Finite Group Databasebeta

← D13×#1952 #15866461

Subgroups — D13×#1952 #15866461

Order 3328.

918 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#108C211yesmaximal, characteristic
2D13×#428C212yesmaximal
3C2×D13×#107C211yesmaximal, characteristic
4D13×#405C211yesmaximal, characteristic
5#13115622C211yesmaximal, characteristic, complemented
6#13115621C211yesmaximal, characteristic, complemented
7#13115620C212yesmaximal, complemented
8#13115619C211yesmaximal, characteristic, complemented
9#13115618C212yesmaximal, complemented
10D13×#343C212yesmaximal
11C13×#1952C211yesmaximal, characteristic, complemented
12C2×M16×D13C2212yes—
13C2×M16×D13C2211yescharacteristic
14C22×C8×D13C2211yescharacteristic
15D13×#117C2211yescharacteristic
16C2×C4⋊C4×D13C2212yes—
17C2×C13×#108C2211yescharacteristic
18C13×#428C2212yes—
19C2×C13×#107C2211yescharacteristic
20C13×#405C2211yescharacteristic
21C2×#88062C2212yes—
22#11718783C2211yescharacteristic
23#11718782C2212yes—
24C2×#88059C2211yescharacteristic
25C2×#88058C2211yescharacteristic
26#11718762C2211yescharacteristic
27#11718658C2211yescharacteristic
28#11718656C2212yes—
29#11718625C2212yes—
30C2×#88047C2212yes—
31D13×#108C418yescomplemented
32#11718542—22no—
33D13×#107—21no—
34D13×#107—21no—
35D13×#107—21no—
36D13×#107—21no—
37D13×#107—22no—
38#11718522—22no—
39D13×#106—22no—
40#11718369—21no—
41D13×#97—21no—
42#11718350—21no—
43C4×C8×D13—21no—
44C13×#343C2212yes—
45#11718146C2212yes—
46#11718146C2212yes—
47#11718122C2212yes—
48C22×C4×D13—22no—
49C22×C4×D13C2311yescharacteristic
50C2×C13×M16C2312yes—
51C2×C13×M16C2311yescharacteristic
52C22×C8×C13C2311yescharacteristic
53C13×#117C2311yescharacteristic
54C2×C13×C4⋊C4C2312yes—
55#88180C2311yescharacteristic
56C2×C4⋊Dic13C2312yes—
57C2×#6101—22no—
58C2×#6099C2312yes—
59C2×#6099C2311yescharacteristic
60C22×#1055C2311yescharacteristic
61M16×D13—24no—
62M16×D13—22no—
63M16×D13C2×C418yes—
64M16×D13Q814yes—
65C2×#6094—22no—
66C2×#6094—21no—
67C2×C8×D13—22no—
68C2×C8×D13—21no—
69C2×C8×D13C2×C414yes—
70C2×C8×D13D411yescharacteristic
71C2×C8×D13D411yescharacteristic
72C2×C8×D13D411yescharacteristic
73C2×C8×D13D411yescharacteristic
74C2×C8×D13Q814yes—
75#88146D411yescharacteristic
76#88146D411yescharacteristic
77C4⋊C4×D13—22no—
78C4⋊C4×D13—22no—
79C4⋊C4×D13—22no—
80C4⋊C4×D13—22no—
81C4⋊C4×D13D411yescharacteristic
82C4⋊C4×D13D411yescharacteristic
83C22⋊C4×D13—21no—
84#88131—21no—
85#88126—21no—
86C42×D13—21no—
87C13×#108C2×C414yescomplemented
88C13×#107—21no—
89C13×#107—21no—
90C13×#107—22no—
91C13×#106—22no—
92C13×#97—21no—
93C4×C8×C13—21no—
94#88062C2×C418yescomplemented
95#88059C2×C414yescomplemented
96#88058—21no—
97#88058—21no—
98#88058—22no—
99#88057—22no—
100#88055—21no—
101#88055—21no—
102C8×Dic13—21no—
103C8×Dic13—21no—
104#88048—22no—
105#88048—22no—
106#88047—22no—
107#88047—22no—
108#88047—22no—
109#88047—22no—
110#88043—21no—
111C4×#1055—21no—
112C2×#1952—131nomaximal, Sylow
113C23×D13#4111yescharacteristic
