Finite Group Databasebeta

← C13×#18442 #15704781

Subgroups — C13×#18442 #15704781

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic
3C13×#3229C211yesmaximal, characteristic, complemented
4C13×#2660C211yesmaximal, characteristic, complemented
5C13×#1611C214yesmaximal, complemented
6C13×#1609C214yesmaximal
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×#498—21no—
28C13×#489—21no—
29C13×#487—21no—
30C13×#483C2214yes—
31C13×#483C2212yes—
32C13×#480C2212yes—
33C13×#477—21no—
34C13×#476—21no—
35C13×#475—22no—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#398C2214yes—
39C13×#395—22no—
40C13×#384—21no—
41C13×#382—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×C13D412yes—
96C4×Q8×C13D411yescharacteristic
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⋊C4—24no—
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D412yes—
111C2×C13×C4⋊C4C2312yes—
112C2×C13×C4⋊C4C2312yes—
113C2×C42×C13—21no—
114C2×C42×C13C2311yescharacteristic
115C13×#107—22no—
116C13×#106—24no—
117C13×#106—22no—
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—24no—
121C13×#103—22no—
122C13×#102—22no—
123C13×C22⋊C8C2312yes—
124C13×C22⋊C8C2312yes—
125C13×#97—21no—
126C4×C8×C13—21no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18442C1311yesmaximal, characteristic, direct product factor, Sylow
131C2×Q8×C13—22no—
132C2×Q8×C13—21no—
133C2×Q8×C13—41no—
134C2×Q8×C13—41no—
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
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⋊C4—84no—
181C13×C4⋊C4C2×D411yescharacteristic
182C13×C4⋊C4C2×D412yes—
183C13×C4⋊C4C2×D411yescharacteristic
184C13×C22⋊C4—22no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—21no—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C13×C22⋊C4—21no—
193C42×C13—24no—
194C42×C13—22no—
195C42×C13—22no—
196C42×C13—22no—
197C42×C13—22no—
198C42×C13—21no—
199C42×C13C2×D411yescharacteristic
200C42×C13C2×D411yescharacteristic
201C42×C13C2×D411yescharacteristic
202C42×C13C2×D411yescharacteristic
203#3563C2×C1311yescharacteristic
204#3238C2×C1311yescharacteristic
205#3229C2×C1311yescharacteristic, complemented
206#2660C2×C1311yescharacteristic, complemented
207#1611C2×C1314yescomplemented
208#1609C2×C1314yes—
209#1506C2×C1311yescharacteristic, complemented
210#1500C2×C1311yescharacteristic
211#1470C2×C1311yescharacteristic, complemented
212C23×C13—21no—
213C23×C13C22×D411yescharacteristic
214Q8×C13—41no—
215Q8×C13—42no—
216Q8×C13—42no—
217Q8×C13—82no—
218Q8×C13—82no—
219Q8×C13—82no—
220D4×C13—41no—
221D4×C13—42no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—21no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—44no—
240C2×C4×C13—82no—
241C2×C4×C13#12011yescharacteristic
242C2×C4×C13#12011yescharacteristic
243C2×C4×C13#12011yescharacteristic
244C2×C4×C13#12011yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C8×C13—42no—
248C8×C13—42no—
249#564—21no—
250#563—21no—
251#557—21no—
252#554—21no—
253#552—21no—
254#552—21no—
255#552—22no—
256#544—21no—
257#544C22×C1312yes—
258#541—21no—
259#541—22no—
260#539C22×C1312yes—
261#533C22×C1311yescharacteristic
262C2×C4⋊Q8C22×C1311yescharacteristic
263#529C22×C1311yescharacteristic
264C2×#125C22×C1311yescharacteristic
265#501—21no—
266#498—21no—
267#489—21no—
268#487—21no—
269#483C22×C1314yes—
270#483C22×C1312yes—
271#480C22×C1312yes—
272#477—21no—
273#476—21no—
274#475—22no—
275#432C22×C1311yescharacteristic
276#431C22×C1311yescharacteristic
277#398C22×C1314yes—
278#395—22no—
279#384—21no—
280#382—21no—
281#376C22×C1311yescharacteristic
282#328C22×C1314yes—
283#328C22×C1312yes—
284#327C22×C1312yes—
285#324C22×C1314yes—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—41no—
289C22×C13—41no—
290C22×C13—41no—
291C22×C13C2×#12011yescharacteristic
292C22×C13#57712yes—
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—21no—
298C4×C13—44no—
299C4×C13—42no—
