Finite Group Databasebeta

← D13×#1740 #15860348

Subgroups — D13×#1740 #15860348

Order 3328.

2350 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#117C212yesmaximal
2C2×D13×#117C211yesmaximal, characteristic
3#13114569C211yesmaximal, characteristic, complemented
4#13114568C212yesmaximal, complemented
5#13114567C214yesmaximal, complemented
6D13×#342C214yesmaximal
7C13×#1740C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
9C2×C13×#117C2212yes—
10C2×C13×#117C2211yescharacteristic
11C2×#88180C2212yes—
12C2×#88180C2211yescharacteristic
13D13×#117—28no—
14D13×#117—22no—
15D13×#117—22no—
16D13×#117—22no—
17D13×#117—22no—
18D13×#117C4116yescomplemented
19C2×#88146—22no—
20C2×#88146C412yescomplemented
21C2×C4⋊C4×D13—22no—
22C2×C4⋊C4×D13C412yescomplemented
23C2×C22⋊C4×D13C2212yes—
24C2×C22⋊C4×D13C2214yes—
25C2×#88131C2212yes—
26C2×#88131C2214yes—
27C2×#88126—22no—
28C2×#88126C412yescomplemented
29C2×C42×D13—22no—
30C2×C42×D13C412yescomplemented
31C13×#342C2214yes—
32#11718119C2218yes—
33#11718118C2214yes—
34C24×D13C2311yescharacteristic
35C23×C4×C13C2311yescharacteristic
36C23×Dic13C2311yescharacteristic
37C22×C4×D13—24no—
38C22×C4×D13C2×C414yes—
39C22×C4×D13C2×C411yescharacteristic
40C22×C4×D13C2×C411yescharacteristic
41C22×C4×D13C2×C411yescharacteristic
42C22×C4×D13C2×C411yescharacteristic
43C22×C4×D13C2×C418yes—
44C22×C4×D13D412yes—
45C22×C4×D13D412yes—
46C22×C4×D13D412yes—
47C22×C4×D13D412yes—
48C22×C4×D13D414yes—
49C22×C4×D13Q814yes—
50C13×#117—24no—
51C13×#117—22no—
52C13×#117—22no—
53C13×#117C2×C418yescomplemented
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4C2×C412yescomplemented
56C2×C13×C22⋊C4C2312yes—
57C2×C13×C22⋊C4C2314yes—
58C2×C42×C13—22no—
59C2×C42×C13C2×C412yescomplemented
60C2×C22⋊Dic13C2312yes—
61C2×C22⋊Dic13C2314yes—
62C2×#6103—24no—
63C2×#6103C2×C414yes—
64#88180—24no—
65#88180—22no—
66#88180—22no—
67#88180C2×C418yescomplemented
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13C2×C412yescomplemented
70C2×#6101—24no—
71C2×#6101C2×C414yescomplemented
72C2×C4×Dic13—22no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13C2×C412yescomplemented
75C2×C4×Dic13C2×C414yescomplemented
76#88146—216no—
77#88146—24no—
78#88146—24no—
79C4⋊C4×D13—216no—
80C4⋊C4×D13—24no—
81C4⋊C4×D13—24no—
82C22⋊C4×D13—24no—
83C22⋊C4×D13—24no—
84C22⋊C4×D13—28no—
85C22⋊C4×D13C2×C4116yes—
86#88131—24no—
87#88131—24no—
88#88131—28no—
89#88131C2×C4116yescomplemented
90#88126—216no—
91#88126—24no—
92#88126—24no—
93C42×D13—216no—
94C42×D13—22no—
95C42×D13—22no—
96C42×D13—22no—
97C42×D13—22no—
98C2×#1740—131nomaximal, Sylow
99C24×C13C2411yescharacteristic
100C23×D13—44no—
101C23×D13C22×C411yescharacteristic
