Finite Group Databasebeta

← D13×#2330 #16021744

Subgroups — D13×#2330 #16021744

Order 3328.

2398 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#125C211yesmaximal, characteristic
2#13117578C211yesmaximal, characteristic, complemented
3#13117577C211yesmaximal, characteristic, complemented
4#13117576C212yesmaximal, complemented
5#13117575C211yesmaximal, characteristic, complemented
6#13117574C214yesmaximal, complemented
7#13117573C212yesmaximal, complemented
8#13117572C214yesmaximal, complemented
9D13×#389C212yesmaximal
10D13×#389C214yesmaximal
11D13×#387C214yesmaximal
12D13×#384C211yesmaximal, characteristic
13C4×C4⋊C4×D13C212yesmaximal
14D13×#376C211yesmaximal, characteristic
15C13×#2330C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17D13×#125C4116yescomplemented
18C2×C4⋊C4×D13C2212yes—
19C2×C4⋊C4×D13C2214yes—
20C2×C4⋊C4×D13C2214yes—
21C2×C4⋊C4×D13C2214yes—
22C2×C4⋊C4×D13C2212yes—
23C2×#88144C2212yes—
24C2×#88143C2214yes—
25C2×C42×D13C2211yescharacteristic
26C2×C42×D13C2214yes—
27C2×C42×D13C2211yescharacteristic
28C2×C42×D13C2211yescharacteristic
29C2×#88124C2211yescharacteristic
30C13×#389C2214yes—
31C13×#389C2212yes—
32C13×#387C2214yes—
33C13×#384C2211yescharacteristic
34C4×C13×C4⋊C4C2212yes—
35C13×#376C2211yescharacteristic
36#11718646C2214yes—
37#11718646C2212yes—
38#11718642C2214yes—
39#11718639C2214yes—
40#11718637C2214yes—
41#11718637C2212yes—
42C4⋊C4×Dic13C2212yes—
43C4⋊C4×Dic13C2212yes—
44#11718634C2212yes—
45#11718634C2214yes—
46#11718633C2214yes—
47#11718633C2214yes—
48#11718633C2214yes—
49#11718596C2211yescharacteristic
50C4×C4⋊Dic13C2212yes—
51#11718594C2214yes—
52#11718593C2211yescharacteristic
53#11718593C2211yescharacteristic
54#11718593C2211yescharacteristic
55C4×#6101C2214yes—
56#11718589C2214yes—
57#11718589C2212yes—
58D13×#95C2214yes—
59D13×#95C2212yes—
60D13×#95C2214yes—
61D13×#95C2212yes—
62#11718316C2214yes—
63#11718315C2214yes—
64#11718314C2214yes—
65#11718313C2214yes—
66#11718310C2214yes—
67#11718309C2212yes—
68#11718309C2212yes—
69#11718308C2214yes—
70#11718308C2214yes—
71#11718308C2214yes—
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2314yes—
74C22×C4×D13C2311yescharacteristic
75C22×C4×D13C2314yes—
76C22×C4×D13C2312yes—
77C22×C4×D13C2312yes—
78C22×C4×D13C2311yescharacteristic
79C13×#125C2×C418yescomplemented
80C2×C13×C4⋊C4C2312yes—
81C2×C13×C4⋊C4C2314yes—
82C2×C13×C4⋊C4C2314yes—
83C2×C13×C4⋊C4C2312yes—
84C2×C13×C4⋊C4C2314yes—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2314yes—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C4⋊Dic13C2312yes—
90C2×C4⋊Dic13C2314yes—
91C2×C4⋊Dic13C2314yes—
92C2×C4⋊Dic13C2312yes—
93C2×C4⋊Dic13C2314yes—
94C2×#6101C2314yes—
95C2×#6101C2314yes—
96C2×#6101C2314yes—
97C2×#6101C2314yes—
98C2×#6101C2314yes—
99C2×#6101C2314yes—
100C2×#6101C2314yes—
101C2×#6101C2314yes—
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2314yes—
106C2×C4×Dic13C2314yes—
107C2×C4×Dic13C2314yes—
108C2×C4×Dic13C2312yes—
109C2×C4×Dic13C2311yescharacteristic
110C2×C4×Dic13C2312yes—
111C2×C4×Dic13C2311yescharacteristic
112C4⋊C4×D13—28no—
113C4⋊C4×D13—48no—
114C4⋊C4×D13—48no—
115C4⋊C4×D13C2×C4132yes—
116C4⋊C4×D13C2×C4116yes—