300C4×C13—41no—
301C4×C13—41no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—41no—
306C4×C13—82no—
307C4×C13#45612yes—
308C22×Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8D4×C1311yescharacteristic
317C4⋊Q8D4×C1311yescharacteristic
318#126—22no—
319#126—22no—
320#126—22no—
321#126—22no—
322#126—21no—
323#125—22no—
324#125—22no—
325#125—22no—
326#125—22no—
327#125—21no—
328#125—22no—
329#125—22no—
330#125—22no—
331#125—22no—
332#125—21no—
333#125—21no—
334#125—21no—
335#125—21no—
336#125—21no—
337#125D4×C1311yescharacteristic
338#124D4×C1311yescharacteristic
339#123—22no—
340#123—21no—
341#123—22no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8C23×C1311yescharacteristic
350C22⋊Q8C23×C1312yes—
351#121C23×C1311yescharacteristic
352C4×Q8—21no—
353C4×Q8—22no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8D4×C1311yescharacteristic
357C4×Q8D4×C1312yes—
358C4×D4—21no—
359C4×D4—22no—
360C4×D4D4×C1311yescharacteristic
361#117—22no—
362#117—21no—
363#117—21no—
364#117—22no—
365#117—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4D4×C1311yescharacteristic
370C2×C4⋊C4D4×C1312yes—
371C2×C4⋊C4D4×C1311yescharacteristic
372C2×C4⋊C4C23×C1312yes—
373C2×C4⋊C4C23×C1312yes—
374C2×C42—21no—
375C2×C42C23×C1311yescharacteristic
376#107—22no—
377#106—24no—
378#106—22no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381#103—24no—
382#103—22no—
383#102—22no—
384C22⋊C8C23×C1312yes—
385C22⋊C8C23×C1312yes—
386#97—21no—
387C4×C8—21no—
388#95—21no—
389#95—24no—
390#95C23×C1312yes—
391C2×C13—22no—
392C2×C13—81no—
393C2×C13#301011yescharacteristic
394C2×C13C2×#45611yescharacteristic
395C2×C13#302811yescharacteristic
396C2×Q8—22no—
397C2×Q8—21no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—82no—
401C2×Q8C2×D4×C1312yes—
402C2×Q8C2×D4×C1311yescharacteristic
403C2×D4—21no—
404C2×D4C2×D4×C1311yescharacteristic
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4C2×D4×C1312yes—
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1312yes—
413C22×C4C24×C1311yescharacteristic
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—84no—
446C4⋊C4C2×D4×C1311yescharacteristic
447C4⋊C4C2×D4×C1312yes—
448C4⋊C4C2×D4×C1311yescharacteristic
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C42—24no—
459C42—22no—
460C42—22no—
461C42—22no—
462C42—22no—
463C42—21no—
464C42C2×D4×C1311yescharacteristic
465C42C2×D4×C1311yescharacteristic
466C42C2×D4×C1311yescharacteristic
467C42C2×D4×C1311yescharacteristic
468C13#1844211yescharacteristic, direct product factor, Sylow
469C23—21no—
470C23C22×D4×C1311yescharacteristic
471Q8—41no—
472Q8—42no—
473Q8—42no—
474Q8—82no—
475Q8—82no—
476Q8—82no—
477D4—41no—
478D4—42no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—82no—
498C2×C4C13×#12011yescharacteristic
499C2×C4C13×#12011yescharacteristic
500C2×C4C13×#12011yescharacteristic
501C2×C4C13×#12011yescharacteristic
502C2×C4C22×D4×C1311yescharacteristic
503C2×C4C22×D4×C1311yescharacteristic
504C8—42no—
505C8—42no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22C2×C13×#12011yescharacteristic
512C22C13×#57712yes—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—44no—
519C4—42no—
520C4—41no—
521C4—41no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—82no—
527C4C13×#45612yes—
528C2—22no—
529C2—81no—
530C2C13×#301011yescharacteristic
531C2C2×C13×#45611yescharacteristic
532C2C13×#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×#3229C2semidirect
4. C13×#2660C2semidirect
5. C13×#1611C2semidirect
7. C13×#1506C2semidirect
9. C13×#1470C2semidirect
130. #18442C13direct (N × H)
205. #3229C2×C13semidirect
206. #2660C2×C13semidirect
207. #1611C2×C13semidirect
209. #1506C2×C13semidirect
211. #1470C2×C13semidirect
468. C13#18442direct (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×#32382
C13×#32292
C13×#26602
C13×#16112
C13×#16092
C13×#15062
C13×#15002
C13×#14702
#1844213