Finite Group Databasebeta

← C13×#18433 #15704772

Subgroups — C13×#18433 #15704772

Order 3328.

872 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic
3C13×#3209C211yesmaximal, characteristic, complemented
4C13×#2660C211yesmaximal, characteristic, complemented
5C13×#1605C214yesmaximal, complemented
6C13×#1603C214yesmaximal
7C13×#1506C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic
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×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#497—21no—
27C13×#494—21no—
28C13×#491—21no—
29C13×#487—21no—
30C13×#462—22no—
31C13×#462—21no—
32C13×#461—21no—
33C13×#451C2214yes—
34C13×#451C2212yes—
35C13×#448C2212yes—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#398—22no—
39C13×#395C2214yes—
40C13×#384—21no—
41C13×#382—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#324C2214yes—
47C22×Q8×C13C2312yes—
48C2×C13×Q16—24no—
49C2×C13×Q16—22no—
50C2×C13×SD16—22no—
51C13×C4⋊Q8—21no—
52C13×C4⋊Q8—22no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8D411yescharacteristic
59C13×C4⋊Q8D411yescharacteristic
60C13×#126—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—21no—
65C13×#125—22no—
66C13×#125—22no—
67C13×#125—22no—
68C13×#125—22no—
69C13×#125—21no—
70C13×#125—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—21no—
76C13×#125—21no—
77C13×#125—21no—
78C13×#125—21no—
79C13×#125D411yescharacteristic
80C13×#124D411yescharacteristic
81C13×#123—22no—
82C13×#123—21no—
83C13×#123—22no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8C2311yescharacteristic
92C13×C22⋊Q8C2312yes—
93C13×#121C2311yescharacteristic
94C4×Q8×C13—21no—
95C4×Q8×C13—22no—
96C4×Q8×C13—21no—
97C4×Q8×C13—21no—
98C4×Q8×C13D411yescharacteristic
99C4×Q8×C13D412yes—
100C4×D4×C13—21no—
101C4×D4×C13—22no—
102C4×D4×C13D411yescharacteristic
103C13×#117—22no—
104C13×#117—21no—
105C13×#117—21no—
106C13×#117—22no—
107C13×#117—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4D412yes—
115C2×C13×C4⋊C4C2312yes—
116C2×C42×C13—21no—
117C2×C42×C13C2311yescharacteristic
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—22no—
121C13×#103—22no—
122C13×#103—24no—
123C13×C22⋊C8C2312yes—
124C13×C22⋊C8C2312yes—
125C13×#97—21no—
126C4×C8×C13—21no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18433C1311yesmaximal, characteristic, direct product factor, Sylow
131C2×Q8×C13—22no—
132C2×Q8×C13—21no—
133C2×Q8×C13—22no—
134C2×Q8×C13—22no—
135C2×Q8×C13—82no—
136C2×Q8×C13C2×D412yes—
137C2×Q8×C13C2×D411yescharacteristic
138C2×D4×C13—21no—
139C2×D4×C13C2×D411yescharacteristic
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2411yescharacteristic
149C13×Q16—82no—
150C13×Q16—84no—
151C13×SD16—82no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—84no—
184C13×C4⋊C4C2×D411yescharacteristic
185C13×C4⋊C4C2×D411yescharacteristic
186C13×C4⋊C4C2×D412yes—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—21no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C42×C13—24no—
197C42×C13—22no—
198C42×C13—22no—
199C42×C13—22no—
200C42×C13—22no—
201C42×C13—21no—
202C42×C13C2×D411yescharacteristic
203C42×C13C2×D411yescharacteristic
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206#3563C2×C1311yescharacteristic
207#3218C2×C1311yescharacteristic
208#3209C2×C1311yescharacteristic, complemented
209#2660C2×C1311yescharacteristic, complemented
210#1605C2×C1314yescomplemented
211#1603C2×C1314yes—
212#1506C2×C1311yescharacteristic, complemented
213#1500C2×C1311yescharacteristic
214#1470C2×C1311yescharacteristic, complemented
215C23×C13—21no—
216C23×C13C22×D411yescharacteristic
217Q8×C13—41no—
218Q8×C13—42no—
219Q8×C13—42no—
220Q8×C13—42no—
221Q8×C13—44no—
222Q8×C13—42no—
223Q8×C13—82no—
224D4×C13—41no—
225D4×C13—42no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—22no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—41no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—44no—
243C2×C4×C13—42no—
244C2×C4×C13—82no—
245C2×C4×C13#12011yescharacteristic
246C2×C4×C13#12011yescharacteristic
247C2×C4×C13#12011yescharacteristic
248C2×C4×C13#12011yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×D411yescharacteristic
251C8×C13—42no—
252C8×C13—42no—
253#564—21no—
254#563—21no—
255#557—21no—
256#554—21no—
257#552—21no—
258#552—21no—
259#552—22no—
260#544—21no—
261#544C22×C1312yes—
262#541—21no—
263#541—22no—
264#539C22×C1312yes—
265#533C22×C1311yescharacteristic
266C2×C4⋊Q8C22×C1311yescharacteristic
267#529C22×C1311yescharacteristic
268C2×#125C22×C1311yescharacteristic
269#497—21no—
270#494—21no—
271#491—21no—
272#487—21no—
273#462—22no—