117#88144C2×C4116yescomplemented
118#88143C2×C4132yescomplemented
119C42×D13—24no—
120C42×D13—48no—
121C42×D13C2×C418yes—
122C42×D13Q818yes—
123#88124C2×C418yescomplemented
124C13×#95C2314yes—
125C13×#95C2314yes—
126C13×#95C2312yes—
127C13×#95C2312yes—
128#88071C2312yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2312yes—
132#88071C2312yes—
133#88071C2312yes—
134#88071C2312yes—
135#88071C2312yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140C2×#2330—131nomaximal, Sylow
141C23×D13C2411yescharacteristic
142C22×C4×C13C2411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C22×C4×C13C2414yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2412yes—
147C22×C4×C13C2412yes—
148C22×C4×C13C2411yescharacteristic
149C22×Dic13C2411yescharacteristic
150C22×Dic13C2411yescharacteristic
151C22×Dic13C2414yes—
152C22×Dic13C2414yes—
153C22×Dic13C2412yes—
154C22×Dic13C2412yes—
155C22×Dic13C2411yescharacteristic
156C2×C4×D13—24no—
157C2×C4×D13—28no—
158C2×C4×D13—24no—
159C2×C4×D13—28no—
160C2×C4×D13—24no—
161C2×C4×D13—24no—
162C2×C4×D13—22no—
163C2×C4×D13—22no—
164C2×C4×D13—28no—
165C2×C4×D13—28no—
166C2×C4×D13—24no—
167C2×C4×D13—28no—
168C2×C4×D13—24no—
169C2×C4×D13C22×C418yes—
170C2×C4×D13C22×C4116yes—
171C2×C4×D13C22×C414yes—
172C2×C4×D13C2×Q818yes—
173C2×C4×D13C2×Q814yes—
174C2×C4×D13#4114yes—
175C13×C4⋊C4—24no—
176C13×C4⋊C4—44no—
177C13×C4⋊C4—44no—
178C13×C4⋊C4C22×C4116yes—
179C13×C4⋊C4C22×C418yes—
180C42×C13—22no—
181C42×C13—44no—
182C42×C13C22×C414yes—
183C42×C13C2×Q814yes—
184C4⋊Dic13—24no—
185C4⋊Dic13—44no—
186C4⋊Dic13—44no—
187C4⋊Dic13C22×C418yes—
188C4⋊Dic13C22×C4116yes—
189#6101—28no—
190#6101—44no—
191#6101—44no—
192#6101—44no—
193#6101—44no—
194#6101C22×C4116yes—
195#6101C22×C4116yes—
196#6101C22×C4116yes—
197C4×Dic13—22no—
198C4×Dic13—22no—
199C4×Dic13—22no—
200C4×Dic13—44no—
201C4×Dic13—44no—
202C4×Dic13—44no—
203C4×Dic13C22×C418yes—
204C4×Dic13C22×C414yes—
205C4×Dic13C2×Q814yes—
206C4×Dic13C2×Q818yes—
207C22×#125—131no—
208#2330—134no—
209#2330—132no—
210#2330—134no—
211#2330—131no—
212#2330—132no—
213#2330—131no—
214#2330—131no—
215#2330D1311yescharacteristic, direct product factor
216C2×#389—132no—
217C2×#389—134no—
218C2×#387—134no—
219C2×#384—131no—
220C2×C4×C4⋊C4—132no—
221C2×#376—131no—
222C23×C13C2511yescharacteristic
223C22×D13C23×C412yes—
224C22×D13C22×Q812yes—
225C22×D13C2×#4112yes—
226C22×D13H(5,𝔽2)14yes—
227C22×D132−1+414yes—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13C23×C414yes—
242C2×C4×C13C23×C418yes—
243C2×C4×C13C23×C412yes—
244C2×C4×C13C22×Q814yes—
245C2×C4×C13C22×Q812yes—
246C2×C4×C13C2×#4112yes—
247C2×Dic13—22no—
248C2×Dic13—24no—
249C2×Dic13—22no—
250C2×Dic13—24no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13C23×C414yes—
261C2×Dic13C23×C418yes—
262C2×Dic13C23×C412yes—
263C2×Dic13C22×Q814yes—
264C2×Dic13C22×Q812yes—
265C2×Dic13C2×#4112yes—
266C4×D13—232no—
267C4×D13—216no—
268C4×D13—216no—
269C4×D13—44no—
270C4×D13—416no—
271C4×D13—44no—
272C4×D13C4×Q8116yes—
273C2×#125—1316no—
274C2×#125—134no—
275C2×#125—132no—
276C2×#125—131no—
277C2×#125C2×D1311yescharacteristic
278C22×C4⋊C4—132no—