102C23×D13C22×C414yes—
103C23×D13C22×C411yescharacteristic
104C23×D13C2×D412yes—
105C23×D13C2×D412yes—
106C23×D13C2×D412yes—
107C23×D13C2×Q812yes—
108C22×C4×C13—24no—
109C22×C4×C13C22×C414yes—
110C22×C4×C13C22×C411yescharacteristic
111C22×C4×C13C22×C411yescharacteristic
112C22×C4×C13C22×C414yes—
113C22×C4×C13C2×D412yes—
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2×D412yes—
116C22×C4×C13C2×Q812yes—
117C22×Dic13—24no—
118C22×Dic13C22×C414yes—
119C22×Dic13C22×C414yes—
120C22×Dic13C22×C411yescharacteristic
121C22×Dic13C22×C411yescharacteristic
122C22×Dic13C2×D412yes—
123C22×Dic13C2×D412yes—
124C22×Dic13C2×D412yes—
125C22×Dic13C2×Q812yes—
126C2×C4×D13—24no—
127C2×C4×D13—24no—
128C2×C4×D13—216no—
129C2×C4×D13—416no—
130C2×C4×D13—48no—
131C2×C4×D13C4214yes—
132C2×C4×D13C4214yes—
133C2×C4×D13C4214yes—
134C2×C4×D13C4214yes—
135C2×C4×D13C22⋊C418yes—
136C2×C4×D13C22⋊C411yescharacteristic
137C2×C4×D13C22⋊C411yescharacteristic
138C2×C4×D13C22⋊C411yescharacteristic
139C2×C4×D13C22⋊C411yescharacteristic
140C2×C4×D13C22⋊C412yes—
141C2×C4×D13C22⋊C418yes—
142C2×C4×D13C22⋊C412yes—
143C2×C4×D13C22⋊C418yes—
144C2×C4×D13C22⋊C412yes—
145C2×C4×D13C22⋊C412yes—
146C2×C4×D13C22⋊C412yes—
147C2×C4×D13C22⋊C412yes—
148C2×C4×D13C22⋊C418yes—
149C2×C4×D13C4⋊C414yes—
150C2×C4×D13C4⋊C414yes—
151C2×C4×D13C4⋊C418yes—
152C2×C4×D13C4⋊C418yes—
153C2×C4×D13C4⋊C414yes—
154C2×C4×D13C4⋊C414yes—
155C2×C4×D13C4⋊C418yes—
156C2×C4×D13C4⋊C418yes—
157C13×C4⋊C4—28no—
158C13×C4⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4C22×C418yes—
162C42×C13—28no—
163C42×C13—22no—
164C42×C13—22no—
165C22⋊Dic13—24no—
166C22⋊Dic13—24no—
167C22⋊Dic13C22×C418yes—
168#6103—28no—
169#6103—216no—
170C4⋊Dic13—28no—
171C4⋊Dic13—24no—
172#6101—28no—
173#6101—216no—
174C4×Dic13—28no—
175C4×Dic13—22no—
176C4×Dic13—22no—
177C4×Dic13—24no—
178C4×Dic13—24no—
179C4×Dic13—216no—
180C22×#117—131no—
181C22×#117—132no—
182#1740—134no—
183#1740—132no—
184#1740—131no—
185#1740D1311yescharacteristic, direct product factor
186C2×#342—134no—
187C23×C13—42no—
188C23×C13C23×C411yescharacteristic
189C23×C13C23×C412yes—
190C23×C13C22×D412yes—
191C23×C13C22×D411yescharacteristic
192C23×C13C22×Q811yescharacteristic
193C22×D13—24no—
194C22×D13—28no—
195C22×D13—48no—
196C22×D13—44no—
197C22×D13—44no—
198C22×D13—42no—
199C22×D13—44no—
200C22×D13C2×C4212yes—
201C22×D13C2×C4212yes—
202C22×D13C2×C22⋊C412yes—
203C22×D13C2×C22⋊C411yescharacteristic
204C22×D13C2×C22⋊C414yes—
205C22×D13C2×C22⋊C414yes—
206C22×D13C2×C22⋊C411yescharacteristic
207C22×D13C2×C4⋊C412yes—
208C22×D13C2×C4⋊C414yes—
209C22×D13C2×C4⋊C414yes—
210C22×D13C2×C4⋊C412yes—
211C2×C4×C13—24no—
212C2×C4×C13—28no—
213C2×C4×C13—48no—