114C22×C4×C13—22no—
115C22×C4×C13C2411yescharacteristic
116C22×Dic13—22no—
117C22×Dic13#4111yescharacteristic
118C2×C4×D13—21no—
119C2×C4×D13—21no—
120C2×C4×D13—42no—
121C2×C4×D13—42no—
122C2×C4×D13—84no—
123C2×C4×D13C22×C412yes—
124C2×C4×D13C2×D411yescharacteristic
125C2×C4×D13C2×D411yescharacteristic
126C2×C4×D13C2×D411yescharacteristic
127C2×C4×D13C2×D411yescharacteristic
128C2×C4×D13C2×Q812yes—
129C2×C4×D13C2×Q812yes—
130C2×C4×D13#4112yes—
131C13×M16—22no—
132C13×M16—21no—
133C13×M16C22×C414yes—
134C13×M16C2×Q812yes—
135C2×C8×C13—21no—
136C2×C8×C13—22no—
137C2×C8×C13C22×C412yes—
138C2×C8×C13C2×D411yescharacteristic
139C2×C8×C13C2×D411yescharacteristic
140C2×C8×C13C2×Q812yes—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—22no—
143C13×C4⋊C4C2×D411yescharacteristic
144C13×C4⋊C4C2×D411yescharacteristic
145C13×C22⋊C4—21no—
146C42×C13—21no—
147C22⋊Dic13—21no—
148#6103—21no—
149#6103—21no—
150C4⋊Dic13—22no—
151C4⋊Dic13—22no—
152C4⋊Dic13C2×D411yescharacteristic
153C4⋊Dic13C2×D411yescharacteristic
154#6101—21no—
155#6101—21no—
156#6101—42no—
157#6101—42no—
158C4×Dic13—21no—
159C4×Dic13—21no—
160C4×Dic13—21no—
161#6099—22no—
162#6099—21no—
163#6099C22×C414yes—
164#6099C2×Q812yes—
165C2×#1055—21no—
166C2×#1055—22no—
167C2×#1055C22×C412yes—
168C2×#1055C2×D411yescharacteristic
169C2×#1055C2×D411yescharacteristic
170C2×#1055C2×Q812yes—
171#6094—28no—
172#6094—24no—
173C8×D13—28no—
174C8×D13—24no—
175C8×D13C4⋊C414yes—
176C8×D13C4⋊C414yes—
177C8×D13C4⋊C414yes—
178C8×D13C4⋊C414yes—
179C22×#108—131no—
180C2×#428—132no—
181C22×#107—131no—
182C2×#405—131no—
183#1952—131no—
184#1952—132no—
185#1952—131no—
186#1952—131no—
187#1952—132no—
188#1952D1311yescharacteristic, direct product factor
189C2×#343—132no—
190C23×C13C2×#4111yescharacteristic
191C22×D13—22no—
192C22×D13—22no—
193C22×D13C4×Q812yes—
194C22×D13#12111yescharacteristic
195C22×D13#12111yescharacteristic
196C22×D13#12512yes—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—42no—
200C2×C4×C13—82no—
201C2×C4×C13C23×C411yescharacteristic
202C2×C4×C13C22×D411yescharacteristic
203C2×C4×C13C22×D411yescharacteristic
204C2×C4×C13C22×Q811yescharacteristic
205C2×C4×C13C22×Q811yescharacteristic
206C2×C4×C13C2×#4111yescharacteristic
207C2×Dic13—21no—
208C2×Dic13—21no—
209C2×Dic13—42no—
210C2×Dic13—82no—
211C2×Dic13C4×Q812yes—
212C2×Dic13#12111yescharacteristic
213C2×Dic13#12111yescharacteristic
214C2×Dic13#12512yes—
215C4×D13—42no—
216C4×D13—42no—
217C4×D13—84no—
218C4×D13—84no—
219C4×D13C2×C4⋊C412yes—
220C4×D13C2×C4⋊C412yes—
221C4×D13C4×D412yes—
222C4×D13C4×D412yes—
223C4×D13C22⋊Q812yes—
224C4×D13C22⋊Q812yes—
225C4×D13C4⋊Q812yes—
226C4×D13C4⋊Q812yes—
227C8×C13—24no—
228C8×C13—22no—
229C8×C13C2×C4⋊C412yes—
230C8×C13C2×C4⋊C412yes—
231#1055—24no—
232#1055—22no—
233#1055C2×C4⋊C412yes—
234#1055C2×C4⋊C412yes—
235C22×M16—131no—
236C22×M16—132no—
237C23×C8—131no—
238C2×#117—131no—
239C22×C4⋊C4—132no—
240C2×#108—132no—
241C2×#108—131no—
242C2×#108—138no—