274#462—21no—
275#461—21no—
276#451C22×C1314yes—
277#451C22×C1312yes—
278#448C22×C1312yes—
279#432C22×C1311yescharacteristic
280#431C22×C1311yescharacteristic
281#398—22no—
282#395C22×C1314yes—
283#384—21no—
284#382—21no—
285#376C22×C1311yescharacteristic
286#328C22×C1314yes—
287#328C22×C1312yes—
288#327C22×C1312yes—
289#324C22×C1314yes—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13C2×#12011yescharacteristic
296C22×C13#57812yes—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—44no—
303C4×C13—42no—
304C4×C13—41no—
305C4×C13—41no—
306C4×C13—42no—
307C4×C13—42no—
308C4×C13—42no—
309C4×C13—41no—
310C4×C13—82no—
311C4×C13#45612yes—
312C22×Q8C23×C1312yes—
313C2×Q16—24no—
314C2×Q16—22no—
315C2×SD16—22no—
316C4⋊Q8—21no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8D4×C1311yescharacteristic
324C4⋊Q8D4×C1311yescharacteristic
325#126—22no—
326#126—22no—
327#126—22no—
328#126—22no—
329#126—21no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125—22no—
334#125—21no—
335#125—22no—
336#125—22no—
337#125—22no—
338#125—22no—
339#125—21no—
340#125—21no—
341#125—21no—
342#125—21no—
343#125—21no—
344#125D4×C1311yescharacteristic
345#124D4×C1311yescharacteristic
346#123—22no—
347#123—21no—
348#123—22no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—21no—
355C22⋊Q8—22no—
356C22⋊Q8C23×C1311yescharacteristic
357C22⋊Q8C23×C1312yes—
358#121C23×C1311yescharacteristic
359C4×Q8—21no—
360C4×Q8—22no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8D4×C1311yescharacteristic
364C4×Q8D4×C1312yes—
365C4×D4—21no—
366C4×D4—22no—
367C4×D4D4×C1311yescharacteristic
368#117—22no—
369#117—21no—
370#117—21no—
371#117—22no—
372#117—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4D4×C1311yescharacteristic
378C2×C4⋊C4D4×C1312yes—
379C2×C4⋊C4D4×C1311yescharacteristic
380C2×C4⋊C4C23×C1312yes—
381C2×C42—21no—
382C2×C42C23×C1311yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—21no—
385#103—22no—
386#103—22no—
387#103—24no—
388C22⋊C8C23×C1312yes—
389C22⋊C8C23×C1312yes—
390#97—21no—
391C4×C8—21no—
392#95—21no—
393#95—24no—
394#95C23×C1312yes—
395C2×C13—22no—
396C2×C13—81no—
397C2×C13#301111yescharacteristic
398C2×C13C2×#45611yescharacteristic
399C2×C13#302711yescharacteristic
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—82no—
405C2×Q8C2×D4×C1312yes—
406C2×Q8C2×D4×C1311yescharacteristic
407C2×D4—21no—
408C2×D4C2×D4×C1311yescharacteristic
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4C2×D4×C1312yes—
414C22×C4C2×D4×C1311yescharacteristic
415C22×C4C2×D4×C1311yescharacteristic
416C22×C4C2×D4×C1312yes—
417C22×C4C24×C1311yescharacteristic
418Q16—82no—
419Q16—84no—
420SD16—82no—
421C2×C8—22no—
422C2×C8—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—84no—
453C4⋊C4C2×D4×C1311yescharacteristic
454C4⋊C4C2×D4×C1311yescharacteristic
455C4⋊C4C2×D4×C1312yes—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C42—24no—
466C42—22no—
467C42—22no—
468C42—22no—
469C42—22no—
470C42—21no—
471C42C2×D4×C1311yescharacteristic
472C42C2×D4×C1311yescharacteristic
473C42C2×D4×C1311yescharacteristic
474C42C2×D4×C1311yescharacteristic
475C13#1843311yescharacteristic, direct product factor, Sylow
476C23—21no—
477C23C22×D4×C1311yescharacteristic
478Q8—41no—
479Q8—42no—
480Q8—42no—
481Q8—42no—
482Q8—44no—
483Q8—42no—
484Q8—82no—
485D4—41no—
486D4—42no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—82no—
506C2×C4C13×#12011yescharacteristic
507C2×C4C13×#12011yescharacteristic
508C2×C4C13×#12011yescharacteristic
509C2×C4C13×#12011yescharacteristic
510C2×C4C22×D4×C1311yescharacteristic
511C2×C4C22×D4×C1311yescharacteristic
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22C2×C13×#12011yescharacteristic
520C22C13×#57812yes—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—44no—
527C4—42no—
528C4—41no—
529C4—41no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—41no—
534C4—82no—
535C4C13×#45612yes—
536C2—22no—
537C2—81no—
538C2C13×#301111yescharacteristic
539C2C2×C13×#45611yescharacteristic
540C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#121C23
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
3. C13×#3209C2semidirect
4. C13×#2660C2semidirect
5. C13×#1605C2semidirect
7. C13×#1506C2semidirect
9. C13×#1470C2semidirect
130. #18433C13direct (N × H)
208. #3209C2×C13semidirect
209. #2660C2×C13semidirect
210. #1605C2×C13semidirect
212. #1506C2×C13semidirect
214. #1470C2×C13semidirect
475. C13#18433direct (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×#32182
C13×#32092
C13×#26602
C13×#16052
C13×#16032
C13×#15062
C13×#15002
C13×#14702
#1843313