C13—22no—
204C42×C13—21no—
205C42×C13C2×D411yescharacteristic
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208C42×C13C2411yescharacteristic
209#3561C2×C1311yescharacteristic
210#3218C2×C1311yescharacteristic, complemented
211#3165C2×C1311yescharacteristic, complemented
212C2×#489C2×C1311yescharacteristic, complemented
213#1664C2×C1314yescomplemented
214#1661C2×C1314yescomplemented
215#1531C2×C1311yescharacteristic, complemented
216#1527C2×C1311yescharacteristic, complemented
217#1524C2×C1311yescharacteristic, complemented
218C23×C13—22no—
219C23×C13—21no—
220C23×C13—42no—
221C23×C13—81no—
222C23×C13—81no—
223C23×C13#12011yescharacteristic
224Q8×C13—41no—
225Q8×C13—42no—
226Q8×C13—42no—
227Q8×C13—42no—
228Q8×C13—42no—
229Q8×C13—42no—
230Q8×C13—81no—
231Q8×C13—82no—
232Q8×C13—82no—
233D4×C13—41no—
234D4×C13—42no—
235D4×C13—42no—
236D4×C13—42no—
237D4×C13—82no—
238D4×C13—82no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—81no—
251C2×C4×C13—82no—
252C2×C4×C13—82no—
253C2×C4×C13—82no—
254C2×C4×C13—82no—
255C2×C4×C13#12011yescharacteristic
256C2×C4×C13#12011yescharacteristic
257C2×C4×C13#12011yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C8×C13—24no—
262C8×C13—42no—
263C8×C13—42no—
264#563C22×C1312yes—
265#562C22×C1312yes—
266#556—21no—
267#551—22no—
268D4×Q8—21no—
269#548—21no—
270#546—21no—
271#543—21no—
272#542—21no—
273#542—22no—
274#538—21no—
275#536—21no—
276#533C22×C1311yescharacteristic
277C2×C4⋊Q8C22×C1311yescharacteristic
278#529C22×C1311yescharacteristic
279C2×#124C22×C1311yescharacteristic
280#501C22×C1314yescomplemented
281#500—21no—
282#498—21no—
283#497C22×C1312yescomplemented
284#491C22×C1312yescomplemented
285#489—22no—
286#489C22×C1314yes—
287#462—21no—
288#461—21no—
289#451—21no—
290#448—21no—
291#432C22×C1311yescharacteristic
292#428—22no—
293C2×#103—21no—
294C2×#102—21no—
295C4×M16C22×C1311yescharacteristic
296C2×#97C22×C1311yescharacteristic
297#330C22×C1314yescomplemented
298#330C22×C1312yescomplemented
299#329C22×C1314yes—
300#329C22×C1312yescomplemented
301C22×C13—21no—
302C22×C13—21no—
303C22×C13—41no—
304C22×C13—42no—
305C22×C13—41no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13—41no—
309C22×C13—162no—
310C22×C13#45612yes—
311C22×C13C2×#12011yescharacteristic
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—21no—
315C4×C13—21no—
316C4×C13—21no—
317C4×C13—41no—
318C4×C13—42no—
319C4×C13—42no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—42no—
323C4×C13—82no—
324C4×C13#45512yes—
325C2×#41—21no—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8D4×C1311yescharacteristic
329C22×D4D4×C1311yescharacteristic
330C2×Q16—22no—
331C2×SD16—22no—
332C2×M16—21no—
333C22×C8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—22no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8D4×C1311yescharacteristic
340C4⋊Q8D4×C1311yescharacteristic
341C4⋊Q8C23×C1312yes—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—21no—
346#125C23×C1311yescharacteristic
347#125C23×C1312yes—
348#124—21no—
349#124—22no—
350#124—22no—
351#124—21no—
352#124—21no—
353#124D4×C1312yes—
354#124C23×C1312yes—
355#124C23×C1311yescharacteristic
356#123—22no—
357#123—22no—
358#123—21no—
359#123—22no—
360#123—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8D4×C1311yescharacteristic
372#121—21no—
373#121—22no—
374#121—22no—
375#121D4×C1311yescharacteristic
376#120—22no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C1311yescharacteristic
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4D4×C1311yescharacteristic
