Finite Group Databasebeta

← C2×D13×#475 #16730392

Subgroups — C2×D13×#475 #16730392

Order 3328.

2358 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2C2×C4×Q8×D13C211yesmaximal, characteristic
3C2×#11718512C211yesmaximal, characteristic, complemented
4C2×#11718681C211yesmaximal, characteristic, complemented
5C2×#11718515C212yesmaximal, complemented
6C2×#11718452C212yesmaximal, complemented
7C2×#11718755C211yesmaximal, characteristic, complemented
8D13×#475C2116yesmaximal, direct product factor
9C2×D13×#106C212yesmaximal
10C2×D13×C4⋊C8C211yesmaximal, characteristic
11C2×D13×#103C212yesmaximal
12C2×C13×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C22×Q8×D13C2211yescharacteristic
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×#88198—21no—
19C22×C8×D13C2212yes—
20D13×C4⋊Q8—24no—
21D13×C4⋊Q8C2218yes—
22C4×Q8×D13—24no—
23C4×Q8×D13C2218yes—
24C2×C4⋊C4×D13—21no—
25C2×C4⋊C4×D13—21no—
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×C4⋊C4×D13C2212yes—
28C2×#88142—21no—
29C2×#88142C2212yes—
30C2×#88141—21no—
31C2×#88141C2211yescharacteristic
32C2×C42×D13—21no—
33C2×C42×D13C2211yescharacteristic
34C2×#88123C2211yescharacteristic
35C2×C4×Dic26—21no—
36C2×C4×Dic26C2211yescharacteristic
37C13×#475C2218yescomplemented
38C2×C13×#106C2212yes—
39C2×C13×C4⋊C8C2211yescharacteristic
40C2×C13×#103C2212yes—
41C2×#88075C2212yes—
42C2×#88057C2212yes—
43C2×#88056C2212yes—
44C2×#88054C2212yes—
45#11718755C2218yescomplemented
46#11718681C2218yescomplemented
47C2×#88050C2212yes—
48C2×#88048C2212yes—
49C2×#88048C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51D13×#106C22116yes—
52#11718515C22116yescomplemented
53#11718512C2218yescomplemented
54D13×C4⋊C8C2218yes—
55D13×#103C22116yes—
56#11718452C22116yescomplemented
57C22×Q8×C13—21no—
58C22×Q8×C13C2311yescharacteristic
59C2×Q8×D13—22no—
60C2×Q8×D13—28no—
61C2×Q8×D13—24no—
62C2×Q8×D13—48no—
63C2×Q8×D13Q818yescomplemented
64C2×Q8×D13C2314yes—
65C22×C4×D13—21no—
66C22×C4×D13—21no—
67C22×C4×D13—22no—
68C22×C4×D13D411yescharacteristic
69C22×C4×D13D411yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C22×Dic26—21no—
72C22×Dic26—21no—
73C22×Dic26—22no—
74C22×Dic26C2311yescharacteristic
75C22×C8×C13C2312yes—
76C13×C4⋊Q8—22no—
77C13×C4⋊Q8C2314yes—
78C4×Q8×C13—22no—
79C4×Q8×C13C2314yes—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2312yes—
84C2×C42×C13—21no—
85C2×C42×C13C2311yescharacteristic
86Q8×Dic13—22no—
87Q8×Dic13C2314yes—
88#88198—28no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2312yes—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13D411yescharacteristic
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C22×#1055C2312yes—
105C2×C8×D13—28no—
106C2×C8×D13C2318yes—
107C4⋊C4×D13—24no—
108C4⋊C4×D13—28no—
109C4⋊C4×D13—28no—
110C4⋊C4×D13—22no—
111C4⋊C4×D13C2318yes—
112C4⋊C4×D13C2314yes—
113#88142—24no—
114#88142—28no—
115#88142C2318yes—
116#88141—28no—
117#88141—22no—
118#88141C2314yes—
119C42×D13—28no—
120C42×D13D414yes—
121C42×D13C2314yes—
122#88123—22no—
123#88123C2314yes—
124C4×Dic26—22no—
125C4×Dic26—28no—
126C4×Dic26C2314yes—
127C13×#106C2318yes—
128C13×C4⋊C8C2314yes—
129C13×#103C2318yes—
130#88075C2318yes—
131#88057C2318yes—
132#88056C2318yes—
133#88054C2318yes—
134#88050C2318yes—
135#88048C2318yes—
136#88048C2318yes—
