Finite Group Databasebeta

← C13×#18432 #15704771

Subgroups — C13×#18432 #15704771

Order 3328.

940 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic
3C13×#3208C211yesmaximal, characteristic, complemented
4C13×#2641C211yesmaximal, characteristic, complemented
5C13×#1599C214yesmaximal, complemented
6C13×#1597C214yesmaximal, complemented
7C13×#1506C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1470C211yesmaximal, characteristic, complemented
10C13×#564—21no—
11C13×#563—21no—
12C13×#557—21no—
13C13×#554—21no—
14C13×#552—21no—
15C13×#552—21no—
16C13×#552—22no—
17C13×#544—21no—
18C13×#544C2212yes—
19C13×#541—21no—
20C13×#541—22no—
21C13×#539C2212yes—
22C13×#533C2211yescharacteristic
23C2×C13×#127C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#496—21no—
27C13×#492—21no—
28C13×#490—21no—
29C13×#486—21no—
30C13×#460—22no—
31C13×#460—21no—
32C13×#459—21no—
33C13×#450C2214yes—
34C13×#450C2212yes—
35C13×#447C2212yes—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#394—22no—
39C13×#394C2214yes—
40C13×#390—21no—
41C13×#390—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#324C2214yes—
47C22×D4×C13—21no—
48C22×D4×C13—21no—
49C22×D4×C13C2312yes—
50C2×C13×SD16—24no—
51C2×C13×SD16—22no—
52C2×C13×D8—22no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—22no—
56C13×C4⋊Q8D411yescharacteristic
57C13×C4⋊Q8D411yescharacteristic
58C13×#127—21no—
59C13×#127—21no—
60C13×#127—21no—
61C13×#127—21no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—22no—
66C13×#126—21no—
67C13×#125—22no—
68C13×#125—22no—
69C13×#125—22no—
70C13×#125—22no—
71C13×#125—21no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#125—22no—
76C13×#125—21no—
77C13×#125—21no—
78C13×#125—21no—
79C13×#125—21no—
80C13×#125—21no—
81C13×#125D411yescharacteristic
82C13×#124D411yescharacteristic
83C13×#123—22no—
84C13×#123—21no—
85C13×#123—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8C2311yescharacteristic
94C13×C22⋊Q8C2312yes—
95C13×#121C2311yescharacteristic
96C4×Q8×C13—21no—
97C4×Q8×C13—22no—
98C4×Q8×C13—21no—
99C4×Q8×C13—21no—
100C4×Q8×C13D411yescharacteristic
101C4×Q8×C13D412yes—
102C4×D4×C13—21no—
103C4×D4×C13—22no—
104C4×D4×C13D411yescharacteristic
105C13×#117—22no—
106C13×#117—21no—
107C13×#117—21no—
108C13×#117—22no—
109C13×#117—21no—
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—22no—
122C13×#102—22no—
123C13×#102—24no—
124C13×C22⋊C8C2312yes—
125C13×C22⋊C8C2312yes—
126C13×#97—21no—
127C4×C8×C13—21no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18432C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—22no—
132C2×Q8×C13—22no—
133C2×Q8×C13—21no—
134C2×Q8×C13C2×D412yes—
135C2×Q8×C13C2×D411yescharacteristic
136C2×D4×C13—21no—
137C2×D4×C13—22no—
138C2×D4×C13—22no—
139C2×D4×C13—44no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13—41no—
143C2×D4×C13—41no—
144C2×D4×C13—82no—
145C2×D4×C13—82no—
146C2×D4×C13C2×D411yescharacteristic
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2411yescharacteristic
155C13×SD16—82no—
156C13×SD16—84no—
157C13×D8—82no—
158C2×C8×C13—22no—
159C2×C8×C13—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4C2×D411yescharacteristic
186C13×C4⋊C4C2×D411yescharacteristic
187C13×C4⋊C4C2×D412yes—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—84no—
198C13×C22⋊C4—84no—
199C42×C13—22no—
200C42×C13—22no—
201C42×C13—22no—
202C42×C13—22no—
203C42×C13—21no—
