Finite Group Databasebeta

← C2×D13×#501 #16732525

Subgroups — C2×D13×#501 #16732525

Order 3328.

2142 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2C2×D13×#125C211yesmaximal, characteristic
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718363C211yesmaximal, characteristic, complemented
5C2×#11718537C212yesmaximal, complemented
6C2×#11718517C212yesmaximal, complemented
7C2×#11718741C211yesmaximal, characteristic, complemented
8D13×#501C2116yesmaximal, direct product factor
9C2×D13×#107C212yesmaximal
10C2×D13×#106C212yesmaximal
11C2×D13×#97C211yesmaximal, characteristic
12C2×C13×#501C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×#88198—21no—
17C22×C8×D13C2212yes—
18D13×C4⋊Q8—24no—
19D13×C4⋊Q8C2218yes—
20D13×#125—24no—
21D13×#125C2218yes—
22C2×C4⋊C4×D13—21no—
23C2×C4⋊C4×D13—21no—
24C2×C4⋊C4×D13—21no—
25C2×C4⋊C4×D13C2211yescharacteristic
26C2×C4⋊C4×D13C2212yes—
27C2×C4⋊C4×D13C2211yescharacteristic
28C2×#88144C2211yescharacteristic
29C2×#88144C2211yescharacteristic
30C2×#88143—21no—
31C2×#88143—21no—
32C2×#88142—21no—
33C2×#88142C2212yes—
34C2×C42×D13C2211yescharacteristic
35C2×#88124C2211yescharacteristic
36C2×#88123C2211yescharacteristic
37C13×#501C2218yescomplemented
38C2×C13×#107C2212yes—
39C2×C13×#106C2212yes—
40C2×C13×#97C2211yescharacteristic
41C2×#88058C2212yes—
42C2×#88057C2212yes—
43C2×#88055C2212yes—
44#11718741C2218yescomplemented
45#11718726C2218yescomplemented
46C2×#88048C2212yes—
47C2×#88048C2212yes—
48C2×#88047C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51D13×#107C22116yes—
52#11718537C22116yescomplemented
53D13×#106C22116yes—
54#11718517C22116yescomplemented
55D13×#97C2218yes—
56#11718363C2218yescomplemented
57C22×Q8×C13—21no—
58C2×Q8×D13—28no—
59C2×Q8×D13—48no—
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13—22no—
63C22×C4×D13D411yescharacteristic
64C22×C4×D13D411yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C22×Dic26—21no—
67C22×Dic26—22no—
68C22×C8×C13C2312yes—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8C2314yes—
71C13×#125—22no—
72C13×#125C2314yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80#88198—28no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2312yes—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—22no—
90C2×#6101—22no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2312yes—
99C2×C8×D13Q8116yescomplemented
100C2×C8×D13C2318yes—
101C4⋊C4×D13—24no—
102C4⋊C4×D13—28no—
103C4⋊C4×D13—28no—
104C4⋊C4×D13—28no—
105C4⋊C4×D13—22no—
106C4⋊C4×D13—22no—
107C4⋊C4×D13C2318yes—
108C4⋊C4×D13C2314yes—
109C4⋊C4×D13C2314yes—
110#88144—22no—
111#88144—22no—
112#88144C2314yes—
113#88144C2314yes—
114#88143—28no—
115#88143—28no—
116#88142—24no—
117#88142—28no—
118#88142C2318yes—
119C42×D13D414yes—
120C42×D13C2314yes—
121#88124—22no—
122#88124C2314yes—
123#88123—22no—
124#88123C2314yes—
125C13×#107C2318yes—
126C13×#106C2318yes—
127C13×#97C2314yes—
128#88058C2318yes—
129#88057C2318yes—
130#88055C2318yes—