137C4⋊#1055C2314yes—
138C22×#475—131nomaximal, Sylow
139C23×D13C2×D411yescharacteristic
140C2×Q8×C13—21no—
141C2×Q8×C13—24no—
142C2×Q8×C13—22no—
143C2×Q8×C13—44no—
144C2×Q8×C13C2×Q814yescomplemented
145C2×Q8×C13C2412yes—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C22×Dic13C2×D411yescharacteristic
158Q8×D13—216no—
159Q8×D13—28no—
160Q8×D13—432no—
161Q8×D13C2×Q8116yescomplemented
162C2×C4×D13—28no—
163C2×C4×D13—24no—
164C2×C4×D13—24no—
165C2×C4×D13—24no—
166C2×C4×D13—28no—
167C2×C4×D13—48no—
168C2×C4×D13—44no—
169C2×C4×D13SD1618yes—
170C2×C4×D13C2×D414yes—
171C2×C4×D13C2×D412yes—
172C2×C4×D13C2×D414yes—
173C2×C4×D13C2×Q814yes—
174C2×C4×D13#4114yes—
175C2×C4×D13C2412yes—
176C2×Dic26—21no—
177C2×Dic26—22no—
178C2×Dic26—28no—
179C2×Dic26—24no—
180C2×Dic26—24no—
181C2×Dic26—28no—
182C2×Dic26—44no—
183C2×Dic26—48no—
184C2×Dic26C2×Q814yescomplemented
185C2×Dic26C2412yes—
186C2×C8×C13—24no—
187C2×C8×C13C2414yes—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—24no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4C2414yes—
193C13×C4⋊C4C2412yes—
194C42×C13—24no—
195C42×C13C2×D412yes—
196C42×C13C2412yes—
197C4⋊Dic13—21no—
198C4⋊Dic13—22no—
199C4⋊Dic13—24no—
200C4⋊Dic13—24no—
201C4⋊Dic13C2414yes—
202C4⋊Dic13C2412yes—
203#6101—24no—
204#6101—24no—
205#6101—24no—
206#6101—28no—
207#6101—28no—
208C4×Dic13—24no—
209C4×Dic13—24no—
210C4×Dic13—24no—
211C4×Dic13C2×D414yes—
212C4×Dic13C2×D412yes—
213C4×Dic13C2×D414yes—
214C4×Dic13C2412yes—
215C2×#1055—24no—
216C2×#1055C2414yes—
217C8×D13—216no—
218C22×C4⋊Q8—131no—
219C22×C4×Q8—131no—
220C2×#475—1316no—
221C2×#475—132no—
222C2×#475—131no—
223C2×#475—132no—
224C2×#475—131no—
225C2×#475—131no—
226C2×#475D1311yescharacteristic, direct product factor
227C22×#106—132no—
228C22×C4⋊C8—131no—
229C22×#103—132no—
230C23×C13C22×D411yescharacteristic
231C22×D13C22⋊Q814yes—
232C22×D13C2×SD1614yes—
233C22×D13#13714yes—
234C22×D13C22×D412yes—
235Q8×C13—24no—
236Q8×C13—22no—
237Q8×C13—48no—
238Q8×C13C22×Q814yescomplemented
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—24no—
244C2×C4×C13—44no—
245C2×C4×C13—42no—
246C2×C4×C13C2×SD1614yes—
247C2×C4×C13C22×D412yes—
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C22×D412yes—
250C2×C4×C13C22×Q812yes—
251C2×C4×C13C2×#4112yes—
252C2×C4×C13C2511yescharacteristic
253C2×Dic13—24no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—24no—
258C2×Dic13—44no—
259C2×Dic13—42no—
260C2×Dic13C22⋊Q814yes—
261C2×Dic13C2×SD1614yes—
262C2×Dic13C22×D412yes—
263C2×Dic13C22×D412yes—
264C2×Dic13C22×D412yes—
265C4×D13—216no—
266C4×D13—28no—
267C4×D13—416no—
268C4×D13—48no—
269C4×D13C22⋊Q818yes—
270C4×D13C2×SD16116yes—
271C4×D13C22×Q814yes—
272C4×D13C2×#4114yes—
273Dic26—24no—
274Dic26—22no—
275Dic26—216no—
276Dic26—48no—
277Dic26—416no—
278Dic26C22×Q814yescomplemented
279C8×C13—24no—
280#1055—24no—
281C23×Q8—131no—
282C23×Q8—261no—
283C23×C8—132no—
284C2×C4⋊Q8—138no—
285C2×C4⋊Q8—132no—
286C2×C4⋊Q8—131no—
287C2×C4⋊Q8—261no—
288C2×C4⋊Q8—264no—
289C2×C4⋊Q8—261no—
290C2×C4⋊Q8C2×D1311yescharacteristic
291C2×C4×Q8—131no—
292C2×C4×Q8—138no—
293C2×C4×Q8—131no—
294C2×C4×Q8—131no—
295C2×C4×Q8—261no—
296C2×C4×Q8—261no—
297C2×C4×Q8—264no—
298C2×C4×Q8C2×D1311yescharacteristic
299C22×C4⋊C4—132no—
300C22×C4⋊C4—131no—
301C22×C4⋊C4—261no—