204C42×C13—42no—
205C42×C13C2×D411yescharacteristic
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208C42×C13C2×D411yescharacteristic
209#3563C2×C1311yescharacteristic, complemented
210#3217C2×C1311yescharacteristic
211#3208C2×C1311yescharacteristic, complemented
212#2641C2×C1311yescharacteristic, complemented
213#1599C2×C1314yescomplemented
214#1597C2×C1314yescomplemented
215#1506C2×C1311yescharacteristic, complemented
216#1500C2×C1311yescharacteristic, complemented
217#1470C2×C1311yescharacteristic, complemented
218C23×C13—21no—
219C23×C13—44no—
220C23×C13—44no—
221C23×C13—42no—
222C23×C13—44no—
223C23×C13C22×D411yescharacteristic
224Q8×C13—41no—
225Q8×C13—42no—
226Q8×C13—42no—
227Q8×C13—82no—
228D4×C13—41no—
229D4×C13—42no—
230D4×C13—42no—
231D4×C13—44no—
232D4×C13—42no—
233D4×C13—82no—
234D4×C13—82no—
235D4×C13—82no—
236D4×C13—82no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—82no—
254C2×C4×C13#12011yescharacteristic
255C2×C4×C13#12011yescharacteristic
256C2×C4×C13#12011yescharacteristic
257C2×C4×C13#12011yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C8×C13—42no—
261C8×C13—42no—
262#564—21no—
263#563—21no—
264#557—21no—
265#554—21no—
266#552—21no—
267#552—21no—
268#552—22no—
269#544—21no—
270#544C22×C1312yes—
271#541—21no—
272#541—22no—
273#539C22×C1312yes—
274#533C22×C1311yescharacteristic
275C2×#127C22×C1311yescharacteristic
276#529C22×C1311yescharacteristic
277C2×#125C22×C1311yescharacteristic
278#496—21no—
279#492—21no—
280#490—21no—
281#486—21no—
282#460—22no—
283#460—21no—
284#459—21no—
285#450C22×C1314yes—
286#450C22×C1312yes—
287#447C22×C1312yes—
288#432C22×C1311yescharacteristic
289#431C22×C1311yescharacteristic
290#394—22no—
291#394C22×C1314yes—
292#390—21no—
293#390—21no—
294#376C22×C1311yescharacteristic
295#328C22×C1314yes—
296#328C22×C1312yes—
297#327C22×C1312yes—
298#324C22×C1314yes—
299C22×C13—21no—
300C22×C13—21no—
301C22×C13—41no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—88no—
305C22×C13—82no—
306C22×C13—82no—
307C22×C13—82no—
308C22×C13C2×#12011yescharacteristic
309C22×C13#57712yes—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—21no—
315C4×C13—42no—
316C4×C13—41no—
317C4×C13—41no—
318C4×C13—42no—
319C4×C13—42no—
320C4×C13—42no—
321C4×C13—41no—
322C4×C13—82no—
323C4×C13#45412yes—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C23×C1312yes—
327C2×SD16—24no—
328C2×SD16—22no—
329C2×D8—22no—
330C4⋊Q8—21no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8D4×C1311yescharacteristic
334C4⋊Q8D4×C1311yescharacteristic
335#127—21no—
336#127—21no—
337#127—21no—
338#127—21no—
339#126—22no—
340#126—22no—
341#126—22no—
342#126—22no—
343#126—21no—
344#125—22no—
345#125—22no—
346#125—22no—
347#125—22no—
348#125—21no—
349#125—22no—
350#125—22no—
351#125—22no—
352#125—22no—
353#125—21no—
354#125—21no—
355#125—21no—
356#125—21no—
357#125—21no—
358#125D4×C1311yescharacteristic
359#124D4×C1311yescharacteristic
360#123—22no—
361#123—21no—
362#123—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8C23×C1311yescharacteristic
371C22⋊Q8C23×C1312yes—
372#121C23×C1311yescharacteristic
373C4×Q8—21no—
374C4×Q8—22no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8D4×C1311yescharacteristic
378C4×Q8D4×C1312yes—
379C4×D4—21no—
380C4×D4—22no—
381C4×D4D4×C1311yescharacteristic
382#117—22no—
383#117—21no—
384#117—21no—
385#117—22no—