243C2×#108C2×D1311yescharacteristic
244#428—132no—
245#428—132no—
246#428—132no—
247#428—262no—
248#428—262no—
249#428C2×D1312yes—
250C2×#107—131no—
251C2×#107—132no—
252C2×#107—262no—
253C2×#107—261no—
254C2×#107—261no—
255C2×#107—261no—
256C2×#107—261no—
257C2×#107C2×D1311yescharacteristic
258C2×#106—262no—
259#405—131no—
260#405—131no—
261#405—131no—
262#405—261no—
263#405—261no—
264#405C2×D1311yescharacteristic
265C2×#97—261no—
266C2×C4×C8—261no—
267#343—132no—
268#343—132no—
269#343—132no—
270#343C2×D1312yes—
271C22×C13—21no—
272C22×C13—21no—
273C22×C13C2×C4×Q811yescharacteristic
274C22×C13C2×#12111yescharacteristic
275C22×C13C2×#12511yescharacteristic
276C2×D13—21no—
277C2×D13—21no—
278C2×D13—24no—
279C2×D13—24no—
280C2×D13#38912yes—
281C2×D13#38912yes—
282C2×D13#47212yes—
283C2×D13#47312yes—
284C4×C13—41no—
285C4×C13—41no—
286C4×C13—82no—
287C4×C13C22×C4⋊C411yescharacteristic
288C4×C13C2×C4×D411yescharacteristic
289C4×C13C2×C22⋊Q811yescharacteristic
290C4×C13C2×C4⋊Q811yescharacteristic
291Dic13—41no—
292Dic13—41no—
293Dic13—82no—
294Dic13#38912yes—
295Dic13#38912yes—
296C23×C4—131no—
297C23×C4—262no—
298C2×M16—131no—
299C2×M16—132no—
300C2×M16—138no—
301C2×M16—134no—
302C2×M16—261no—
303C2×M16—262no—
304C2×M16—262no—
305C2×M16—264no—
306C2×M16C22×D1312yes—
307C2×M16C22×D1311yescharacteristic
308C22×C8—131no—
309C22×C8—134no—
310C22×C8—131no—
311C22×C8—131no—
312C22×C8—131no—
313C22×C8—131no—
314C22×C8—134no—
315C22×C8—261no—
316C22×C8—262no—
317C22×C8C22×D1311yescharacteristic
318#117—131no—
319#117—131no—
320#117—131no—
321#117—261no—
322#117—261no—
323#117C22×D1311yescharacteristic
324C2×C4⋊C4—131no—
325C2×C4⋊C4—131no—
326C2×C4⋊C4—132no—
327C2×C4⋊C4—262no—
328C2×C4⋊C4—262no—
329C2×C4⋊C4—262no—
330C2×C4⋊C4—262no—
331C2×C4⋊C4—262no—
332C2×C4⋊C4C22×D1312yes—
333C2×C22⋊C4—261no—
334C2×C42—261no—
335#108—138no—
336#108—134no—
337#108C4×D1314yescomplemented
338#107—21no—
339#107—21no—
340#107—22no—
341#107—262no—
342#107—262no—
343#107—262no—
344#107—262no—
345#107—261no—
346#107—261no—
347#107—262no—
348#106—22no—
349#106—262no—
350#106—262no—
351#106—262no—
352#97—21no—
353#97—261no—
354#97—261no—
355#97—261no—
356C4×C8—21no—
357C4×C8—261no—
358C4×C8—261no—
359C4×C8—261no—
360C2×C13—21no—
361C2×C13—21no—
362C2×C13C2×#38911yescharacteristic
363C2×C13C2×#47211yescharacteristic
364C2×C13C2×#47311yescharacteristic
365D13—22no—
366D13#195214yesdirect product factor
367C24—131no—
368C22×C4—22no—
369C22×C4—131no—
370C22×C4—132no—
371C22×C4—131no—
372C22×C4—131no—
373C22×C4—131no—
374C22×C4—131no—
375C22×C4—132no—
376C22×C4—132no—
377C22×C4—132no—
378C22×C4—261no—
379C22×C4—261no—
380C22×C4—262no—
381C22×C4—522no—
382C22×C4—522no—
383C22×C4—1044no—
384C22×C4C23×D1311yescharacteristic
385M16—22no—
386M16—21no—
387M16—134no—
388M16—132no—
389M16—268no—
390M16—264no—
391M16—262no—
392M16—261no—
393M16C2×C4×D1314yes—
394M16Q8×D1312yes—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—132no—