131#88048C2318yes—
132#88048C2318yes—
133#88047C2318yes—
134#88047C2318yes—
135#88043C2314yes—
136C22×#501—131nomaximal, Sylow
137C23×D13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—44no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152Q8×D13—432no—
153C2×C4×D13—24no—
154C2×C4×D13—24no—
155C2×C4×D13—24no—
156C2×C4×D13—24no—
157C2×C4×D13—28no—
158C2×C4×D13—44no—
159C2×C4×D13—48no—
160C2×C4×D13—44no—
161C2×C4×D13C2×D414yes—
162C2×C4×D13C2×D414yes—
163C2×C4×D13C2×D412yes—
164C2×C4×D13C2×Q818yes—
165C2×C4×D13C2412yes—
166C2×Dic26—24no—
167C2×Dic26—28no—
168C2×Dic26—48no—
169C2×Dic26—44no—
170C2×C8×C13C2×Q818yescomplemented
171C2×C8×C13C2414yes—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—24no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C2412yes—
179C13×C4⋊C4C2414yes—
180C13×C4⋊C4C2412yes—
181C42×C13C2×D412yes—
182C42×C13C2412yes—
183C4⋊Dic13—22no—
184C4⋊Dic13—24no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—24no—
188C4⋊Dic13—24no—
189C4⋊Dic13C2414yes—
190C4⋊Dic13C2412yes—
191C4⋊Dic13C2412yes—
192#6101—24no—
193#6101—24no—
194#6101—28no—
195#6101—28no—
196#6101—24no—
197#6101—24no—
198#6101—24no—
199#6101—24no—
200C4×Dic13C2×D412yes—
201C4×Dic13C2×D414yes—
202C4×Dic13C2×D414yes—
203C4×Dic13C2412yes—
204C2×#1055C2×Q818yescomplemented
205C2×#1055C2414yes—
206C8×D13C2×Q8132yescomplemented
207C22×C4⋊Q8—131no—
208C22×#125—131no—
209C2×#501—1316no—
210C2×#501—132no—
211C2×#501—132no—
212C2×#501—131no—
213C2×#501—131no—
214C2×#501—131no—
215C2×#501D1311yescharacteristic, direct product factor
216C22×#107—132no—
217C22×#106—132no—
218C22×#97—131no—
219C23×C13C22×D411yescharacteristic
220C22×D13C4⋊Q814yes—
221C22×D13AGL(1,ℤ/8)14yes—
222C22×D13#13714yes—
223C22×D13C22×D412yes—
224Q8×C13—48no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—44no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13C22×D412yes—
234C2×C4×C13C22×D412yes—
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C22×Q814yes—
237C2×C4×C13C2511yescharacteristic
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—24no—
243C2×Dic13—44no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13C4⋊Q814yes—
247C2×Dic13C22×D412yes—
248C2×Dic13C22×D412yes—
249C2×Dic13C22×D412yes—
250C4×D13—28no—
251C4×D13—28no—
252C4×D13—48no—
253C4×D13—416no—
254C4×D13—48no—
255C4×D13C4⋊Q818yes—
256C4×D13C22×Q818yes—
257Dic26—416no—
258Dic26—48no—
259C8×C13C22×Q818yescomplemented
260#1055C22×Q818yescomplemented
261C23×Q8—261no—
262C23×C8—132no—
263C2×C4⋊Q8—138no—
264C2×C4⋊Q8—132no—
265C2×C4⋊Q8—131no—
266C2×C4⋊Q8—261no—
267C2×C4⋊Q8—264no—
268C2×C4⋊Q8—261no—
269C2×C4⋊Q8C2×D1311yescharacteristic
270C2×#125—138no—
271C2×#125—131no—
272C2×#125—131no—
273C2×#125—131no—
274C2×#125—261no—
275C2×#125—261no—
276C2×#125—264no—
277C2×#125C2×D1311yescharacteristic
278C22×C4⋊C4—131no—
279C22×C4⋊C4—132no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—261no—
282C22×C4⋊C4—261no—
283C22×C4⋊C4—261no—