386#117—22no—
387#117—21no—
388#117D4×C1312yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42C23×C1311yescharacteristic
395#107—24no—
396#106—24no—
397C4⋊C8—21no—
398#103—24no—
399#103—22no—
400#103—22no—
401#102—24no—
402C22⋊C8—21no—
403#97—21no—
404#97C23×C1312yes—
405#97C23×C1312yes—
406#97C23×C1312yes—
407C4×C8—21no—
408C2×C13—22no—
409C2×C13—81no—
410C2×C13—82no—
411C2×C13C2×#45511yescharacteristic
412C2×C13C2×#45611yescharacteristic
413C2×C13#302111yescharacteristic
414C24—21no—
415#41—82no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—42no—
422C2×Q8—41no—
423C2×Q8—82no—
424C2×Q8—82no—
425C2×Q8C2×D4×C1312yes—
426C2×Q8C2×D4×C1311yescharacteristic
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—42no—
432C2×D4C2×D4×C1312yes—
433C2×D4C2×D4×C1311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—41no—
440C22×C4C2×D4×C1311yescharacteristic
441C22×C4C2×D4×C1311yescharacteristic
442C22×C4C2×D4×C1311yescharacteristic
443Q16—82no—
444SD16—82no—
445M16—24no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—42no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×D4×C1311yescharacteristic
467C4⋊C4C2×D4×C1311yescharacteristic
468C4⋊C4C2×D4×C1312yes—
469C4⋊C4C2×D4×C1312yes—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C42—22no—
486C42—22no—
487C42—21no—
488C42C2×D4×C1311yescharacteristic
489C42C2×D4×C1311yescharacteristic
490C42C2×D4×C1311yescharacteristic
491C42C24×C1311yescharacteristic
492C13#1903211yescharacteristic, direct product factor, Sylow
493C23—22no—
494C23—21no—
495C23—42no—
496C23—81no—
497C23—81no—
498C23C13×#12011yescharacteristic
499Q8—41no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504Q8—42no—
505Q8—81no—
506Q8—82no—
507Q8—82no—
508D4—41no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—82no—
513D4—82no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4C13×#12011yescharacteristic
531C2×C4C13×#12011yescharacteristic
532C2×C4C13×#12011yescharacteristic
533C2×C4C22×D4×C1311yescharacteristic
534C2×C4C22×D4×C1311yescharacteristic
535C2×C4C22×D4×C1311yescharacteristic
536C8—24no—
537C8—42no—
538C8—42no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22—42no—
545C22—42no—
546C22—41no—
547C22—162no—
548C22C13×#45612yes—
549C22C2×C13×#12011yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—82no—
562C4C13×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C2×C13×#45511yescharacteristic
567C2C2×C13×#45611yescharacteristic
568C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3561C2
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×#3218C2semidirect
3. C13×#3165C2semidirect
4. C2×C13×#489C2semidirect
5. C13×#1664C2semidirect
6. C13×#1661C2semidirect
7. C13×#1531C2semidirect
8. C13×#1527C2semidirect
9. C13×#1524C2semidirect
26. C13×#501C22semidirect
29. C13×#497C22semidirect
30. C13×#491C22semidirect
43. C13×#330C22semidirect
44. C13×#330C22semidirect
46. C13×#329C22semidirect
130. #19032C13direct (N × H)
210. #3218C2×C13semidirect
211. #3165C2×C13semidirect
212. C2×#489C2×C13semidirect
213. #1664C2×C13semidirect
214. #1661C2×C13semidirect
215. #1531C2×C13semidirect
216. #1527C2×C13semidirect
217. #1524C2×C13semidirect
280. #501C22×C13semidirect
283. #497C22×C13semidirect
284. #491C22×C13semidirect
297. #330C22×C13semidirect
298. #330C22×C13semidirect
300. #329C22×C13semidirect
492. C13#19032direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35612
C13×#32182
C13×#31652
C2×C13×#4892
C13×#16642
C13×#16612
C13×#15312
C13×#15272
C13×#15242
#1903213