Finite Group Databasebeta

← C2×D13×#519 #16769501

Subgroups — C2×D13×#519 #16769501

Order 3328.

11230 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D13C211yesmaximal, characteristic
2C2×#11719517C211yesmaximal, characteristic, complemented
3C2×#11719221C216yesmaximal, complemented
4C2×#11719277C218yesmaximal, complemented
5D13×#519C2132yesmaximal, direct product factor
6C2×C4×Q8×D13C218yesmaximal, complemented
7C2×D13×#117C216yesmaximal
8C2×C13×#519C211yesmaximal, characteristic, complemented
9C23×Q8×C13C2211yescharacteristic
10C22×Q8×D13C4132yescomplemented
11C22×Q8×D13C2214yes—
12C22×Q8×D13C22116yes—
13C22×Q8×D13C2214yes—
14C23×C4×D13C2213yes—
15C23×Dic26C2213yes—
16C13×#519C22116yescomplemented
17C2×C4×Q8×C13C2218yescomplemented
18C2×C13×#117C2216yes—
19#11719517C22116yescomplemented
20C2×Q8×Dic13C2218yescomplemented
21C2×#88180C2216yes—
22#11719277C221128yescomplemented
23C4×Q8×D13C221128yescomplemented
24D13×#117C22196yes—
25#11719221C22196yescomplemented
26C2×#88146C22112yes—
27C2×C4⋊C4×D13C22112yes—
28C2×#88141C22124yescomplemented
29C2×C22⋊C4×D13C2214yes—
30C2×#88131C22112yes—
31C2×#88126C22112yes—
32C2×C42×D13C22112yes—
33C2×C4×Dic26C22124yescomplemented
34C24×D13C2311yescharacteristic
35C22×Q8×C13C2×C4116yescomplemented
36C22×Q8×C13C2314yes—
37C22×Q8×C13C2318yes—
38C23×C4×C13C2313yes—
39C23×Dic13C2313yes—
40C2×Q8×D13C2×C4164yes—
41C2×Q8×D13C2×C4164yescomplemented
42C2×Q8×D13C2×C41256yescomplemented
43C2×Q8×D13C23132yes—
44C2×Q8×D13C23132yes—
45C22×C4×D13C2×C4148yes—
46C22×C4×D13C2318yes—
47C22×C4×D13C2316yes—
48C22×C4×D13C2316yes—
49C22×C4×D13C23124yes—
50C22×Dic26C2×C4148yescomplemented
51C22×Dic26C23112yes—
52C22×Dic26C23124yes—
53C4×Q8×C13C23164yescomplemented
54C13×#117C23148yes—
55C2×C13×C4⋊C4C23112yes—
56C2×C13×C22⋊C4C2314yes—
57C2×C42×C13C23112yes—
58C2×C22⋊Dic13C2314yes—
59Q8×Dic13C23164yescomplemented
60C2×#6103C2318yes—
61#88180C23148yes—
62C2×C4⋊Dic13C23112yes—
63C2×#6101C23124yes—
64C2×C4×Dic13C23124yes—
65C2×C4×Dic13C23112yes—
66#88146C23196yes—
67C4⋊C4×D13C23196yes—
68#88141C231192yescomplemented
69C22⋊C4×D13C23132yes—
70#88131C23196yes—
71#88126C23196yes—
72C42×D13C23196yes—
73C4×Dic26C231192yescomplemented
74C22×#519—131nomaximal, Sylow
75C24×C13C2411yescharacteristic
76C23×D13—28no—
77C23×D13C22×C418yes—
78C23×D13C2414yes—
79C23×D13C2411yescharacteristic
80C23×D13C2411yescharacteristic
81C2×Q8×C13C22×C4132yes—
82C2×Q8×C13C22×C4164yescomplemented
83C2×Q8×C13C24116yes—
84C22×C4×C13C22×C4124yes—
85C22×C4×C13C2418yes—
86C22×C4×C13C2416yes—
87C22×C4×C13C24112yes—
88C22×Dic13C22×C4124yes—
89C22×Dic13C2418yes—
90C22×Dic13C24112yes—
91C22×Dic13C2416yes—
92Q8×D13C22×C41256yes—
93Q8×D13C22×C41256yescomplemented
94C2×C4×D13—232no—
95C2×C4×D13C22×C4148yes—
96C2×C4×D13C22×C41192yes—
97C2×C4×D13C22×C4148yes—
98C2×C4×D13C24132yes—
99C2×C4×D13C24124yes—
100C2×C4×D13C24124yes—
101C2×Dic26C22×C4196yes—
102C2×Dic26C22×C41192yescomplemented
103C2×Dic26C24148yes—
104C13×C4⋊C4C24148yes—
105C13×C22⋊C4C24116yes—