398C2×C8—131no—
399C2×C8—131no—
400C2×C8—132no—
401C2×C8—134no—
402C2×C8—134no—
403C2×C8—134no—
404C2×C8—134no—
405C2×C8—268no—
406C2×C8—264no—
407C2×C8—261no—
408C2×C8—262no—
409C2×C8C2×C4×D1312yes—
410C2×C8D4×D1311yescharacteristic
411C2×C8D4×D1311yescharacteristic
412C2×C8Q8×D1312yes—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—131no—
416C4⋊C4—131no—
417C4⋊C4—261no—
418C4⋊C4—261no—
419C4⋊C4—262no—
420C4⋊C4—262no—
421C4⋊C4—522no—
422C4⋊C4—522no—
423C4⋊C4D4×D1311yescharacteristic
424C4⋊C4D4×D1311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—261no—
427C22⋊C4—261no—
428C22⋊C4—261no—
429C42—21no—
430C42—261no—
431C42—261no—
432C42—261no—
433C13C2×#195211yescharacteristic, complemented, Sylow
434C23—131no—
435C23—132no—
436C23—131no—
437C23—132no—
438C23—262no—
439C23—262no—
440C23#41×D1311yescharacteristic
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4—132no—
446C2×C4—131no—
447C2×C4—131no—
448C2×C4—132no—
449C2×C4—132no—
450C2×C4—132no—
451C2×C4—132no—
452C2×C4—132no—
453C2×C4—132no—
454C2×C4—132no—
455C2×C4—132no—
456C2×C4—132no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—522no—
462C2×C4—1044no—
463C2×C4—1044no—
464C2×C4—1042no—
465C2×C4C22×C4×D1311yescharacteristic
466C2×C4C2×D4×D1311yescharacteristic
467C2×C4C2×D4×D1311yescharacteristic
468C2×C4C2×Q8×D1311yescharacteristic
469C2×C4C2×Q8×D1311yescharacteristic
470C2×C4#41×D1311yescharacteristic
471C8—24no—
472C8—22no—
473C8—132no—
474C8—132no—
475C8—264no—
476C8—262no—
477C8C4⋊C4×D1312yes—
478C8C4⋊C4×D1312yes—
479C22—21no—
480C22—21no—
481C22—132no—
482C22—132no—
483C22—132no—
484C22—132no—
485C22—264no—
486C22—264no—
487C22—261no—
488C22—261no—
489C22C4×Q8×D1311yescharacteristic
490C22D13×#12111yescharacteristic
491C22D13×#12511yescharacteristic
492C4—41no—
493C4—41no—
494C4—82no—
495C4—132no—
496C4—132no—
497C4—521no—
498C4—521no—
499C4—1042no—
500C4C2×C4⋊C4×D1311yescharacteristic
501C4C4×D4×D1311yescharacteristic
502C4D13×C22⋊Q811yescharacteristic
503C4D13×C4⋊Q811yescharacteristic
504C2—21no—
505C2—21no—
506C2—134no—
507C2—262no—
508C2D13×#38911yescharacteristic
509C2D13×#47211yescharacteristic
510C2D13×#47311yescharacteristic
subgroupG/H
centerC22D13×#121
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1952C2
socleC22×C13C2×#121
prime radicalC23×D13#41
cosocleC22×C4×C13C24
hypercenter#1952D13
hypocenterC13C2×#1952
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
5. #13115622C2semidirect
6. #13115621C2semidirect
7. #13115620C2semidirect
8. #13115619C2semidirect
9. #13115618C2semidirect
11. C13×#1952C2semidirect
31. D13×#108C4semidirect
87. C13×#108C2×C4semidirect
94. #88062C2×C4semidirect
95. #88059C2×C4semidirect
188. #1952D13direct (N × H)
337. #108C4×D13semidirect
366. D13#1952direct (N × H)
433. C13C2×#1952semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1082
D13×#4282
C2×D13×#1072
D13×#4052
#131156222
#131156212
#131156202
#131156192
#131156182
D13×#3432
C13×#19522
C2×#195213