Finite Group Databasebeta

← C13×#18438 #15704777

Subgroups — C13×#18438 #15704777

Order 3328.

908 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic, complemented
3C13×#3229C211yesmaximal, characteristic, complemented
4C13×#2640C211yesmaximal, characteristic, complemented
5C13×#1612C214yesmaximal, complemented
6C13×#1608C214yesmaximal, complemented
7C13×#1506C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1469C211yesmaximal, characteristic, complemented
10C13×#563—21no—
11C13×#562—21no—
12C13×#556—21no—
13C13×#551—22no—
14D4×Q8×C13—21no—
15C13×#548—21no—
16C13×#546—21no—
17C13×#543C2212yes—
18C13×#542—21no—
19C13×#542—22no—
20C13×#538C2212yes—
21C13×#536—21no—
22C13×#533C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C13×#501—21no—
27C13×#498—21no—
28C13×#489—21no—
29C13×#487—21no—
30C13×#483C2212yes—
31C13×#483C2214yes—
32C13×#480C2212yes—
33C13×#477—21no—
34C13×#476—21no—
35C13×#475—22no—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#397C2214yes—
39C13×#393—22no—
40C13×#391—21no—
41C13×#390—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#323C2214yes—
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13D411yescharacteristic
52C13×C4⋊Q8—21no—
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—21no—
64C13×#125—21no—
65C13×#125D411yescharacteristic
66C13×#124—21no—
67C13×#124—22no—
68C13×#124—22no—
69C13×#124—21no—
70C13×#124—21no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124D411yescharacteristic
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—21no—
78C13×#123—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8C2311yescharacteristic
89C13×C22⋊Q8C2312yes—
90C13×#121—21no—
91C13×#121—22no—
92C13×#121—22no—
93C13×#121C2311yescharacteristic
94C13×#120—22no—
95C4×Q8×C13—21no—
96C4×Q8×C13—21no—
97C4×Q8×C13D412yes—
98C4×Q8×C13D411yescharacteristic
99C4×D4×C13—21no—
100C4×D4×C13—22no—
101C4×D4×C13—21no—
102C4×D4×C13—22no—
103C4×D4×C13D411yescharacteristic
104C13×#117—22no—
105C13×#117—21no—
106C13×#117—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4C2312yes—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—24no—
111C2×C13×C22⋊C4D412yes—
112C2×C13×C22⋊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#18438C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13C2×D412yes—
132C13×#41—82no—
133C2×Q8×C13—22no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—42no—
138C2×Q8×C13—41no—
139C2×Q8×C13—41no—
140C2×Q8×C13—82no—
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—21no—
149C2×D4×C13—42no—
150C2×D4×C13C2×D411yescharacteristic
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2411yescharacteristic
161C2×C8×C13—22no—
162C2×C8×C13—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
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×D412yes—
182C13×C4⋊C4C2×D411yescharacteristic
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—21no—
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—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—84no—
199C42×C13—22no—
200C42×C13—22no—
201C42×C13—21no—
202C42×C13—42no—
203C42×C13C2×D411yescharacteristic
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206C42×C13C2×D411yescharacteristic
207#3561C2×C1311yescharacteristic
208#3238C2×C1311yescharacteristic, complemented
209#3229C2×C1311yescharacteristic, complemented
210#2640C2×C1311yescharacteristic, complemented
211#1612C2×C1314yescomplemented
212#1608C2×C1314yescomplemented
213#1506C2×C1311yescharacteristic, complemented
214#1500C2×C1311yescharacteristic, complemented
215#1469C2×C1311yescharacteristic, complemented
216C23×C13—22no—
217C23×C13—21no—
218C23×C13—24no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13C22×D411yescharacteristic
222Q8×C13—41no—
223Q8×C13—42no—
224Q8×C13—42no—
225Q8×C13—42no—
226Q8×C13—81no—
227Q8×C13—82no—
228Q8×C13—82no—
229Q8×C13—82no—
230D4×C13—41no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—81no—
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—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—44no—
252C2×C4×C13—82no—
253C2×C4×C13—82no—
254C2×C4×C13—82no—
255C2×C4×C13#12011yescharacteristic
256C2×C4×C13#12011yescharacteristic
257C2×C4×C13#12011yescharacteristic
258C2×C4×C13#12011yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C8×C13—42no—
262C8×C13—42no—
263#563—21no—
264#562—21no—
265#556—21no—
266#551—22no—
267D4×Q8—21no—
268#548—21no—
269#546—21no—
270#543C22×C1312yes—
271#542—21no—
272#542—22no—
273#538C22×C1312yes—
274#536—21no—
275#533C22×C1311yescharacteristic
276C2×C4⋊Q8C22×C1311yescharacteristic
277#529C22×C1311yescharacteristic
278C2×#124C22×C1311yescharacteristic
279#501—21no—
280#498—21no—
281#489—21no—
282#487—21no—
283#483C22×C1312yes—
284#483C22×C1314yes—
285#480C22×C1312yes—
286#477—21no—
287#476—21no—
288#475—22no—
289#432C22×C1311yescharacteristic
290#431C22×C1311yescharacteristic