106C42×C13C24148yes—
107C22⋊Dic13C24116yes—
108#6103C24132yes—
109C4⋊Dic13C24148yes—
110#6101C24196yes—
111C4×Dic13C24196yes—
112C4×Dic13C24148yes—
113C24×Q8—131no—
114C2×#519—131no—
115C2×#519—1332no—
116C2×#519—138no—
117C2×#519—136no—
118C2×#519D1311yescharacteristic, direct product factor
119C22×C4×Q8—138no—
120C22×#117—136no—
121C23×C13—24no—
122C23×C13C23×C414yes—
123C23×C13C2512yes—
124C23×C13C2511yescharacteristic
125C22×D13—24no—
126C22×D13—232no—
127C22×D13—216no—
128C22×D13C23×C414yes—
129C22×D13C23×C4116yes—
130C22×D13C23×C414yes—
131C22×D132−1+418yes—
132C22×D13C2512yes—
133C22×D13C2512yes—
134Q8×C13C23×C4164yes—
135C2×C4×C13—216no—
136C2×C4×C13C23×C4124yes—
137C2×C4×C13C23×C4148yes—
138C2×C4×C13C25116yes—
139C2×C4×C13C25112yes—
140C2×Dic13—216no—
141C2×Dic13C23×C4124yes—
142C2×Dic13C23×C4148yes—
143C2×Dic13C25116yes—
144C2×Dic13C25112yes—
145C4×D13—264no—
146C4×D13C23×C4196yes—
147C4×D13C23×C4196yes—
148Dic26C23×C41192yes—
149C23×Q8—1332no—
150C23×Q8—134no—
151C23×Q8—134no—
152C23×Q8—1316no—
153C23×Q8—133no—
154C23×Q8C2×D1311yescharacteristic
155C24×C4—133no—
156#519—1316no—
157#519—13128no—
158#519—1396no—
159#519C2×D13116yesdirect product factor
160C2×C4×Q8—138no—
161C2×C4×Q8—13128no—
162C2×C4×Q8—1324no—
163C2×C4×Q8—1324no—
164C2×C4×Q8C2×D1318yescomplemented
165C2×#117—136no—
166C2×#117—1396no—
167C2×#117—1312no—
168C2×#117—1312no—
169C2×#117—1312no—
170C2×#117C2×D1316yes—
171C22×C4⋊C4—1312no—
172C22×C22⋊C4—134no—
173C22×C42—1312no—
174C22×C13—24no—
175C22×C13—28no—
176C22×C13C24×C414yes—
177C22×C13C24×C412yes—
178C22×C13C2×2−1+414yes—
179C22×C13C2611yescharacteristic
180C2×D13—24no—
181C2×D13—28no—
182C2×D13—232no—
183C2×D13#519116yesdirect product factor
184C2×D13C24×C414yes—
185C2×D13C24×C414yes—
186C2×D13C2×2−1+418yes—
187C4×C13—216no—
188C4×C13C24×C4124yes—
189Dic13—216no—
190Dic13C24×C4124yes—
191C25—131no—
192C22×Q8—1364no—
193C22×Q8—1364no—
194C22×Q8—13256no—
195C22×Q8—1332no—
196C22×Q8—1332no—
197C22×Q8—1348no—
198C22×Q8—1312no—
199C22×Q8—1324no—
200C22×Q8C4×D13116yescomplemented
201C22×Q8C22×D1314yes—
202C22×Q8C22×D1318yes—
203C23×C4—133no—
204C23×C4—1348no—
205C23×C4—136no—
206C23×C4—1324no—
207C23×C4—136no—
208C23×C4—138no—
209C23×C4C22×D1313yes—
210C4×Q8—1364no—
211C4×Q8—13192no—
212C4×Q8—13192no—
213C4×Q8C22×D13164yescomplemented
214#117—1348no—
215#117—1396no—
216#117—1396no—
217#117—1396no—
218#117C22×D13148yes—
219C2×C4⋊C4—1324no—
220C2×C4⋊C4—1312no—
221C2×C4⋊C4—1396no—
222C2×C4⋊C4C22×D13112yes—
223C2×C22⋊C4—134no—
224C2×C22⋊C4—138no—
225C2×C22⋊C4—1332no—
226C2×C22⋊C4C22×D1314yes—
227C2×C42—1324no—
228C2×C42—1312no—
229C2×C42—1396no—
230C2×C42C22×D13112yes—
231C2×C13—24no—
232C2×C13C2×#51914yescomplemented
233C2×C13C25×C411yescharacteristic
234C2×C13C22×2−1+412yes—
235D13—24no—
236D13C2×#51918yesdirect product factor
237C24—131no—
238C24—138no—
239C24—134no—
240C24—131no—
241C24—268no—
242C24C23×D1311yescharacteristic
243C2×Q8—13256no—
244C2×Q8—13256no—
245C2×Q8—1396no—
246C2×Q8—13192no—
247C2×Q8—1348no—