214C2×C4×C13—44no—
215C2×C4×C13C2×C4212yes—
216C2×C4×C13C2×C4212yes—
217C2×C4×C13C2×C22⋊C414yes—
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C2×C22⋊C414yes—
220C2×C4×C13C2×C22⋊C412yes—
221C2×C4×C13C2×C22⋊C411yescharacteristic
222C2×C4×C13C2×C4⋊C412yes—
223C2×C4×C13C2×C4⋊C412yes—
224C2×C4×C13C2×C4⋊C414yes—
225C2×C4×C13C2×C4⋊C414yes—
226C2×Dic13—24no—
227C2×Dic13—28no—
228C2×Dic13—48no—
229C2×Dic13—44no—
230C2×Dic13C2×C4212yes—
231C2×Dic13C2×C4212yes—
232C2×Dic13C2×C22⋊C414yes—
233C2×Dic13C2×C22⋊C411yescharacteristic
234C2×Dic13C2×C22⋊C411yescharacteristic
235C2×Dic13C2×C22⋊C414yes—
236C2×Dic13C2×C22⋊C412yes—
237C2×Dic13C2×C4⋊C414yes—
238C2×Dic13C2×C4⋊C414yes—
239C2×Dic13C2×C4⋊C412yes—
240C2×Dic13C2×C4⋊C412yes—
241C4×D13—432no—
242C4×D13—48no—
243C4×D13—48no—
244C4×D13#9514yes—
245C4×D13#9518yes—
246C4×D13#9514yes—
247C4×D13#9518yes—
248C4×D13#9518yes—
249C4×D13#9518yes—
250C4×D13#9518yes—
251C4×D13#9514yes—
252C4×D13#9514yes—
253C4×D13#9518yes—
254C24×C4—131no—
255C2×#117—131no—
256C2×#117—132no—
257C2×#117—132no—
258C2×#117—132no—
259C2×#117—132no—
260C2×#117—1316no—
261C2×#117—134no—
262C2×#117—262no—
263C2×#117—262no—
264C2×#117—268no—
265C2×#117—262no—
266C2×#117—262no—
267C2×#117—262no—
268C2×#117—262no—
269C2×#117C2×D1312yes—
270C2×#117C2×D1311yescharacteristic
271C22×C4⋊C4—132no—
272C22×C4⋊C4—262no—
273C22×C22⋊C4—134no—
274C22×C22⋊C4—132no—
275C22×C42—132no—
276C22×C42—262no—
277#342—134no—
278#342—138no—
279#342C2×D1314yes—
280C22×C13—22no—
281C22×C13—24no—
282C22×C13—42no—
283C22×C13—41no—
284C22×C13—41no—
285C22×C13C22×C4211yescharacteristic
286C22×C13C22×C22⋊C412yes—
287C22×C13C22×C22⋊C411yescharacteristic
288C22×C13C22×C4⋊C411yescharacteristic
289C22×C13C22×C4⋊C412yes—
290C2×D13—22no—
291C2×D13—24no—
292C2×D13—28no—
293C2×D13—24no—
294C2×D13—24no—
295C2×D13—28no—
296C2×D13—42no—
297C2×D13—44no—
298C2×D13—44no—
299C2×D13—42no—
300C2×D13C2×#9512yes—
301C2×D13C2×#9514yes—
302C2×D13C2×#9512yes—
303C2×D13#41014yes—
304C4×C13—48no—
305C4×C13—44no—
306C4×C13C2×#9512yes—
307C4×C13C2×#9514yes—
308C4×C13C2×#9512yes—
309Dic13—48no—
310Dic13—44no—
311Dic13C2×#9512yes—
312Dic13C2×#9512yes—
313Dic13C2×#9514yes—
314C25—131no—
315C23×C4—131no—
316C23×C4—131no—
317C23×C4—131no—
318C23×C4—131no—
319C23×C4—138no—
320C23×C4—131no—
321C23×C4—132no—
322C23×C4—132no—
323C23×C4—132no—
324C23×C4—134no—
325C23×C4—132no—
326C23×C4—134no—
327C23×C4—134no—
328C23×C4—264no—
329C23×C4C22×D1311yescharacteristic
330#117—24no—
331#117—22no—
332#117—22no—
333#117—138no—
334#117—1316no—
335#117—2616no—
336#117—264no—
337#117—264no—
338#117—264no—
339#117—264no—
340#117—268no—
341#117—264no—
342#117—264no—
343#117—2616no—