386#117—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4D4×C1311yescharacteristic
389C2×C4⋊C4D4×C1312yes—
390C2×C4⋊C4D4×C1311yescharacteristic
391C2×C4⋊C4C23×C1312yes—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C42—21no—
395C2×C42C23×C1311yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398#102—22no—
399#102—22no—
400#102—24no—
401C22⋊C8C23×C1312yes—
402C22⋊C8C23×C1312yes—
403#97—21no—
404C4×C8—21no—
405#95—21no—
406#95C23×C1312yes—
407C2×C13—22no—
408C2×C13—81no—
409C2×C13—162no—
410C2×C13#301011yescharacteristic
411C2×C13C2×#45411yescharacteristic
412C2×C13#302711yescharacteristic
413C24—22no—
414C2×Q8—22no—
415C2×Q8—21no—
416C2×Q8C2×D4×C1312yes—
417C2×Q8C2×D4×C1311yescharacteristic
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—44no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—82no—
427C2×D4—82no—
428C2×D4C2×D4×C1311yescharacteristic
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4C2×D4×C1312yes—
433C22×C4C2×D4×C1311yescharacteristic
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1312yes—
436C22×C4C24×C1311yescharacteristic
437SD16—82no—
438SD16—84no—
439D8—82no—
440C2×C8—22no—
441C2×C8—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4C2×D4×C1311yescharacteristic
468C4⋊C4C2×D4×C1311yescharacteristic
469C4⋊C4C2×D4×C1312yes—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—84no—
480C22⋊C4—84no—
481C42—22no—
482C42—22no—
483C42—22no—
484C42—22no—
485C42—21no—
486C42—42no—
487C42C2×D4×C1311yescharacteristic
488C42C2×D4×C1311yescharacteristic
489C42C2×D4×C1311yescharacteristic
490C42C2×D4×C1311yescharacteristic
491C13#1843211yescharacteristic, direct product factor, Sylow
492C23—21no—
493C23—44no—
494C23—44no—
495C23—42no—
496C23—44no—
497C23C22×D4×C1311yescharacteristic
498Q8—41no—
499Q8—42no—
500Q8—42no—
501Q8—82no—
502D4—41no—
503D4—42no—
504D4—42no—
505D4—44no—
506D4—42no—
507D4—82no—
508D4—82no—
509D4—82no—
510D4—82no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—82no—
528C2×C4C13×#12011yescharacteristic
529C2×C4C13×#12011yescharacteristic
530C2×C4C13×#12011yescharacteristic
531C2×C4C13×#12011yescharacteristic
532C2×C4C22×D4×C1311yescharacteristic
533C2×C4C22×D4×C1311yescharacteristic
534C8—42no—
535C8—42no—
536C22—21no—
537C22—21no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—88no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22C2×C13×#12011yescharacteristic
546C22C13×#57712yes—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—41no—
554C4—41no—
555C4—42no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—82no—
560C4C13×#45412yes—
561C2—22no—
562C2—81no—
563C2—162no—
564C2C13×#301011yescharacteristic
565C2C2×C13×#45411yescharacteristic
566C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3217C2
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×#3563C2semidirect
3. C13×#3208C2semidirect
4. C13×#2641C2semidirect
5. C13×#1599C2semidirect
6. C13×#1597C2semidirect
7. C13×#1506C2semidirect
8. C13×#1500C2semidirect
9. C13×#1470C2semidirect
130. #18432C13direct (N × H)
209. #3563C2×C13semidirect
211. #3208C2×C13semidirect
212. #2641C2×C13semidirect
213. #1599C2×C13semidirect
214. #1597C2×C13semidirect
215. #1506C2×C13semidirect
216. #1500C2×C13semidirect
217. #1470C2×C13semidirect
491. C13#18432direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#32172
C13×#32082
C13×#26412
C13×#15992
C13×#15972
C13×#15062
C13×#15002
C13×#14702
#1843213