302C22×C4⋊C4—261no—
303C22×C42—131no—
304C22×C42—261no—
305#475—138no—
306#475—138no—
307#475—1316no—
308#475—138no—
309#475—1316no—
310#475C2×D1318yesdirect product factor
311C2×#106—132no—
312C2×#106—132no—
313C2×#106—132no—
314C2×#106—1316no—
315C2×#106C2×D1312yes—
316C2×C4⋊C8—132no—
317C2×C4⋊C8—131no—
318C2×C4⋊C8—138no—
319C2×C4⋊C8C2×D1311yescharacteristic
320C2×#103—132no—
321C2×#103—132no—
322C2×#103—132no—
323C2×#103—1316no—
324C2×#103C2×D1312yes—
325C22×C13C2×C22⋊Q812yes—
326C22×C13C22×SD1612yes—
327C22×C13C2×#13712yes—
328C22×C13C23×D411yescharacteristic
329C2×D13#475116yesdirect product factor
330C2×D13C2×C22⋊Q814yes—
331C2×D13C22×SD1614yes—
332C2×D13C2×#13714yes—
333C4×C13—24no—
334C4×C13—22no—
335C4×C13—44no—
336C4×C13—42no—
337C4×C13C2×C22⋊Q812yes—
338C4×C13C22×SD1614yes—
339C4×C13C23×Q811yescharacteristic
340C4×C13C22×#4111yescharacteristic
341Dic13—24no—
342Dic13—22no—
343Dic13—44no—
344Dic13—42no—
345Dic13C2×C22⋊Q814yes—
346Dic13C22×SD1614yes—
347C22×Q8—21no—
348C22×Q8—138no—
349C22×Q8—134no—
350C22×Q8—131no—
351C22×Q8—261no—
352C22×Q8—262no—
353C22×Q8—262no—
354C22×Q8—264no—
355C22×Q8—268no—
356C22×Q8—261no—
357C22×Q8—528no—
358C22×Q8C22×D1311yescharacteristic
359C23×C4—131no—
360C23×C4—131no—
361C23×C4—131no—
362C23×C4—261no—
363C23×C4—262no—
364C23×C4—261no—
365C22×C8—132no—
366C22×C8—138no—
367C22×C8—268no—
368C22×C8C22×D1312yes—
369C4⋊Q8—22no—
370C4⋊Q8—138no—
371C4⋊Q8—134no—
372C4⋊Q8—268no—
373C4⋊Q8—264no—
374C4⋊Q8—268no—
375C4⋊Q8—262no—
376C4⋊Q8C22×D1314yes—
377C4×Q8—22no—
378C4×Q8—134no—
379C4×Q8—134no—
380C4×Q8—134no—
381C4×Q8—268no—
382C4×Q8—268no—
383C4×Q8—262no—
384C4×Q8—262no—
385C4×Q8—262no—
386C4×Q8C22×D1314yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—132no—
391C2×C4⋊C4—134no—
392C2×C4⋊C4—138no—
393C2×C4⋊C4—262no—
394C2×C4⋊C4—264no—
395C2×C4⋊C4—268no—
396C2×C4⋊C4—268no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—262no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C4⋊C4C22×D1312yes—
406C2×C42—21no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—131no—
410C2×C42—134no—
411C2×C42—134no—
412C2×C42—268no—
413C2×C42—261no—
414C2×C42—261no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417#106—138no—
418#106—138no—
419#106—138no—
420#106C22×D1318yes—
421C4⋊C8—138no—
422C4⋊C8—134no—
423C4⋊C8C22×D1314yes—
424#103—138no—
425#103—138no—
426#103—138no—
427#103C22×D1318yes—
428C2×C13C2×#47514yescomplemented
429C2×C13C22×C22⋊Q811yescharacteristic
430C2×C13C23×SD1611yescharacteristic
431C2×C13C22×#13711yescharacteristic
432D13C2×#47518yesdirect product factor
433C24—131no—
434C2×Q8—21no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—44no—
438C2×Q8—1316no—
439C2×Q8—134no—
440C2×Q8—132no—
441C2×Q8—264no—
442C2×Q8—268no—
443C2×Q8—268no—
444C2×Q8—2616no—
445C2×Q8—268no—
446C2×Q8—261no—
447C2×Q8—264no—
448C2×Q8—262no—
449C2×Q8—528no—
450C2×Q8—5232no—
451C2×Q8—524no—
452C2×Q8Q8×D1314yescomplemented
453C2×Q8C23×D1312yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—138no—
460C22×C4—134no—
461C22×C4—132no—
462C22×C4—134no—
463C22×C4—134no—
464C22×C4—132no—
465C22×C4—131no—
466C22×C4—134no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—268no—
470C22×C4—264no—
471C22×C4—268no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—262no—