344#117—262no—
345#117—264no—
346#117—262no—
347#117C4×D1318yescomplemented
348C2×C4⋊C4—22no—
349C2×C4⋊C4—134no—
350C2×C4⋊C4—132no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—2616no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4C4×D1312yescomplemented
357C2×C22⋊C4—134no—
358C2×C22⋊C4—1316no—
359C2×C22⋊C4—132no—
360C2×C22⋊C4—134no—
361C2×C22⋊C4—268no—
362C2×C22⋊C4—264no—
363C2×C22⋊C4—264no—
364C2×C22⋊C4—264no—
365C2×C22⋊C4C22×D1312yes—
366C2×C22⋊C4C22×D1314yes—
367C2×C42—22no—
368C2×C42—134no—
369C2×C42—132no—
370C2×C42—2616no—
371C2×C42—262no—
372C2×C42—262no—
373C2×C42—262no—
374C2×C42—262no—
375C2×C42—264no—
376C2×C42—262no—
377C2×C42C4×D1312yescomplemented
378C2×C13—22no—
379C2×C13—21no—
380C2×C13—22no—
381C2×C13—21no—
382C2×C13C22×#9511yescharacteristic
383C2×C13C2×#41012yes—
384D13—22no—
385D13—24no—
386D13#174014yesdirect product factor
387C24—131no—
388C24—132no—
389C24—134no—
390C24—131no—
391C24—132no—
392C24—132no—
393C24—132no—
394C24—524no—
395C24C23×D1311yescharacteristic
396C22×C4—24no—
397C22×C4—131no—
398C22×C4—131no—
399C22×C4—134no—
400C22×C4—132no—
401C22×C4—132no—
402C22×C4—132no—
403C22×C4—132no—
404C22×C4—134no—
405C22×C4—134no—
406C22×C4—134no—
407C22×C4—134no—
408C22×C4—131no—
409C22×C4—138no—
410C22×C4—131no—
411C22×C4—132no—
412C22×C4—132no—
413C22×C4—138no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—138no—
417C22×C4—132no—
418C22×C4—138no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—132no—
422C22×C4—134no—
423C22×C4—138no—
424C22×C4—138no—
425C22×C4—134no—
426C22×C4—134no—
427C22×C4—134no—
428C22×C4—138no—
429C22×C4—138no—
430C22×C4—134no—
431C22×C4—2616no—
432C22×C4—264no—
433C22×C4—264no—
434C22×C4—264no—
435C22×C4—5216no—
436C22×C4—528no—
437C22×C4C2×C4×D1314yes—
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4C2×C4×D1314yes—
440C22×C4C2×C4×D1311yescharacteristic
441C22×C4D4×D1312yes—
442C22×C4D4×D1312yes—
443C22×C4D4×D1312yes—
444C22×C4Q8×D1312yes—
445C4⋊C4—28no—
446C4⋊C4—24no—
447C4⋊C4—268no—
448C4⋊C4—2616no—
449C4⋊C4—264no—
450C4⋊C4—268no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—138no—
454C22⋊C4—268no—
455C22⋊C4—2616no—
456C22⋊C4—264no—
457C22⋊C4—264no—
458C22⋊C4C2×C4×D1318yes—
459C42—28no—
460C42—22no—
461C42—22no—
462C42—264no—
463C42—264no—
464C42—2616no—
465C42—262no—
466C42—268no—
467C42—262no—
468C13C2×#174011yescharacteristic, complemented, Sylow
469C23—42no—
470C23—131no—
471C23—132no—
472C23—132no—
473C23—134no—
474C23—131no—
475C23—132no—
476C23—134no—
477C23—132no—
478C23—134no—
479C23—134no—
480C23—132no—
481C23—264no—
482C23—268no—
483C23—522no—
484C23—524no—
485C23—528no—
486C23—524no—
487C23—524no—
