Finite Group Databasebeta

← D13×#2159 #16015949

Subgroups — D13×#2159 #16015949

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×M32C211yesmaximal, characteristic
2D13×#427C211yesmaximal, characteristic
3C2×D13×#107C211yesmaximal, characteristic
4#13116625C211yesmaximal, characteristic, complemented
5#13116624C211yesmaximal, characteristic, complemented
6#13116623C212yesmaximal, complemented
7#13116622C211yesmaximal, characteristic, complemented
8#13116621C212yesmaximal, complemented
9D13×#367C212yesmaximal, complemented
10D13×#366C212yesmaximal, complemented
11C13×#2159C211yesmaximal, characteristic, complemented
12C22×C8×D13C2211yescharacteristic
13D13×#117—21no—
14C2×C4⋊C4×D13—21no—
15C2×C13×M32C2211yescharacteristic
16C13×#427C2211yescharacteristic
17C2×C13×#107C2211yescharacteristic
18#11718767C2211yescharacteristic
19C2×#88058C2211yescharacteristic
20C2×#88052C2211yescharacteristic
21#11718659—21no—
22C2×#88047—21no—
23D13×M32C418yescomplemented
24C2×#88038C2212yes—
25C2×C16×D13C2212yes—
26#11718541C2211yescharacteristic
27#11718541C2211yescharacteristic
28D13×#107—21no—
29D13×#107—21no—
30D13×#107C2212yes—
31D13×#107C2212yes—
32D13×#107C2211yescharacteristic
33D13×#107C2211yescharacteristic
34#11718521—21no—
35D13×#106—21no—
36C13×#367C2212yescomplemented
37C13×#366C2212yescomplemented
38#11718097C2212yescomplemented
39#11718096C2212yescomplemented
40#11718082C2212yescomplemented
41#11718082C2212yescomplemented
42#11718081C2212yescomplemented
43#11718081C2212yescomplemented
44C22×C4×D13—41no—
45C22×C4×D13D411yescharacteristic
46C22×C8×C13C2311yescharacteristic
47C13×#117—21no—
48C2×C13×C4⋊C4—21no—
49#88180—21no—
50C2×C4⋊Dic13—21no—
51C2×#6101—41no—
52C22×#1055D411yescharacteristic
53C2×C8×D13C2×C414yes—
54C2×C8×D13D411yescharacteristic
55C2×C8×D13D411yescharacteristic
56C2×C8×D13Q814yes—
57C2×C8×D13C2311yescharacteristic
58C2×C8×D13C2311yescharacteristic
59#88146—21no—
60#88146—21no—
61C4⋊C4×D13—22no—
62C4⋊C4×D13—22no—
63C4⋊C4×D13—21no—
64C4⋊C4×D13—21no—
65C4⋊C4×D13—41no—
66C4⋊C4×D13—41no—
67C22⋊C4×D13—41no—
68#88131—41no—
69#88126—41no—
70C42×D13—41no—
71C13×M32C2×C414yescomplemented
72C2×C13×C16C2312yes—
73C13×#107—21no—
74C13×#107C2312yes—
75C13×#107C2311yescharacteristic
76C13×#107C2311yescharacteristic
77C13×#106—21no—
78#88058—21no—
79#88058C2312yes—
80#88058C2311yescharacteristic
81#88058C2311yescharacteristic
82#88057—21no—
83#88052C2×C414yescomplemented
84C2×#6090C2312yes—
85#88048—21no—
86#88048—21no—
87#88047—21no—
88#88047—21no—
89#88047—22no—
90#88047—22no—
91#88038C2×C418yescomplemented
92C16×D13C2×C418yescomplemented
93C2×#2159—131nomaximal, Sylow
94C23×D13D811yescharacteristic
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C22×Dic13—41no—
98C22×Dic13D811yescharacteristic
99C2×C4×D13—41no—
100C2×C4×D13—41no—
101C2×C4×D13—42no—
102C2×C4×D13—42no—
103C2×C4×D13—84no—
104C2×C4×D13C4⋊C414yes—
105C2×C4×D13D811yescharacteristic
106C2×C4×D13D811yescharacteristic
107C2×C4×D13Q1614yes—
108C2×C4×D13C2×D411yescharacteristic
109C2×C4×D13C2×D411yescharacteristic
110C2×C8×C13C22×C412yes—
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2×Q812yes—
113C2×C8×C13C2411yescharacteristic
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—22no—
117C13×C4⋊C4—41no—
118C13×C22⋊C4—41no—
119C42×C13—41no—
120C22⋊Dic13—41no—
121#6103—41no—
122#6103—41no—
123C4⋊Dic13—22no—
124C4⋊Dic13—21no—
125C4⋊Dic13—21no—
126C4⋊Dic13—41no—
127#6101—41no—
128#6101—41no—
129#6101—42no—
130#6101—42no—