279C22×C4⋊C4—134no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—134no—
282C22×C4⋊C4—134no—
283C22×C42—131no—
284C22×C42—131no—
285C22×C42—131no—
286C22×C42—134no—
287#389—134no—
288#389—134no—
289#389—134no—
290#389—134no—
291#389—132no—
292#389—134no—
293#389—132no—
294#389—134no—
295#389—132no—
296#389—134no—
297#389—134no—
298#389—134no—
299#389C2×D1314yes—
300#389C2×D1312yes—
301#387—134no—
302#387—134no—
303#387—134no—
304#387—134no—
305#387—134no—
306#387—134no—
307#387—134no—
308#387C2×D1314yes—
309#384—134no—
310#384—132no—
311#384—131no—
312#384C2×D1311yescharacteristic
313C4×C4⋊C4—132no—
314C4×C4⋊C4—132no—
315C4×C4⋊C4—134no—
316C4×C4⋊C4—132no—
317C4×C4⋊C4—134no—
318C4×C4⋊C4C2×D1312yes—
319#376—131no—
320#376—131no—
321#376—131no—
322#376—132no—
323#376—132no—
324#376C2×D1311yescharacteristic
325C2×#95—132no—
326C2×#95—132no—
327C2×#95—134no—
328C2×#95—134no—
329C22×C13C24×C411yescharacteristic
330C22×C13C23×Q811yescharacteristic
331C22×C13C22×#4111yescharacteristic
332C22×C13C2×H(5,𝔽2)12yes—
333C22×C13C2×2−1+412yes—
334C2×D13C2×C4×Q814yes—
335C2×D13#52018yes—
336C2×D13#54014yes—
337C2×D13#54114yes—
338C2×D13#54418yes—
339C4×C13—28no—
340C4×C13—24no—
341C4×C13—24no—
342C4×C13—41no—
343C4×C13—44no—
344C4×C13—41no—
345C4×C13C2×C4×Q814yes—
346Dic13—28no—
347Dic13—24no—
348Dic13—24no—
349Dic13—41no—
350Dic13—44no—
351Dic13—41no—
352Dic13C2×C4×Q814yes—
353C23×C4—131no—
354C23×C4—132no—
355C23×C4—134no—
356C23×C4—132no—
357C23×C4—131no—
358C23×C4—134no—
359C23×C4—131no—
360#125—1332no—
361#125—1316no—
362#125—138no—
363#125C4×D1318yescomplemented
364C2×C4⋊C4—134no—
365C2×C4⋊C4—134no—
366C2×C4⋊C4—134no—
367C2×C4⋊C4—132no—
368C2×C4⋊C4—134no—
369C2×C4⋊C4—1316no—
370C2×C4⋊C4—1332no—
371C2×C4⋊C4—134no—
372C2×C4⋊C4—132no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—134no—
377C2×C4⋊C4—134no—
378C2×C4⋊C4—134no—
379C2×C4⋊C4—268no—
380C2×C4⋊C4—528no—
381C2×C4⋊C4—528no—
382C2×C4⋊C4C22×D1312yes—
383C2×C4⋊C4C22×D1314yes—
384C2×C4⋊C4C22×D1314yes—
385C2×C4⋊C4C22×D1312yes—
386C2×C4⋊C4C22×D1314yes—
387C2×C42—132no—
388C2×C42—131no—
389C2×C42—132no—
390C2×C42—131no—
391C2×C42—138no—
392C2×C42—138no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—134no—
397C2×C42—134no—
398C2×C42—134no—
399C2×C42—264no—
400C2×C42—528no—
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1314yes—
403C2×C42C22×D1311yescharacteristic
404C2×C42C22×D1311yescharacteristic
405#95—132no—
406#95—132no—
407#95—132no—
408#95—132no—
409#95—132no—
410#95—132no—
411#95—134no—
412#95—134no—
413#95—134no—
414#95—134no—
415#95—134no—
416#95—134no—
417#95C22×D1312yes—
418#95C22×D1312yes—
419#95C22×D1314yes—
420#95C22×D1314yes—
421C2×C13C22×C4×Q811yescharacteristic
422C2×C13C2×#52012yes—
423C2×C13C2×#54011yescharacteristic
424C2×C13C2×#54111yescharacteristic
425C2×C13C2×#54412yes—
426D13#233018yesdirect product factor
427C24—131no—
428C22×C4—131no—
429C22×C4—134no—
430C22×C4—134no—
431C22×C4—134no—
432C22×C4—132no—
433C22×C4—132no—
434C22×C4—134no—
435C22×C4—138no—
436C22×C4—1316no—
437C22×C4—138no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—134no—
441C22×C4—264no—
442C22×C4—268no—
443C22×C4—264no—
444C22×C4—264no—
445C22×C4—268no—