284C22×C42—131no—
285#501—138no—
286#501—138no—
287#501—1316no—
288#501—1316no—
289#501—138no—
290#501C2×D1318yesdirect product factor
291C2×#107—132no—
292C2×#107—132no—
293C2×#107—132no—
294C2×#107—1316no—
295C2×#107C2×D1312yes—
296C2×#106—132no—
297C2×#106—132no—
298C2×#106—132no—
299C2×#106—1316no—
300C2×#106C2×D1312yes—
301C2×#97—132no—
302C2×#97—131no—
303C2×#97—138no—
304C2×#97C2×D1311yescharacteristic
305C22×C13C2×C4⋊Q812yes—
306C22×C13C2×AGL(1,ℤ/8)12yes—
307C22×C13C2×#13712yes—
308C22×C13C23×D411yescharacteristic
309C2×D13#501116yesdirect product factor
310C2×D13C2×C4⋊Q814yes—
311C2×D13C2×AGL(1,ℤ/8)14yes—
312C2×D13C2×#13714yes—
313C4×C13—22no—
314C4×C13—22no—
315C4×C13—44no—
316C4×C13—42no—
317C4×C13—42no—
318C4×C13C2×C4⋊Q812yes—
319C4×C13C23×Q812yes—
320Dic13—22no—
321Dic13—22no—
322Dic13—44no—
323Dic13—42no—
324Dic13—42no—
325Dic13C2×C4⋊Q814yes—
326C22×Q8—21no—
327C22×Q8—262no—
328C22×Q8—268no—
329C22×Q8—261no—
330C22×Q8—528no—
331C23×C4—131no—
332C23×C4—131no—
333C23×C4—131no—
334C23×C4—261no—
335C23×C4—261no—
336C23×C4—262no—
337C22×C8—132no—
338C22×C8—1316no—
339C22×C8—138no—
340C22×C8C22×D1312yes—
341C4⋊Q8—22no—
342C4⋊Q8—138no—
343C4⋊Q8—134no—
344C4⋊Q8—268no—
345C4⋊Q8—264no—
346C4⋊Q8—268no—
347C4⋊Q8—262no—
348C4⋊Q8C22×D1314yes—
349#125—22no—
350#125—134no—
351#125—134no—
352#125—134no—
353#125—268no—
354#125—268no—
355#125—262no—
356#125—262no—
357#125—262no—
358#125C22×D1314yes—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—132no—
365C2×C4⋊C4—134no—
366C2×C4⋊C4—134no—
367C2×C4⋊C4—138no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—264no—
371C2×C4⋊C4—268no—
372C2×C4⋊C4—268no—
373C2×C4⋊C4—268no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—262no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1312yes—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—134no—
392C2×C42—134no—
393C2×C42C22×D1311yescharacteristic
394#107—138no—
395#107—138no—
396#107—138no—
397#107C22×D1318yes—
398#106—138no—
399#106—138no—
400#106—138no—
401#106C22×D1318yes—
402#97—138no—
403#97—134no—
404#97C22×D1314yes—
405C2×C13C2×#50114yescomplemented
406C2×C13C22×C4⋊Q811yescharacteristic
407C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
408C2×C13C22×#13711yescharacteristic
409D13C2×#50118yesdirect product factor
410C24—131no—
411C2×Q8—24no—
412C2×Q8—44no—
413C2×Q8—268no—
414C2×Q8—264no—
415C2×Q8—524no—
416C2×Q8—528no—
417C2×Q8—5232no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—131no—
422C22×C4—132no—
423C22×C4—138no—
424C22×C4—132no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—134no—
428C22×C4—134no—
429C22×C4—264no—
430C22×C4—264no—
431C22×C4—264no—
432C22×C4—264no—
433C22×C4—268no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—262no—
437C22×C4—528no—
438C22×C4—524no—
439C22×C4—524no—
440C22×C4D4×D1311yescharacteristic
441C22×C4D4×D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—138no—
444C2×C8—134no—
445C2×C8—1332no—
446C2×C8Q8×D1318yescomplemented