131C4×Dic13—41no—
132C4×Dic13—41no—
133C4×Dic13—41no—
134C2×#1055C4⋊C414yes—
135C2×#1055C2×D411yescharacteristic
136C2×#1055C2×D411yescharacteristic
137C8×D13C4⋊C414yes—
138C8×D13C4⋊C414yes—
139C8×D13C22×C412yes—
140C8×D13C22×C412yes—
141C8×D13C2×Q812yes—
142C8×D13C2×Q812yes—
143C13×C16C22×C414yescomplemented
144#6090C22×C414yescomplemented
145C22×M32—131no—
146C2×#427—131no—
147C22×#107—131no—
148#2159—131no—
149#2159—131no—
150#2159—131no—
151#2159—132no—
152#2159—132no—
153#2159D1311yescharacteristic, direct product factor
154C2×#367—132no—
155C2×#366—132no—
156C23×C13C2×D811yescharacteristic
157C22×D13—22no—
158C22×D13—22no—
159C22×D13#10714yes—
160C22×D13C2×D811yescharacteristic
161C22×D13C2×D811yescharacteristic
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—82no—
166C2×C4×C13C2×C4⋊C412yes—
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C2×Q1612yes—
169C2×C4×C13C22×D411yescharacteristic
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—42no—
173C2×Dic13—82no—
174C2×Dic13#10714yes—
175C2×Dic13C2×D811yescharacteristic
176C2×Dic13C2×D811yescharacteristic
177C4×D13—84no—
178C4×D13—82no—
179C4×D13—84no—
180C4×D13—82no—
181C4×D13#10714yes—
182C4×D13#10714yes—
183C4×D13C2×C4⋊C412yes—
184C4×D13C2×C4⋊C412yes—
185C4×D13C2×Q1612yes—
186C4×D13C2×Q1612yes—
187C8×C13C2×C4⋊C412yes—
188C8×C13C23×C411yescharacteristic
189C8×C13C22×Q811yescharacteristic
190#1055C2×C4⋊C412yes—
191#1055C2×C4⋊C412yes—
192C23×C8—131no—
193C2×#117—261no—
194C22×C4⋊C4—261no—
195C2×M32—131no—
196C2×M32—138no—
197C2×M32—132no—
198C2×M32C2×D1311yescharacteristic
199C22×C16—132no—
200#427—131no—
201#427—131no—
202#427—131no—
203#427—261no—
204#427—261no—
205#427C2×D1311yescharacteristic
206C2×#107—131no—
207C2×#107—132no—
208C2×#107—132no—
209C2×#107—131no—
210C2×#107—131no—
211C2×#107—261no—
212C2×#107—261no—
213C2×#107—261no—
214C2×#107C2×D1311yescharacteristic
215C2×#106—261no—
216#367—132no—
217#367—132no—
218#367—132no—
219#367C2×D1312yescomplemented
220#366—132no—
221#366—132no—
222#366—132no—
223#366C2×D1312yescomplemented
224C22×C13—21no—
225C22×C13—21no—
226C22×C13C2×#10712yes—
227C22×C13C22×D811yescharacteristic
228C2×D13—21no—
229C2×D13—21no—
230C2×D13—28no—
231C2×D13C2×#10712yes—
232C2×D13C2×#10712yes—
233C2×D13#50912yes—
234C2×D13#51012yes—
235C4×C13—82no—
236C4×C13—81no—
237C4×C13—81no—
238C4×C13C2×#10712yes—
239C4×C13C22×C4⋊C411yescharacteristic
240C4×C13C22×Q1611yescharacteristic
241Dic13—82no—
242Dic13—81no—
243Dic13—81no—
244Dic13C2×#10712yes—
245Dic13C2×#10712yes—
246C23×C4—131no—
247C23×C4—521no—
248C22×C8—131no—
249C22×C8—134no—
250C22×C8—131no—
251C22×C8—131no—
252C22×C8—134no—
253C22×C8—131no—
254C22×C8—131no—
255C22×C8C22×D1311yescharacteristic
256#117—21no—
257#117—261no—
258#117—261no—
259#117—261no—
260#117—521no—
261#117—521no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—262no—
264C2×C4⋊C4—262no—
265C2×C4⋊C4—261no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—521no—
269C2×C4⋊C4—521no—
270C2×C4⋊C4—521no—
271C2×C22⋊C4—521no—
272C2×C42—521no—
273M32—134no—
274M32—138no—
275M32C4×D1314yescomplemented
276C2×C16—132no—
277C2×C16—138no—
278C2×C16C22×D1312yes—
279#107—21no—
280#107—131no—
281#107—132no—
282#107—131no—
283#107—262no—
284#107—262no—
285#107—261no—
286#107—261no—
287#107—261no—
288#107C22×D1311yescharacteristic
289#107C22×D1312yes—
290#107C22×D1311yescharacteristic
291#106—21no—
292#106—261no—
293#106—261no—
294#106—261no—
295C2×C13—22no—
296C2×C13C22×#10711yescharacteristic
