Finite Group Databasebeta

← C13×#19027 #15705366

Subgroups — C13×#19027 #15705366

Order 3328.

884 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic, complemented
3C13×#3139C211yesmaximal, characteristic, complemented
4C2×C13×#489C211yesmaximal, characteristic, complemented
5C13×#1664C214yesmaximal, complemented
6C13×#1662C214yesmaximal, 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×#501C2212yescomplemented
27C13×#491C2214yescomplemented
28C13×#489—22no—
29C13×#489C2214yes—
30C13×#489C2212yescomplemented
31C13×#487—21no—
32C13×#487—21no—
33C13×#483—21no—
34C13×#480—21no—
35C13×#477—21no—
36C13×#476—21no—
37C13×#432C2211yescharacteristic
38C13×#419—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×M16—21no—
53C22×C8×C13—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—22no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8D411yescharacteristic
60C13×C4⋊Q8D411yescharacteristic
61C13×C4⋊Q8C2312yes—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—21no—
66C13×#125C2312yes—
67C13×#125C2311yescharacteristic
68C13×#124—21no—
69C13×#124—22no—
70C13×#124—22no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124D412yes—
74C13×#124C2312yes—
75C13×#124C2311yescharacteristic
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—21no—
79C13×#123—22no—
80C13×#123—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8D411yescharacteristic
92C13×#121—21no—
93C13×#121—22no—
94C13×#121—22no—
95C13×#121D411yescharacteristic
96C13×#120—22no—
97C4×Q8×C13—21no—
98C4×Q8×C13—21no—
99C4×Q8×C13—21no—
100C4×Q8×C13D411yescharacteristic
101C4×D4×C13—22no—
102C4×D4×C13—21no—
103C4×D4×C13—22no—
104C4×D4×C13—21no—
105C4×D4×C13D411yescharacteristic
106C13×#117—22no—
107C13×#117—21no—
108C13×#117D412yes—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C42×C13C2311yescharacteristic
115C13×#107—22no—
116C13×#106—22no—
117C13×C4⋊C8—21no—
118C13×#103—24no—
119C13×#103—22no—
120C13×#103—24no—
121C13×#103—24no—
122C13×#102—24no—
123C13×#102—22no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19027C1311yesmaximal, 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—44no—
140C2×Q8×C13—41no—
141C2×Q8×C13—82no—
142C2×Q8×C13C2×D411yescharacteristic
143C2×Q8×C13C2×D412yes—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—42no—
149C2×D4×C13C2×D411yescharacteristic
150C2×D4×C13C2×D412yes—
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×M16—42no—
161C2×C8×C13—22no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13—42no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4C2×D412yes—
182C13×C4⋊C4C2×D412yes—
183C13×C4⋊C4C2×D411yescharacteristic
184C13×C4⋊C4C2×D411yescharacteristic
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—21no—
200C42×C13—22no—
201C42×C13—22no—
202C42×C13—21no—
203C42×C13C2×D411yescharacteristic
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206C42×C13C2411yescharacteristic
207#3561C2×C1311yescharacteristic
208#3238C2×C1311yescharacteristic, complemented
209#3139C2×C1311yescharacteristic, complemented
210C2×#489C2×C1311yescharacteristic, complemented
211#1664C2×C1314yescomplemented
212#1662C2×C1314yescomplemented
213#1531C2×C1311yescharacteristic, complemented
214#1527C2×C1311yescharacteristic, complemented
215#1524C2×C1311yescharacteristic, complemented
216C23×C13—22no—
217C23×C13—21no—
218C23×C13—42no—
219C23×C13—81no—
220C23×C13—81no—
221C23×C13#12011yescharacteristic
222Q8×C13—42no—
223Q8×C13—41no—
224Q8×C13—44no—
225Q8×C13—42no—
226Q8×C13—42no—
227Q8×C13—81no—
228Q8×C13—82no—
229Q8×C13—82no—
230D4×C13—42no—
231D4×C13—41no—
232D4×C13—42no—
233D4×C13—42no—
234D4×C13—82no—
235D4×C13—82no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—41no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—81no—
248C2×C4×C13—82no—
249C2×C4×C13—82no—
250C2×C4×C13—82no—
251C2×C4×C13—82no—
252C2×C4×C13#12011yescharacteristic
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13#12011yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C8×C13—42no—
259C8×C13—42no—
260C8×C13—42no—
261#563C22×C1312yes—
262#562C22×C1312yes—
263#556—21no—
264#551—22no—
265D4×Q8—21no—
266#548—21no—
267#546—21no—
268#543—21no—
269#542—21no—
270#542—22no—
271#538—21no—
272#536—21no—
273#533C22×C1311yescharacteristic
274C2×C4⋊Q8C22×C1311yescharacteristic
275#529C22×C1311yescharacteristic
276C2×#124C22×C1311yescharacteristic
277#501C22×C1312yescomplemented
278#491C22×C1314yescomplemented
279#489—22no—
280#489C22×C1314yes—
281#489C22×C1312yescomplemented
282#487—21no—
283#487—21no—
284#483—21no—
285#480—21no—
286#477—21no—
287#476—21no—
288#432C22×C1311yescharacteristic
289#419—22no—
290C2×#103—21no—
291C2×#102—21no—
292C4×M16C22×C1311yescharacteristic
293C2×#97C22×C1311yescharacteristic
294#330C22×C1314yescomplemented
295#330C22×C1312yescomplemented
296#329C22×C1314yes—
297#329C22×C1312yescomplemented
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—41no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—41no—