488C23C22×C4×D1311yescharacteristic
489C23C22×C4×D1312yes—
490C23C2×D4×D1312yes—
491C23C2×D4×D1311yescharacteristic
492C23C2×Q8×D1311yescharacteristic
493C2×C4—24no—
494C2×C4—28no—
495C2×C4—48no—
496C2×C4—44no—
497C2×C4—132no—
498C2×C4—132no—
499C2×C4—134no—
500C2×C4—131no—
501C2×C4—131no—
502C2×C4—134no—
503C2×C4—132no—
504C2×C4—132no—
505C2×C4—132no—
506C2×C4—134no—
507C2×C4—134no—
508C2×C4—138no—
509C2×C4—134no—
510C2×C4—134no—
511C2×C4—138no—
512C2×C4—138no—
513C2×C4—138no—
514C2×C4—138no—
515C2×C4—134no—
516C2×C4—138no—
517C2×C4—134no—
518C2×C4—268no—
519C2×C4—264no—
520C2×C4—528no—
521C2×C4—5232no—
522C2×C4—528no—
523C2×C4—528no—
524C2×C4—524no—
525C2×C4C42×D1312yes—
526C2×C4C42×D1312yes—
527C2×C4C22⋊C4×D1311yescharacteristic
528C2×C4C22⋊C4×D1314yes—
529C2×C4C22⋊C4×D1314yes—
530C2×C4C22⋊C4×D1312yes—
531C2×C4C22⋊C4×D1311yescharacteristic
532C2×C4C4⋊C4×D1312yes—
533C2×C4C4⋊C4×D1314yes—
534C2×C4C4⋊C4×D1314yes—
535C2×C4C4⋊C4×D1312yes—
536C22—22no—
537C22—24no—
538C22—42no—
539C22—41no—
540C22—41no—
541C22—134no—
542C22—132no—
543C22—132no—
544C22—134no—
545C22—268no—
546C22—264no—
547C22—264no—
548C22—268no—
549C22—262no—
550C22—264no—
551C22—524no—
552C22—522no—
553C22—522no—
554C22—524no—
555C22C2×C42×D1311yescharacteristic
556C22C2×C22⋊C4×D1312yes—
557C22C2×C22⋊C4×D1311yescharacteristic
558C22C2×C4⋊C4×D1311yescharacteristic
559C22C2×C4⋊C4×D1312yes—
560C4—48no—
561C4—44no—
562C4—132no—
563C4—132no—
564C4—134no—
565C4—528no—
566C4—524no—
567C4D13×#9514yes—
568C4D13×#9512yes—
569C4D13×#9512yes—
570C2—22no—
571C2—21no—
572C2—21no—
573C2—22no—
574C2—134no—
575C2—264no—
576C2—262no—
577C2C2×D13×#9511yescharacteristic
578C2D13×#41012yes—
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC13×#1740C2
socleC22×C13C22×C22⋊C4
prime radicalC24×D13C23
cosocleC24×C13C24
hypercenter#1740D13
hypocenterC13C2×#1740
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
3. #13114569C2semidirect
4. #13114568C2semidirect
5. #13114567C2semidirect
7. C13×#1740C2semidirect
18. D13×#117C4semidirect
20. C2×#88146C4semidirect
22. C2×C4⋊C4×D13C4semidirect
28. C2×#88126C4semidirect
30. C2×C42×D13C4semidirect
53. C13×#117C2×C4semidirect
55. C2×C13×C4⋊C4C2×C4semidirect
59. C2×C42×C13C2×C4semidirect
67. #88180C2×C4semidirect
69. C2×C4⋊Dic13C2×C4semidirect
71. C2×#6101C2×C4semidirect
74. C2×C4×Dic13C2×C4semidirect
75. C2×C4×Dic13C2×C4semidirect
89. #88131C2×C4semidirect
185. #1740D13direct (N × H)
347. #117C4×D13semidirect
356. C2×C4⋊C4C4×D13semidirect
377. C2×C42C4×D13semidirect
386. D13#1740direct (N × H)
468. C13C2×#1740semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1172
#131145692
#131145682
#131145672
D13×#3422
C13×#17402
C2×#174013