297C2×C13C2×#50911yescharacteristic
298C2×C13C2×#51011yescharacteristic
299D13—22no—
300D13#215914yesdirect product factor
301C24—131no—
302C22×C4—41no—
303C22×C4—131no—
304C22×C4—134no—
305C22×C4—131no—
306C22×C4—131no—
307C22×C4—134no—
308C22×C4—131no—
309C22×C4—131no—
310C22×C4—521no—
311C22×C4—521no—
312C22×C4—522no—
313C22×C4—522no—
314C22×C4—521no—
315C22×C4—1044no—
316C22×C4D4×D1311yescharacteristic
317C2×C8—134no—
318C2×C8—131no—
319C2×C8—131no—
320C2×C8—134no—
321C2×C8—134no—
322C2×C8—132no—
323C2×C8—132no—
324C2×C8—132no—
325C2×C8—132no—
326C2×C8C2×C4×D1312yes—
327C2×C8D4×D1311yescharacteristic
328C2×C8Q8×D1312yes—
329C2×C8C23×D1311yescharacteristic
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—41no—
334C4⋊C4—261no—
335C4⋊C4—261no—
336C4⋊C4—262no—
337C4⋊C4—522no—
338C4⋊C4—522no—
339C4⋊C4—521no—
340C4⋊C4—521no—
341C4⋊C4—521no—
342C22⋊C4—41no—
343C22⋊C4—521no—
344C22⋊C4—521no—
345C22⋊C4—521no—
346C42—41no—
347C42—521no—
348C42—521no—
349C42—521no—
350C16—134no—
351C16C2×C4×D1314yescomplemented
352C13C2×#215911yescharacteristic, complemented, Sylow
353C23—131no—
354C23—131no—
355C23—134no—
356C23—262no—
357C23—262no—
358C23D8×D1311yescharacteristic
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—131no—
364C2×C4—131no—
365C2×C4—134no—
366C2×C4—132no—
367C2×C4—132no—
368C2×C4—132no—
369C2×C4—132no—
370C2×C4—134no—
371C2×C4—134no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—522no—
375C2×C4—1042no—
376C2×C4—1042no—
377C2×C4—1044no—
378C2×C4—1044no—
379C2×C4—1042no—
380C2×C4C4⋊C4×D1312yes—
381C2×C4D8×D1311yescharacteristic
382C2×C4Q16×D1312yes—
383C2×C4C2×D4×D1311yescharacteristic
384C8—132no—
385C8—132no—
386C8C4⋊C4×D1312yes—
387C8C22×C4×D1311yescharacteristic
388C8C2×Q8×D1311yescharacteristic
389C22—21no—
390C22—21no—
391C22—132no—
392C22—132no—
393C22—132no—
394C22—132no—
395C22—268no—
396C22—261no—
397C22—261no—
398C22D13×#10712yes—
399C22C2×D8×D1311yescharacteristic
400C4—82no—
401C4—81no—
402C4—81no—
403C4—132no—
404C4—132no—
405C4—1041no—
406C4—1042no—
407C4—1041no—
408C4D13×#10712yes—
409C4C2×C4⋊C4×D1311yescharacteristic
410C4C2×Q16×D1311yescharacteristic
411C2—22no—
412C2—134no—
413C2—262no—
414C2C2×D13×#10711yescharacteristic
415C2D13×#50911yescharacteristic
416C2D13×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2159C2
socleC22×C13C22×D8
prime radicalC23×D13D8
cosocleC2×C8×C13C24
hypercenter#2159D13
hypocenterC13C2×#2159
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
4. #13116625C2semidirect
5. #13116624C2semidirect
6. #13116623C2semidirect
7. #13116622C2semidirect
8. #13116621C2semidirect
9. D13×#367C2semidirect
10. D13×#366C2semidirect
11. C13×#2159C2semidirect
23. D13×M32C4semidirect
36. C13×#367C22semidirect
37. C13×#366C22semidirect
38. #11718097C22semidirect
39. #11718096C22semidirect
40. #11718082C22semidirect
41. #11718082C22semidirect
42. #11718081C22semidirect
43. #11718081C22semidirect
71. C13×M32C2×C4semidirect
83. #88052C2×C4semidirect
91. #88038C2×C4semidirect
92. C16×D13C2×C4semidirect
143. C13×C16C22×C4semidirect
144. #6090C22×C4semidirect
153. #2159D13direct (N × H)
219. #367C2×D13semidirect
223. #366C2×D13semidirect
275. M32C4×D13semidirect
300. D13#2159direct (N × H)
351. C16C2×C4×D13semidirect
352. C13C2×#2159semidirect

Maximal subgroups

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

subgroupindex
C2×D13×M322
D13×#4272
C2×D13×#1072
#131166252
#131166242
#131166232
#131166222
#131166212
D13×#3672
D13×#3662
C13×#21592
C2×#215913