291#397C22×C1314yes—
292#393—22no—
293#391—21no—
294#390—21no—
295#376C22×C1311yescharacteristic
296#328C22×C1312yes—
297#328C22×C1314yes—
298#327C22×C1312yes—
299#323C22×C1314yes—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—41no—
303C22×C13—42no—
304C22×C13—41no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—41no—
308C22×C13—84no—
309C22×C13C2×#12011yescharacteristic
310C22×C13#57712yes—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—21no—
315C4×C13—21no—
316C4×C13—41no—
317C4×C13—41no—
318C4×C13—42no—
319C4×C13—42no—
320C4×C13—41no—
321C4×C13—42no—
322C4×C13—82no—
323C4×C13—82no—
324C4×C13#45512yes—
325C2×#41—21no—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8D4×C1311yescharacteristic
329C22×D4D4×C1311yescharacteristic
330C4⋊Q8—21no—
331C4⋊Q8—22no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8D4×C1311yescharacteristic
337C4⋊Q8D4×C1311yescharacteristic
338#126—22no—
339#126—22no—
340#126—22no—
341#126—21no—
342#125—21no—
343#125D4×C1311yescharacteristic
344#124—21no—
345#124—22no—
346#124—22no—
347#124—21no—
348#124—21no—
349#124—21no—
350#124—21no—
351#124D4×C1311yescharacteristic
352#123—22no—
353#123—22no—
354#123—22no—
355#123—21no—
356#123—22no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8C23×C1311yescharacteristic
367C22⋊Q8C23×C1312yes—
368#121—21no—
369#121—22no—
370#121—22no—
371#121C23×C1311yescharacteristic
372#120—22no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8D4×C1311yescharacteristic
376C4×Q8D4×C1312yes—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4—22no—
381C4×D4D4×C1311yescharacteristic
382#117—22no—
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C23×C1312yes—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4D4×C1312yes—
390C2×C22⋊C4C23×C1312yes—
391C2×C42—21no—
392C2×C42C23×C1311yescharacteristic
393#107—22no—
394#106—24no—
395#106—22no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398#103—24no—
399#103—22no—
400#102—22no—
401C22⋊C8C23×C1312yes—
402C22⋊C8C23×C1312yes—
403#97—21no—
404C4×C8—21no—
405#95—21no—
406#95—24no—
407#95C23×C1312yes—
408C2×C13—22no—
409C2×C13—81no—
410C2×C13—82no—
411C2×C13#301011yescharacteristic
412C2×C13C2×#45511yescharacteristic
413C2×C13#302811yescharacteristic
414C24C2×D4×C1312yes—
415#41—82no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—42no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—82no—
424C2×Q8—82no—
425C2×Q8C2×D4×C1311yescharacteristic
426C2×Q8C2×D4×C1312yes—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4C2×D4×C1311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4C2×D4×C1311yescharacteristic
441C22×C4C2×D4×C1311yescharacteristic
442C22×C4C2×D4×C1312yes—
443C22×C4C24×C1311yescharacteristic
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C1311yescharacteristic
464C4⋊C4C2×D4×C1312yes—
465C4⋊C4C2×D4×C1311yescharacteristic
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—21no—
481C22⋊C4—84no—
482C42—22no—
483C42—22no—
484C42—21no—
485C42—42no—
486C42C2×D4×C1311yescharacteristic
487C42C2×D4×C1311yescharacteristic
488C42C2×D4×C1311yescharacteristic
489C42C2×D4×C1311yescharacteristic
490C13#1843811yescharacteristic, direct product factor, Sylow
491C23—22no—
492C23—21no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23C22×D4×C1311yescharacteristic
497Q8—41no—
498Q8—42no—
499Q8—42no—
500Q8—42no—
501Q8—81no—
502Q8—82no—
503Q8—82no—
504Q8—82no—
505D4—41no—
506D4—42no—
507D4—42no—
508D4—81no—
509D4—82no—
510D4—82no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4C13×#12011yescharacteristic
531C2×C4C13×#12011yescharacteristic
532C2×C4C13×#12011yescharacteristic
533C2×C4C13×#12011yescharacteristic
534C2×C4C22×D4×C1311yescharacteristic
535C2×C4C22×D4×C1311yescharacteristic
536C8—42no—
537C8—42no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—42no—
545C22—41no—
546C22—84no—
547C22C2×C13×#12011yescharacteristic
548C22C13×#57712yes—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—42no—
560C4—82no—
561C4—82no—
562C4C13×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C13×#301011yescharacteristic
567C2C2×C13×#45511yescharacteristic
568C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3561C2
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
2. C13×#3238C2semidirect
3. C13×#3229C2semidirect
4. C13×#2640C2semidirect
5. C13×#1612C2semidirect
6. C13×#1608C2semidirect
7. C13×#1506C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
130. #18438C13direct (N × H)
208. #3238C2×C13semidirect
209. #3229C2×C13semidirect
210. #2640C2×C13semidirect
211. #1612C2×C13semidirect
212. #1608C2×C13semidirect
213. #1506C2×C13semidirect
214. #1500C2×C13semidirect
215. #1469C2×C13semidirect
490. C13#18438direct (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×#32292
C13×#26402
C13×#16122
C13×#16082
C13×#15062
C13×#15002
C13×#14692
#1843813