446C22×C4—264no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—268no—
450C22×C4—268no—
451C22×C4—264no—
452C22×C4—268no—
453C22×C4—264no—
454C22×C4C23×D1311yescharacteristic
455C22×C4C23×D1311yescharacteristic
456C22×C4C23×D1314yes—
457C22×C4C23×D1314yes—
458C22×C4C23×D1312yes—
459C22×C4C23×D1312yes—
460C22×C4C23×D1311yescharacteristic
461C4⋊C4—24no—
462C4⋊C4—44no—
463C4⋊C4—44no—
464C4⋊C4—1316no—
465C4⋊C4—1316no—
466C4⋊C4—1316no—
467C4⋊C4—1316no—
468C4⋊C4—138no—
469C4⋊C4—268no—
470C4⋊C4—264no—
471C4⋊C4—524no—
472C4⋊C4—524no—
473C4⋊C4—524no—
474C4⋊C4—524no—
475C4⋊C4—524no—
476C4⋊C4—524no—
477C4⋊C4C2×C4×D13116yes—
478C4⋊C4C2×C4×D1318yes—
479C42—22no—
480C42—44no—
481C42—138no—
482C42—134no—
483C42—138no—
484C42—134no—
485C42—262no—
486C42—262no—
487C42—262no—
488C42—524no—
489C42—524no—
490C42—524no—
491C42C2×C4×D1314yes—
492C42Q8×D1314yes—
493C13C2×#233011yescharacteristic, complemented, Sylow
494C23—132no—
495C23—132no—
496C23—132no—
497C23—134no—
498C23—134no—
499C23C24×D1311yescharacteristic
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—132no—
514C2×C4—132no—
515C2×C4—132no—
516C2×C4—1316no—
517C2×C4—134no—
518C2×C4—138no—
519C2×C4—134no—
520C2×C4—2616no—
521C2×C4—2616no—
522C2×C4—2632no—
523C2×C4—262no—
524C2×C4—264no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—264no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—264no—
532C2×C4—264no—
533C2×C4—262no—
534C2×C4—264no—
535C2×C4—262no—
536C2×C4—524no—
537C2×C4—524no—
538C2×C4—5216no—
539C2×C4C22×C4×D1314yes—
540C2×C4C22×C4×D1318yes—
541C2×C4C22×C4×D1312yes—
542C2×C4C2×Q8×D1314yes—
543C2×C4C2×Q8×D1312yes—
544C2×C4#41×D1312yes—
545C22—134no—
546C22—138no—
547C22—134no—
548C22—138no—
549C22—134no—
550C22C23×C4×D1311yescharacteristic
551C22C22×Q8×D1311yescharacteristic
552C22C2×#41×D1311yescharacteristic
553C22D13×H(5,𝔽2)12yes—
554C22D13×2−1+412yes—
555C4—24no—
556C4—28no—
557C4—24no—
558C4—41no—
559C4—41no—
560C4—44no—
561C4—134no—
562C4—264no—
563C4—264no—
564C4—268no—
565C4—521no—
566C4—521no—
567C4—524no—
568C4C4×Q8×D1314yes—
569C2—138no—
570C2C2×C4×Q8×D1311yescharacteristic
571C2D13×#52012yes—
572C2D13×#54011yescharacteristic
573C2D13×#54111yescharacteristic
574C2D13×#54412yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2330C2
socle, cosocleC23×C13C25
prime radicalC23×D13C24
hypercenter#2330D13
hypocenterC13C2×#2330
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2330

Complements

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

NH ≅ G/Ntype
2. #13117578C2semidirect
3. #13117577C2semidirect
4. #13117576C2semidirect
5. #13117575C2semidirect
6. #13117574C2semidirect
7. #13117573C2semidirect
8. #13117572C2semidirect
15. C13×#2330C2semidirect
17. D13×#125C4semidirect
79. C13×#125C2×C4semidirect
117. #88144C2×C4semidirect
118. #88143C2×C4semidirect
123. #88124C2×C4semidirect
215. #2330D13direct (N × H)
363. #125C4×D13semidirect
426. D13#2330direct (N × H)
493. C13C2×#2330semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1252
#131175782
#131175772
#131175762
#131175752
#131175742
#131175732
#131175722
D13×#3892
D13×#3872
D13×#3842
C4×C4⋊C4×D132
D13×#3762
C13×#23302
C2×#233013