Finite Group Databasebeta

← C13×#18443 #15704782

Subgroups — C13×#18443 #15704782

Order 3328.

832 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic
3C13×#3230C211yesmaximal, characteristic, complemented
4C13×#2642C211yesmaximal, characteristic, complemented
5C13×#1617C214yesmaximal, complemented
6C13×#1615C214yesmaximal
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×#501—21no—
27C13×#500—21no—
28C13×#489—21no—
29C13×#487—21no—
30C13×#484C2214yes—
31C13×#484C2212yes—
32C13×#481C2212yes—
33C13×#477—22no—
34C13×#475—21no—
35C13×#474—21no—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#400—22no—
39C13×#400C2214yes—
40C13×#391—21no—
41C13×#391—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#324C2214yes—
47C22×Q8×C13—21no—
48C13×C4⋊Q8—21no—
49C13×C4⋊Q8—22no—
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8—21no—
52C13×C4⋊Q8—21no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8D411yescharacteristic
56C13×C4⋊Q8D411yescharacteristic
57C13×#126—22no—
58C13×#126—22no—
59C13×#126—22no—
60C13×#126—22no—
61C13×#126—21no—
62C13×#125—22no—
63C13×#125—22no—
64C13×#125—22no—
65C13×#125—22no—
66C13×#125—21no—
67C13×#125—22no—
68C13×#125—22no—
69C13×#125—22no—
70C13×#125—22no—
71C13×#125—21no—
72C13×#125—21no—
73C13×#125—21no—
74C13×#125—21no—
75C13×#125—21no—
76C13×#125D411yescharacteristic
77C13×#124D411yescharacteristic
78C13×#123—22no—
79C13×#123—21no—
80C13×#123—22no—
81C13×C22⋊Q8—21no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8C2311yescharacteristic
89C13×C22⋊Q8C2312yes—
90C13×#121C2311yescharacteristic
91C4×Q8×C13—21no—
92C4×Q8×C13—22no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13D411yescharacteristic
96C4×Q8×C13D412yes—
97C4×D4×C13—21no—
98C4×D4×C13—22no—
99C4×D4×C13D411yescharacteristic
100C13×#117—22no—
101C13×#117—21no—
102C13×#117—21no—
103C13×#117—22no—
104C13×#117—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4D412yes—
110C2×C13×C4⋊C4C2312yes—
111C2×C13×C4⋊C4C2312yes—
112C2×C42×C13—21no—
113C2×C42×C13C2311yescharacteristic
114C13×#107—22no—
115C13×#107—24no—
116C13×#106—22no—
117C13×C4⋊C8—21no—
118C13×C4⋊C8—21no—
119C13×#103—22no—
120C13×#103—24no—
121C13×#102—22no—
122C13×C22⋊C8C2312yes—
123C13×C22⋊C8C2312yes—
124C13×#97—21no—
125C4×C8×C13—21no—
126C13×#95—24no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18443C1311yesmaximal, characteristic, direct product factor, Sylow
131C2×Q8×C13—22no—
132C2×Q8×C13—21no—
133C2×Q8×C13—44no—
134C2×Q8×C13—41no—
135C2×Q8×C13—41no—
136C2×Q8×C13C2×D412yes—
137C2×Q8×C13C2×D411yescharacteristic
138C2×D4×C13—21no—
139C2×D4×C13C2×D411yescharacteristic
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2411yescharacteristic
149C2×C8×C13—22no—
150C2×C8×C13—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—41no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4C2×D411yescharacteristic
181C13×C4⋊C4C2×D411yescharacteristic
182C13×C4⋊C4C2×D412yes—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—21no—
188C13×C22⋊C4—21no—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C42×C13—22no—
193C42×C13—22no—
194C42×C13—22no—
195C42×C13—22no—
196C42×C13—21no—
197C42×C13—42no—
198C42×C13C2×D411yescharacteristic
199C42×C13C2×D411yescharacteristic
200C42×C13C2×D411yescharacteristic
201C42×C13C2×D411yescharacteristic
202#3563C2×C1311yescharacteristic
203#3239C2×C1311yescharacteristic
204#3230C2×C1311yescharacteristic, complemented
205#2642C2×C1311yescharacteristic, complemented
206#1617C2×C1314yescomplemented
207#1615C2×C1314yes—
208#1506C2×C1311yescharacteristic, complemented
209#1500C2×C1311yescharacteristic
210#1470C2×C1311yescharacteristic, complemented
211C23×C13—21no—
212C23×C13C22×D411yescharacteristic
213Q8×C13—41no—
214Q8×C13—42no—
215Q8×C13—42no—
216Q8×C13—82no—
217Q8×C13—82no—
218Q8×C13—82no—
219D4×C13—41no—
220D4×C13—42no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—22no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—44no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—82no—
240C2×C4×C13#12011yescharacteristic
241C2×C4×C13#12011yescharacteristic
242C2×C4×C13#12011yescharacteristic
243C2×C4×C13#12011yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C8×C13—42no—
247C8×C13—42no—
248#564—21no—
249#563—21no—
250#557—21no—
251#554—21no—
252#552—21no—
253#552—21no—
254#552—22no—
255#544—21no—
256#544C22×C1312yes—
257#541—21no—
258#541—22no—
259#539C22×C1312yes—
260#533C22×C1311yescharacteristic
261C2×C4⋊Q8C22×C1311yescharacteristic
262#529C22×C1311yescharacteristic
263C2×#125C22×C1311yescharacteristic