248C2×Q8C2×C4×D13132yes—
249C2×Q8C2×C4×D13164yescomplemented
250C2×Q8C23×D13116yes—
251C22×C4—1324no—
252C22×C4—1312no—
253C22×C4—136no—
254C22×C4—1348no—
255C22×C4—1348no—
256C22×C4—13192no—
257C22×C4—1324no—
258C22×C4—1324no—
259C22×C4—138no—
260C22×C4—1332no—
261C22×C4—2632no—
262C22×C4C2×C4×D13124yes—
263C22×C4C23×D1318yes—
264C22×C4C23×D13112yes—
265C22×C4C23×D1316yes—
266C4⋊C4—1396no—
267C4⋊C4—1348no—
268C4⋊C4C23×D13148yes—
269C22⋊C4—1316no—
270C22⋊C4—1332no—
271C22⋊C4C23×D13116yes—
272C42—1396no—
273C42—1348no—
274C42C23×D13148yes—
275C13C22×#51911yescharacteristic, complemented, Sylow
276C23—24no—
277C23—134no—
278C23—138no—
279C23—132no—
280C23—1316no—
281C23—134no—
282C23—132no—
283C23—2632no—
284C23—2616no—
285C23—264no—
286C23C22×C4×D1314yes—
287C23C24×D1312yes—
288C23C24×D1311yescharacteristic
289Q8—13192no—
290Q8C22×C4×D13164yes—
291C2×C4—216no—
292C2×C4—1348no—
293C2×C4—1324no—
294C2×C4—1312no—
295C2×C4—1396no—
296C2×C4—1396no—
297C2×C4—1316no—
298C2×C4—2664no—
299C2×C4—2616no—
300C2×C4C22×C4×D13124yes—
301C2×C4C22×C4×D13148yes—
302C2×C4C24×D13116yes—
303C2×C4C24×D13112yes—
304C22—28no—
305C22—24no—
306C22—1316no—
307C22—134no—
308C22—138no—
309C22—134no—
310C22—2632no—
311C22—268no—
312C22—264no—
313C22C23×C4×D1314yes—
314C22C23×C4×D1312yes—
315C22D13×2−1+414yes—
316C22C25×D1311yescharacteristic
317C4—216no—
318C4—1324no—
319C4—2616no—
320C4C23×C4×D13124yes—
321C2—24no—
322C2—138no—
323C2—264no—
324C2D13×#51914yesdirect product factor
325C2C24×C4×D1311yescharacteristic
326C2C2×D13×2−1+412yes—
subgroupG/H
centerC23C24×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC2×C13×#519C2
socleC23×C13C25
prime radicalC24×D13C23
cosocleC22×C13C26
hypercenterC2×#519D13
hypocenterC13C22×#519
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#11719517C2semidirect
3. C2×#11719221C2semidirect
4. C2×#11719277C2semidirect
5. D13×#519C2direct (N × H)
6. C2×C4×Q8×D13C2semidirect
8. C2×C13×#519C2semidirect
10. C22×Q8×D13C4semidirect
16. C13×#519C22semidirect
17. C2×C4×Q8×C13C22semidirect
19. #11719517C22semidirect
20. C2×Q8×Dic13C22semidirect
22. #11719277C22semidirect
23. C4×Q8×D13C22semidirect
25. #11719221C22semidirect
28. C2×#88141C22semidirect
33. C2×C4×Dic26C22semidirect
35. C22×Q8×C13C2×C4semidirect
41. C2×Q8×D13C2×C4semidirect
42. C2×Q8×D13C2×C4semidirect
50. C22×Dic26C2×C4semidirect
53. C4×Q8×C13C23semidirect
59. Q8×Dic13C23semidirect
68. #88141C23semidirect
73. C4×Dic26C23semidirect
82. C2×Q8×C13C22×C4semidirect
93. Q8×D13C22×C4semidirect
102. C2×Dic26C22×C4semidirect
118. C2×#519D13direct (N × H)
159. #519C2×D13direct (N × H)
164. C2×C4×Q8C2×D13semidirect
183. C2×D13#519direct (N × H)
200. C22×Q8C4×D13semidirect
213. C4×Q8C22×D13semidirect
232. C2×C13C2×#519semidirect
236. D13C2×#519direct (N × H)
249. C2×Q8C2×C4×D13semidirect
275. C13C22×#519semidirect
324. C2D13×#519direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D132
C2×#117195172
C2×#117192212
C2×#117192772
D13×#5192
C2×C4×Q8×D132
C2×D13×#1172
C2×C13×#5192
C22×#51913