447C2×C8C23×D1314yes—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—132no—
455C4⋊C4—134no—
456C4⋊C4—132no—
457C4⋊C4—264no—
458C4⋊C4—264no—
459C4⋊C4—268no—
460C4⋊C4—264no—
461C4⋊C4—264no—
462C4⋊C4—264no—
463C4⋊C4—264no—
464C4⋊C4—268no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—262no—
468C4⋊C4—264no—
469C4⋊C4—264no—
470C4⋊C4—264no—
471C4⋊C4C23×D1312yes—
472C4⋊C4C23×D1314yes—
473C4⋊C4C23×D1312yes—
474C42—134no—
475C42—134no—
476C42—132no—
477C42—132no—
478C42D4×D1312yes—
479C42C23×D1312yes—
480C13C22×#50111yescharacteristic, complemented, Sylow
481C23—134no—
482C23—134no—
483C23—134no—
484C23—132no—
485C23C2×D4×D1311yescharacteristic
486Q8—48no—
487Q8—528no—
488Q8—5216no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—134no—
498C2×C4—132no—
499C2×C4—138no—
500C2×C4—138no—
501C2×C4—132no—
502C2×C4—132no—
503C2×C4—268no—
504C2×C4—268no—
505C2×C4—262no—
506C2×C4—262no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—264no—
510C2×C4—528no—
511C2×C4—528no—
512C2×C4—5216no—
513C2×C4—522no—
514C2×C4—524no—
515C2×C4—522no—
516C2×C4C2×D4×D1312yes—
517C2×C4C2×D4×D1312yes—
518C2×C4C2×D4×D1311yescharacteristic
519C2×C4C2×Q8×D1314yes—
520C2×C4C24×D1311yescharacteristic
521C8—138no—
522C8C2×Q8×D1318yescomplemented
523C22—134no—
524C22—134no—
525C22—134no—
526C22—1316no—
527C22D13×C4⋊Q812yes—
528C22D13×AGL(1,ℤ/8)12yes—
529C22D13×#13712yes—
530C22C22×D4×D1311yescharacteristic
531C4—22no—
532C4—22no—
533C4—42no—
534C4—44no—
535C4—42no—
536C4—134no—
537C4—262no—
538C4—262no—
539C4—522no—
540C4—524no—
541C4—522no—
542C4D13×C4⋊Q812yes—
543C4C22×Q8×D1312yes—
544C2—138no—
545C2D13×#50114yesdirect product factor
546C2C2×D13×C4⋊Q811yescharacteristic
547C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
548C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#501C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#501D13
hypocenterC13C22×#501
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. C2×#11718726C2semidirect
4. C2×#11718363C2semidirect
5. C2×#11718537C2semidirect
6. C2×#11718517C2semidirect
7. C2×#11718741C2semidirect
8. D13×#501C2direct (N × H)
12. C2×C13×#501C2semidirect
37. C13×#501C22semidirect
44. #11718741C22semidirect
45. #11718726C22semidirect
52. #11718537C22semidirect
54. #11718517C22semidirect
56. #11718363C22semidirect
99. C2×C8×D13Q8semidirect
170. C2×C8×C13C2×Q8semidirect
204. C2×#1055C2×Q8semidirect
206. C8×D13C2×Q8semidirect
215. C2×#501D13direct (N × H)
259. C8×C13C22×Q8semidirect
260. #1055C22×Q8semidirect
290. #501C2×D13direct (N × H)
309. C2×D13#501direct (N × H)
405. C2×C13C2×#501semidirect
409. D13C2×#501direct (N × H)
446. C2×C8Q8×D13semidirect
480. C13C22×#501semidirect
522. C8C2×Q8×D13semidirect
545. C2D13×#501direct (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×D13×#1252
C2×#117187262
C2×#117183632
C2×#117185372
C2×#117185172
C2×#117187412
D13×#5012
C2×D13×#1072
C2×D13×#1062
C2×D13×#972
C2×C13×#5012
C22×#50113