Finite Group Databasebeta

← D13×#2083 #15891877

Subgroups — D13×#2083 #15891877

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#107C212yesmaximal
2D13×#389C211yesmaximal, characteristic
3D13×#384C211yesmaximal, characteristic
4#13116311C212yesmaximal, complemented
5#13116310C212yesmaximal, complemented
6#13116309C211yesmaximal, characteristic, complemented
7#13116308C211yesmaximal, characteristic, complemented
8#13116307C211yesmaximal, characteristic, complemented
9D13×#340C212yesmaximal
10D13×#336C211yesmaximal, characteristic
11C13×#2083C211yesmaximal, characteristic, complemented
12C22×C8×D13C2212yes—
13C2×C4⋊C4×D13—21no—
14C2×C4⋊C4×D13—21no—
15C2×C4⋊C4×D13—21no—
16C2×C4⋊C4×D13C2212yes—
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×C42×D13C2211yescharacteristic
20C2×C13×#107C2212yes—
21C13×#389C2211yescharacteristic
22C13×#384C2211yescharacteristic
23C2×#88058C2212yes—
24#11718646C2211yescharacteristic
25#11718637—21no—
26#11718637—21no—
27#11718637C2212yes—
28#11718634C2211yescharacteristic
29#11718633—21no—
30C2×#88047C2212yes—
31C2×#88047C2212yes—
32#11718596C2211yescharacteristic
33#11718589C2211yescharacteristic
34D13×#107—28no—
35D13×#95—21no—
36#11718308—21no—
37C13×#340C2212yes—
38C13×#336C2211yescharacteristic
39#11718143C2212yes—
40#11718142C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718116C2211yescharacteristic
44C22×C4×D13—21no—
45C22×C4×D13—22no—
46C22×C4×D13—21no—
47C22×C4×D13D411yescharacteristic
48C22×C4×D13D411yescharacteristic
49C22×C4×D13C2311yescharacteristic
50C22×C8×C13C2312yes—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2312yes—
55C2×C13×C4⋊C4C2311yescharacteristic
56C2×C13×C4⋊C4C2311yescharacteristic
57C2×C42×C13C2311yescharacteristic
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13C2312yes—
62C2×C4⋊Dic13C2311yescharacteristic
63C2×C4⋊Dic13C2311yescharacteristic
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—21no—
67C2×#6101—22no—
68C2×#6101—22no—
69C2×#6101—21no—
70C2×#6101—22no—
71C2×C4×Dic13D411yescharacteristic
72C2×C4×Dic13D411yescharacteristic
73C2×C4×Dic13C2311yescharacteristic
74C22×#1055C2312yes—
75C2×C8×D13—24no—
76C2×C8×D13—24no—
77C2×C8×D13Q818yes—
78C4⋊C4×D13—22no—
79C4⋊C4×D13—24no—
80C4⋊C4×D13—24no—
81C4⋊C4×D13—24no—
82C4⋊C4×D13—44no—
83C4⋊C4×D13—44no—
84C4⋊C4×D13—44no—
85C4⋊C4×D13D414yes—
86C42×D13—24no—
87C13×#107—24no—
88C13×#95—21no—
89#88071—21no—
90#88071—21no—
91#88071—21no—
92#88058—24no—
93#88047—24no—
94#88047—24no—
95C2×#2083—131nomaximal, Sylow
96C23×D13C2×D411yescharacteristic
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2411yescharacteristic
103C22×Dic13—21no—
104C22×Dic13—21no—
105C22×Dic13—22no—
106C22×Dic13C2×D411yescharacteristic
107C22×Dic13C2×D411yescharacteristic
108C22×Dic13C2×D411yescharacteristic
109C2×C4×D13—22no—
110C2×C4×D13—22no—
111C2×C4×D13—22no—
112C2×C4×D13—22no—
113C2×C4×D13—24no—
114C2×C4×D13—42no—
115C2×C4×D13—42no—
116C2×C4×D13—44no—
117C2×C4×D13—42no—
118C2×C4×D13—44no—
119C2×C4×D13—42no—
120C2×C4×D13—44no—
121C2×C4×D13—42no—
122C2×C4×D13D814yes—
123C2×C4×D13Q1614yes—
124C2×C4×D13C2×D412yes—
125C2×C4×D13C2×Q814yes—
126C2×C4×D13#4114yes—
127C2×C4×D13#4112yes—
128C2×C8×C13—22no—
129C2×C8×C13—22no—
130C2×C8×C13C2×Q814yes—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—42no—
136C13×C4⋊C4—42no—
137C13×C4⋊C4—42no—
138C13×C4⋊C4C2×D412yes—
139C42×C13—22no—
140C4⋊Dic13—21no—
141C4⋊Dic13—22no—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144C4⋊Dic13—42no—
145C4⋊Dic13—42no—
146C4⋊Dic13—42no—
147C4⋊Dic13C2×D412yes—
148#6101—24no—
149#6101—44no—
150#6101—42no—
151#6101—44no—