264#501—21no—
265#500—21no—
266#489—21no—
267#487—21no—
268#484C22×C1314yes—
269#484C22×C1312yes—
270#481C22×C1312yes—
271#477—22no—
272#475—21no—
273#474—21no—
274#432C22×C1311yescharacteristic
275#431C22×C1311yescharacteristic
276#400—22no—
277#400C22×C1314yes—
278#391—21no—
279#391—21no—
280#376C22×C1311yescharacteristic
281#328C22×C1314yes—
282#328C22×C1312yes—
283#327C22×C1312yes—
284#324C22×C1314yes—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—41no—
288C22×C13—41no—
289C22×C13—41no—
290C22×C13C2×#12011yescharacteristic
291C22×C13#57812yes—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—42no—
298C4×C13—41no—
299C4×C13—41no—
300C4×C13—42no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—41no—
304C4×C13—82no—
305C4×C13—82no—
306C4×C13#45412yes—
307C22×Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8D4×C1311yescharacteristic
316C4⋊Q8D4×C1311yescharacteristic
317#126—22no—
318#126—22no—
319#126—22no—
320#126—22no—
321#126—21no—
322#125—22no—
323#125—22no—
324#125—22no—
325#125—22no—
326#125—21no—
327#125—22no—
328#125—22no—
329#125—22no—
330#125—22no—
331#125—21no—
332#125—21no—
333#125—21no—
334#125—21no—
335#125—21no—
336#125D4×C1311yescharacteristic
337#124D4×C1311yescharacteristic
338#123—22no—
339#123—21no—
340#123—22no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—21no—
347C22⋊Q8—22no—
348C22⋊Q8C23×C1311yescharacteristic
349C22⋊Q8C23×C1312yes—
350#121C23×C1311yescharacteristic
351C4×Q8—21no—
352C4×Q8—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8D4×C1311yescharacteristic
356C4×Q8D4×C1312yes—
357C4×D4—21no—
358C4×D4—22no—
359C4×D4D4×C1311yescharacteristic
360#117—22no—
361#117—21no—
362#117—21no—
363#117—22no—
364#117—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C1311yescharacteristic
368C2×C4⋊C4D4×C1312yes—
369C2×C4⋊C4D4×C1311yescharacteristic
370C2×C4⋊C4C23×C1312yes—
371C2×C4⋊C4C23×C1312yes—
372C2×C42—21no—
373C2×C42C23×C1311yescharacteristic
374#107—22no—
375#107—24no—
376#106—22no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379#103—22no—
380#103—24no—
381#102—22no—
382C22⋊C8C23×C1312yes—
383C22⋊C8C23×C1312yes—
384#97—21no—
385C4×C8—21no—
386#95—21no—
387#95—24no—
388#95—24no—
389#95C23×C1312yes—
390C2×C13—22no—
391C2×C13—81no—
392C2×C13#301111yescharacteristic
393C2×C13C2×#45411yescharacteristic
394C2×C13#302811yescharacteristic
395C2×Q8—22no—
396C2×Q8—21no—
397C2×Q8—44no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8C2×D4×C1312yes—
401C2×Q8C2×D4×C1311yescharacteristic
402C2×D4—21no—
403C2×D4C2×D4×C1311yescharacteristic
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4C2×D4×C1312yes—
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1312yes—
412C22×C4C24×C1311yescharacteristic
413C2×C8—22no—
414C2×C8—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4C2×D4×C1311yescharacteristic
445C4⋊C4C2×D4×C1311yescharacteristic
446C4⋊C4C2×D4×C1312yes—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—21no—
461C42—42no—
462C42C2×D4×C1311yescharacteristic
463C42C2×D4×C1311yescharacteristic
464C42C2×D4×C1311yescharacteristic
465C42C2×D4×C1311yescharacteristic
466C13#1844311yescharacteristic, direct product factor, Sylow
467C23—21no—
468C23C22×D4×C1311yescharacteristic
469Q8—41no—
470Q8—42no—
471Q8—42no—
472Q8—82no—
473Q8—82no—
474Q8—82no—
475D4—41no—
476D4—42no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—82no—
496C2×C4C13×#12011yescharacteristic
497C2×C4C13×#12011yescharacteristic
498C2×C4C13×#12011yescharacteristic
499C2×C4C13×#12011yescharacteristic
500C2×C4C22×D4×C1311yescharacteristic
501C2×C4C22×D4×C1311yescharacteristic
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C2×C13×#12011yescharacteristic
510C22C13×#57812yes—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—41no—
518C4—41no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—41no—
523C4—82no—
524C4—82no—
525C4C13×#45412yes—
526C2—22no—
527C2—81no—
528C2C13×#301111yescharacteristic
529C2C2×C13×#45411yescharacteristic
530C2C13×#302811yescharacteristic
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×#3230C2semidirect
4. C13×#2642C2semidirect
5. C13×#1617C2semidirect
7. C13×#1506C2semidirect
9. C13×#1470C2semidirect
130. #18443C13direct (N × H)
204. #3230C2×C13semidirect
205. #2642C2×C13semidirect
206. #1617C2×C13semidirect
208. #1506C2×C13semidirect
210. #1470C2×C13semidirect
466. C13#18443direct (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×#32392
C13×#32302
C13×#26422
C13×#16172
C13×#16152
C13×#15062
C13×#15002
C13×#14702
#1844313