475C22×C4—528no—
476C22×C4—524no—
477C22×C4D4×D1311yescharacteristic
478C22×C4D4×D1311yescharacteristic
479C22×C4C23×D1311yescharacteristic
480C2×C8—24no—
481C2×C8—134no—
482C2×C8—2616no—
483C2×C8—264no—
484C2×C8C23×D1314yes—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—134no—
490C4⋊C4—132no—
491C4⋊C4—264no—
492C4⋊C4—268no—
493C4⋊C4—264no—
494C4⋊C4—264no—
495C4⋊C4—268no—
496C4⋊C4—261no—
497C4⋊C4—262no—
498C4⋊C4—264no—
499C4⋊C4—264no—
500C4⋊C4C23×D1314yes—
501C4⋊C4C23×D1312yes—
502C42—24no—
503C42—134no—
504C42—132no—
505C42—134no—
506C42—132no—
507C42—264no—
508C42—264no—
509C42—264no—
510C42D4×D1312yes—
511C42C23×D1312yes—
512C13C22×#47511yescharacteristic, complemented, Sylow
513C23—134no—
514C23—134no—
515C23—134no—
516C23—132no—
517C23C2×D4×D1311yescharacteristic
518Q8—24no—
519Q8—22no—
520Q8—48no—
521Q8—134no—
522Q8—2616no—
523Q8—264no—
524Q8—262no—
525Q8—5216no—
526Q8—528no—
527Q8C2×Q8×D1314yescomplemented
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—134no—
536C2×C4—134no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—1316no—
540C2×C4—138no—
541C2×C4—134no—
542C2×C4—134no—
543C2×C4—132no—
544C2×C4—268no—
545C2×C4—2616no—
546C2×C4—262no—
547C2×C4—264no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—264no—
551C2×C4—528no—
552C2×C4—5216no—
553C2×C4—524no—
554C2×C4—522no—
555C2×C4SD16×D1314yes—
556C2×C4C2×D4×D1312yes—
557C2×C4C2×D4×D1312yes—
558C2×C4C2×D4×D1311yescharacteristic
559C2×C4C2×Q8×D1312yes—
560C2×C4#41×D1312yes—
561C2×C4C24×D1311yescharacteristic
562C8—24no—
563C8—264no—
564C22—134no—
565C22—134no—
566C22—134no—
567C22—1316no—
568C22D13×C22⋊Q812yes—
569C22C2×SD16×D1312yes—
570C22D13×#13712yes—
571C22C22×D4×D1311yescharacteristic
572C4—22no—
573C4—24no—
574C4—44no—
575C4—42no—
576C4—134no—
577C4—134no—
578C4—262no—
579C4—264no—
580C4—524no—
581C4—522no—
582C4D13×C22⋊Q812yes—
583C4C2×SD16×D1314yes—
584C4C22×Q8×D1311yescharacteristic
585C4C2×#41×D1311yescharacteristic
586C2—138no—
587C2D13×#47514yesdirect product factor
588C2C2×D13×C22⋊Q811yescharacteristic
589C2C22×SD16×D1311yescharacteristic
590C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#475C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#475D13
hypocenterC13C22×#475
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. C2×#11718512C2semidirect
4. C2×#11718681C2semidirect
5. C2×#11718515C2semidirect
6. C2×#11718452C2semidirect
7. C2×#11718755C2semidirect
8. D13×#475C2direct (N × H)
12. C2×C13×#475C2semidirect
37. C13×#475C22semidirect
45. #11718755C22semidirect
46. #11718681C22semidirect
52. #11718515C22semidirect
53. #11718512C22semidirect
56. #11718452C22semidirect
63. C2×Q8×D13Q8semidirect
144. C2×Q8×C13C2×Q8semidirect
161. Q8×D13C2×Q8semidirect
184. C2×Dic26C2×Q8semidirect
226. C2×#475D13direct (N × H)
238. Q8×C13C22×Q8semidirect
278. Dic26C22×Q8semidirect
310. #475C2×D13direct (N × H)
329. C2×D13#475direct (N × H)
428. C2×C13C2×#475semidirect
432. D13C2×#475direct (N × H)
452. C2×Q8Q8×D13semidirect
512. C13C22×#475semidirect
527. Q8C2×Q8×D13semidirect
587. C2D13×#475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
C2×C4×Q8×D132
C2×#117185122
C2×#117186812
C2×#117185152
C2×#117184522
C2×#117187552
D13×#4752
C2×D13×#1062
C2×D13×C4⋊C82
C2×D13×#1032
C2×C13×#4752
C22×#47513