306C22×C13—162no—
307C22×C13#45412yes—
308C22×C13C2×#12011yescharacteristic
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—41no—
315C4×C13—42no—
316C4×C13—42no—
317C4×C13—41no—
318C4×C13—41no—
319C4×C13—42no—
320C4×C13—82no—
321C4×C13#45512yes—
322C2×#41—21no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8D4×C1311yescharacteristic
326C22×D4D4×C1311yescharacteristic
327C2×M16—21no—
328C22×C8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—22no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8D4×C1311yescharacteristic
335C4⋊Q8D4×C1311yescharacteristic
336C4⋊Q8C23×C1312yes—
337#126—22no—
338#126—22no—
339#126—22no—
340#126—21no—
341#125C23×C1311yescharacteristic
342#125C23×C1312yes—
343#124—21no—
344#124—22no—
345#124—22no—
346#124—21no—
347#124—21no—
348#124D4×C1312yes—
349#124C23×C1312yes—
350#124C23×C1311yescharacteristic
351#123—22no—
352#123—22no—
353#123—21no—
354#123—22no—
355#123—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8D4×C1311yescharacteristic
367#121—21no—
368#121—22no—
369#121—22no—
370#121D4×C1311yescharacteristic
371#120—22no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8D4×C1311yescharacteristic
376C4×D4—22no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4D4×C1311yescharacteristic
381#117—22no—
382#117—21no—
383#117D4×C1312yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42C23×C1311yescharacteristic
390#107—22no—
391#106—22no—
392C4⋊C8—21no—
393#103—24no—
394#103—22no—
395#103—24no—
396#103—24no—
397#102—24no—
398#102—22no—
399C22⋊C8—21no—
400#97—21no—
401#97C23×C1312yes—
402#97C23×C1312yes—
403#97C23×C1312yes—
404C4×C8—21no—
405C2×C13—22no—
406C2×C13—81no—
407C2×C13—82no—
408C2×C13C2×#45511yescharacteristic
409C2×C13C2×#45411yescharacteristic
410C2×C13#302211yescharacteristic
411C24—21no—
412#41—82no—
413C2×Q8—22no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—42no—
419C2×Q8—44no—
420C2×Q8—41no—
421C2×Q8—82no—
422C2×Q8C2×D4×C1311yescharacteristic
423C2×Q8C2×D4×C1312yes—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—42no—
429C2×D4C2×D4×C1311yescharacteristic
430C2×D4C2×D4×C1312yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—41no—
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1311yescharacteristic
439C22×C4C2×D4×C1311yescharacteristic
440M16—42no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—42no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C1312yes—
462C4⋊C4C2×D4×C1312yes—
463C4⋊C4C2×D4×C1311yescharacteristic
464C4⋊C4C2×D4×C1311yescharacteristic
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C42—22no—
481C42—22no—
482C42—21no—
483C42C2×D4×C1311yescharacteristic
484C42C2×D4×C1311yescharacteristic
485C42C2×D4×C1311yescharacteristic
486C42C24×C1311yescharacteristic
487C13#1902711yescharacteristic, direct product factor, Sylow
488C23—22no—
489C23—21no—
490C23—42no—
491C23—81no—
492C23—81no—
493C23C13×#12011yescharacteristic
494Q8—42no—
495Q8—41no—
496Q8—44no—
497Q8—42no—
498Q8—42no—
499Q8—81no—
500Q8—82no—
501Q8—82no—
502D4—42no—
503D4—41no—
504D4—42no—
505D4—42no—
506D4—82no—
507D4—82no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—81no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4C13×#12011yescharacteristic
525C2×C4C13×#12011yescharacteristic
526C2×C4C13×#12011yescharacteristic
527C2×C4C22×D4×C1311yescharacteristic
528C2×C4C22×D4×C1311yescharacteristic
529C2×C4C22×D4×C1311yescharacteristic
530C8—42no—
531C8—42no—
532C8—42no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—42no—
537C22—41no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—162no—
542C22C13×#45412yes—
543C22C2×C13×#12011yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—42no—
551C4—42no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—82no—
556C4C13×#45512yes—
557C2—22no—
558C2—82no—
559C2—81no—
560C2C2×C13×#45511yescharacteristic
561C2C2×C13×#45411yescharacteristic
562C2C13×#302211yescharacteristic
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×#3238C2semidirect
3. C13×#3139C2semidirect
4. C2×C13×#489C2semidirect
5. C13×#1664C2semidirect
6. C13×#1662C2semidirect
7. C13×#1531C2semidirect
8. C13×#1527C2semidirect
9. C13×#1524C2semidirect
26. C13×#501C22semidirect
27. C13×#491C22semidirect
30. C13×#489C22semidirect
43. C13×#330C22semidirect
44. C13×#330C22semidirect
46. C13×#329C22semidirect
130. #19027C13direct (N × H)
208. #3238C2×C13semidirect
209. #3139C2×C13semidirect
210. C2×#489C2×C13semidirect
211. #1664C2×C13semidirect
212. #1662C2×C13semidirect
213. #1531C2×C13semidirect
214. #1527C2×C13semidirect
215. #1524C2×C13semidirect
277. #501C22×C13semidirect
278. #491C22×C13semidirect
281. #489C22×C13semidirect
294. #330C22×C13semidirect
295. #330C22×C13semidirect
297. #329C22×C13semidirect
487. C13#19027direct (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×#32382
C13×#31392
C2×C13×#4892
C13×#16642
C13×#16622
C13×#15312
C13×#15272
C13×#15242
#1902713