152#6101—42no—
153#6101—42no—
154#6101—44no—
155C4×Dic13—22no—
156C4×Dic13—22no—
157C4×Dic13—22no—
158C2×#1055—22no—
159C2×#1055—22no—
160C2×#1055C2×Q814yes—
161C8×D13—216no—
162C22×#107—132no—
163C2×#389—131no—
164C2×#384—131no—
165#2083—132no—
166#2083—131no—
167#2083—131no—
168#2083—132no—
169#2083—131no—
170#2083D1311yescharacteristic, direct product factor
171C2×#340—132no—
172C2×#336—131no—
173C23×C13C22×D411yescharacteristic
174C22×D13#12112yes—
175C22×D13#12312yes—
176C22×D13C4⋊Q812yes—
177C22×D13C2×D812yes—
178C22×D13C2×Q1612yes—
179C22×D13AGL(1,ℤ/8)12yes—
180C22×D13#13712yes—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—22no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—41no—
194C2×C4×C13C2×D812yes—
195C2×C4×C13C2×Q1612yes—
196C2×C4×C13C22×D411yescharacteristic
197C2×C4×C13C22×Q812yes—
198C2×C4×C13C2×#4112yes—
199C2×C4×C13C2×#4111yescharacteristic
200C2×Dic13—21no—
201C2×Dic13—21no—
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13—22no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207C2×Dic13—42no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—42no—
211C2×Dic13—42no—
212C2×Dic13—41no—
213C2×Dic13#12112yes—
214C2×Dic13#12312yes—
215C2×Dic13C4⋊Q812yes—
216C2×Dic13C2×D812yes—
217C2×Dic13C2×Q1612yes—
218C4×D13—28no—
219C4×D13—28no—
220C4×D13—48no—
221C4×D13—88no—
222C4×D13—84no—
223C4×D13C22⋊Q818yes—
224C4×D13#12518yes—
225C8×C13—24no—
226#1055—24no—
227C23×C8—132no—
228C22×C4⋊C4—131no—
229C22×C4⋊C4—132no—
230C22×C4⋊C4—131no—
231C22×C4⋊C4—261no—
232C22×C4⋊C4—261no—
233C22×C4⋊C4—261no—
234C22×C42—131no—
235C2×#107—132no—
236C2×#107—132no—
237C2×#107—132no—
238C2×#107—268no—
239C2×#107C2×D1312yes—
240#389—131no—
241#389—131no—
242#389—131no—
243#389—261no—
244#389—261no—
245#389C2×D1311yescharacteristic
246#384—132no—
247#384—131no—
248#384—261no—
249#384—261no—
250#384C2×D1311yescharacteristic
251C2×#95—261no—
252#340—132no—
253#340—132no—
254#340—132no—
255#340C2×D1312yes—
256#336—132no—
257#336—131no—
258#336C2×D1311yescharacteristic
259C22×C13C2×#12111yescharacteristic
260C22×C13C2×#12311yescharacteristic
261C22×C13C2×C4⋊Q811yescharacteristic
262C22×C13C22×D811yescharacteristic
263C22×C13C22×Q1611yescharacteristic
264C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C13C2×#13711yescharacteristic
266C2×D13#39814yes—
267C2×D13#45914yes—
268C2×D13#46214yes—
269C2×D13#48014yes—
270C2×D13#48414yes—
271C2×D13#50014yes—
272C2×D13#50114yes—
273C4×C13—22no—
274C4×C13—22no—
275C4×C13—42no—
276C4×C13—81no—
277C4×C13—82no—
278C4×C13C2×C22⋊Q812yes—
279C4×C13C2×#12512yes—
280Dic13—22no—
281Dic13—22no—
282Dic13—42no—
283Dic13—81no—
284Dic13—82no—
285Dic13#39814yes—
286C23×C4—131no—
287C23×C4—131no—
288C23×C4—131no—
289C23×C4—261no—
290C23×C4—262no—
291C23×C4—261no—
292C22×C8—132no—
293C22×C8—138no—
294C22×C8—264no—
295C22×C8—264no—
296C22×C8C22×D1312yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—131no—
301C2×C4⋊C4—134no—
302C2×C4⋊C4—131no—
303C2×C4⋊C4—132no—
304C2×C4⋊C4—262no—
305C2×C4⋊C4—264no—
306C2×C4⋊C4—264no—
307C2×C4⋊C4—264no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4—262no—
310C2×C4⋊C4—261no—
311C2×C4⋊C4—262no—
312C2×C4⋊C4—262no—
313C2×C4⋊C4—261no—
314C2×C4⋊C4—261no—
315C2×C4⋊C4—261no—
316C2×C4⋊C4—261no—
317C2×C4⋊C4—261no—
318C2×C4⋊C4—524no—
319C2×C4⋊C4—524no—
320C2×C4⋊C4—524no—
321C2×C4⋊C4C22×D1311yescharacteristic
322C2×C4⋊C4C22×D1312yes—
323C2×C4⋊C4C22×D1311yescharacteristic
324C2×C42—131no—
325C2×C42—131no—
326C2×C42—131no—
327C2×C42—264no—
328C2×C42C22×D1311yescharacteristic
329#107—24no—
330#107—264no—
331#107—264no—
332#107—264no—
333#95—21no—
334#95—261no—
335#95—261no—
336#95—261no—
337C2×C13C2×#39811yescharacteristic
338C2×C13C2×#45911yescharacteristic
339C2×C13C2×#46211yescharacteristic
340C2×C13C2×#48011yescharacteristic
341C2×C13C2×#48411yescharacteristic
342C2×C13C2×#50011yescharacteristic
343C2×C13C2×#50111yescharacteristic
344D13#208318yesdirect product factor
345C24—131no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—131no—
350C22×C4—132no—
351C22×C4—134no—
352C22×C4—134no—
353C22×C4—132no—
354C22×C4—131no—
355C22×C4—131no—
356C22×C4—134no—
357C22×C4—134no—
358C22×C4—262no—
359C22×C4—262no—
360C22×C4—262no—
361C22×C4—262no—
362C22×C4—264no—
363C22×C4—261no—
364C22×C4—261no—
365C22×C4—262no—
366C22×C4—522no—
367C22×C4—522no—
368C22×C4—524no—
369C22×C4—522no—
370C22×C4—524no—
371C22×C4—522no—
372C22×C4—524no—
373C22×C4—522no—
374C22×C4D4×D1311yescharacteristic
375C22×C4D4×D1311yescharacteristic
376C22×C4C23×D1311yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—134no—
380C2×C8—2616no—
381C2×C8—262no—
382C2×C8—262no—
383C2×C8Q8×D1314yes—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—132no—
392C4⋊C4—264no—
393C4⋊C4—261no—
394C4⋊C4—262no—
395C4⋊C4—262no—
396C4⋊C4—262no—
397C4⋊C4—522no—
398C4⋊C4—524no—
399C4⋊C4—522no—
400C4⋊C4—522no—
401C4⋊C4—524no—
402C4⋊C4—522no—
403C4⋊C4—524no—
404C4⋊C4—522no—
405C4⋊C4—522no—
406C4⋊C4D4×D1312yes—
407C42—22no—
408C42—262no—
409C42—262no—
410C42—262no—
411C13C2×#208311yescharacteristic, complemented, Sylow
412C23—132no—
413C23—132no—
414C23—132no—
415C23—132no—
416C23—132no—
417C23—132no—
418C23—132no—
419C23C2×D4×D1311yescharacteristic
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—132no—
434C2×C4—132no—
435C2×C4—132no—
436C2×C4—138no—
437C2×C4—138no—
438C2×C4—132no—
439C2×C4—132no—
440C2×C4—268no—
441C2×C4—268no—
442C2×C4—261no—
443C2×C4—261no—
444C2×C4—261no—
445C2×C4—261no—
446C2×C4—262no—
447C2×C4—528no—
448C2×C4—521no—
449C2×C4—521no—
450C2×C4—521no—
451C2×C4—522no—
452C2×C4—522no—
453C2×C4—521no—
454C2×C4—522no—
455C2×C4—521no—
456C2×C4—1044no—
457C2×C4—1048no—
458C2×C4D8×D1312yes—
459C2×C4Q16×D1312yes—
460C2×C4C2×D4×D1311yescharacteristic
461C2×C4C2×Q8×D1312yes—
462C2×C4#41×D1312yes—
463C2×C4#41×D1311yescharacteristic
464C8—24no—
465C8—264no—
466C22—134no—
467C22—134no—
468C22—134no—
469C22—134no—
470C22—134no—
471C22—134no—
472C22—134no—
473C22D13×#12111yescharacteristic
474C22D13×#12311yescharacteristic
475C22D13×C4⋊Q811yescharacteristic
476C22C2×D8×D1311yescharacteristic
477C22C2×Q16×D1311yescharacteristic
478C22D13×AGL(1,ℤ/8)11yescharacteristic
479C22D13×#13711yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—81no—
484C4—82no—
485C4—134no—
486C4—262no—
487C4—262no—
488C4—522no—
489C4—1041no—
490C4—1042no—
491C4D13×C22⋊Q812yes—
492C4D13×#12512yes—
493C2—138no—
494C2D13×#39811yescharacteristic
495C2D13×#45911yescharacteristic
496C2D13×#46211yescharacteristic
497C2D13×#48011yescharacteristic
498C2D13×#48411yescharacteristic
499C2D13×#50011yescharacteristic
500C2D13×#50111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2083C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenter#2083D13
hypocenterC13C2×#2083
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #13116311C2semidirect
5. #13116310C2semidirect
6. #13116309C2semidirect
7. #13116308C2semidirect
8. #13116307C2semidirect
11. C13×#2083C2semidirect
170. #2083D13direct (N × H)
344. D13#2083direct (N × H)
411. C13C2×#2083semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1072
D13×#3892
D13×#3842
#131163112
#131163102
#131163092
#131163082
#131163072
D13×#3402
D13×#3362
C13×#20832
C2×#208313