Finite Group Databasebeta

← C2×#13129647 #16776816

Subgroups — C2×#13129647 #16776816

Order 3328.

60570 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129647C2164yesmaximal, direct product factor
2C2×#11719652C2112yesmaximal, complemented
3C2×#11719648C2115yesmaximal, complemented
4C22×#88256C2115yesmaximal, complemented
5C2×D13×H(5,𝔽2)C2120yesmaximal, complemented
6C2×C13×#585C211yesmaximal, characteristic, complemented
7C13×#585C22132yescomplemented
8C2×C13×2−1+4C2216yescomplemented
9C2×C13×H(5,𝔽2)C22110yescomplemented
10C22×C13×#41C22115yescomplemented
11#11719652C221384yescomplemented
12D13×H(5,𝔽2)C221640yescomplemented
13#11719648C221480yescomplemented
14C2×#88257C22120yescomplemented
15C2×#88256C221120yescomplemented
16C2×#88256C22160yescomplemented
17C2×#88256C221480yescomplemented
18C2×#41×D13C221120yescomplemented
19C2×#88254C22130yescomplemented
20C22×#6131C22130yescomplemented
21C2×#88251C22190yescomplemented
22C22×D4×D13C22190yescomplemented
23C22×#6127C22145yescomplemented
24C23×D52C22115yescomplemented
25C24×D13C23130yescomplemented
26C13×2−1+4C23196yescomplemented
27C13×H(5,𝔽2)C231160yescomplemented
28C2×C13×#41C23160yescomplemented
29C2×C13×#41C23120yescomplemented
30C2×C13×#41C231240yescomplemented
31C22×Q8×C13C23115yescomplemented
32C22×D4×C13C23145yescomplemented
33C23×C4×C13C23115yescomplemented
34C22×C22⋊D13C23190yescomplemented
35#88257C231320yescomplemented
36#88256C231960yescomplemented
37#88256C2311920yescomplemented
38#41×D13C2311920yescomplemented
39#88254C231480yescomplemented
40C2×#6131C231120yescomplemented
41C2×#6131C231480yescomplemented
42C2×Q8×D13C23140yescomplemented
43#88251C2311440yescomplemented
44C2×#6129C231120yescomplemented
45C2×D4×D13C231360yescomplemented
46C2×D4×D13C2311440yescomplemented
47C2×#6127C23160yescomplemented
48C2×#6127C231180yescomplemented
49C2×#6127C231720yescomplemented
50C22×D52C23145yescomplemented
51C22×D52C23190yescomplemented
52C22×D52C231240yescomplemented
53C22×C4×D13C23190yescomplemented
54C22×Dic26C23115yescomplemented
55C2×H(7,𝔽2)—131nomaximal, Sylow
56C24×C13C24115yes—
57C23×D13—860no—
58C23×D13C24190yes—
59C23×D13C241240yescomplemented
60C13×#41C241480yescomplemented
61C13×#41C241160yescomplemented
62C2×Q8×C13C24120yes—
63C2×Q8×C13C241120yescomplemented
64C2×D4×C13C24160yes—
65C2×D4×C13C241360yescomplemented
66C22×C4×C13C24115yes—
67C22×C4×C13C24145yes—
68C22×C4×C13C241120yescomplemented
69C2×C22⋊D13C241120yes—
70C2×C22⋊D13C241720yescomplemented
71C22×Dic13C24130yes—
72#6131C241960yescomplemented
73Q8×D13C241320yescomplemented
74#6129C241960yescomplemented
75D4×D13C2412880yescomplemented
76#6127C241480yescomplemented
77#6127C2411440yescomplemented
78C2×D52C24110yes—
79C2×D52C24190yes—
80C2×D52C241360yescomplemented
81C2×D52C241720yescomplemented
82C2×C4×D13C241120yes—
83C2×C4×D13C241720yescomplemented
84C2×Dic26C2416yes—
85C2×Dic26C24130yes—
86C2×Dic26C241120yescomplemented
87H(7,𝔽2)—1364no—
88C2×#585—1312no—
89C2×#585—1315no—
90C2×#585D1311yescharacteristic, complemented
91C22×H(5,𝔽2)—1320no—
92C22×H(5,𝔽2)—1315no—
93C23×C13—430no—
94C23×C13C25115yes—
95C23×C13C25160yes—
96C22×D13—4180no—
97C22×D13—8240no—
98C22×D13C25120yes—
99C22×D13C251360yes—
100Q8×C13C25180yes—
101D4×C13C251240yes—
102C2×C4×C13C2511yescharacteristic
103C2×C4×C13C25115yes—
104C2×C4×C13C25160yes—
105C2×C4×C13C251180yes—
106C22⋊D13C251480yes—
107C2×Dic13C25112yes—
108C2×Dic13C251120yes—
109D52C25140yes—
110D52C251360yes—
111C4×D13C251480yes—
112Dic26C25124yes—
113Dic26C251120yes—
114#585—13384no—
115#585—13480no—
116#585C2×D13132yescomplemented
117C2×2−1+4—1320no—
118C2×2−1+4—1330no—
119C2×2−1+4C2×D1316yescomplemented
120C2×H(5,𝔽2)—13640no—
121C2×H(5,𝔽2)—13120no—
122C2×H(5,𝔽2)—1360no—
123C2×H(5,𝔽2)—13480no—
124C2×H(5,𝔽2)—1390no—
125C2×H(5,𝔽2)C2×D13110yescomplemented
126C22×#41—13120no—
127C22×#41—1330no—
128C22×#41—1345no—
129C22×#41C2×D13115yescomplemented
130C23×D4—1390no—
131C23×D4—1315no—
132C22×C13—230no—
133C22×C13—460no—
134C22×C13C26130yes—
135C22×C13C2611yescharacteristic
136C2×D13—240no—
137C2×D13—4360no—
138C2×D13C26140yes—
139C4×C13C2612yes—
140C4×C13C26130yes—
141Dic13C26124yes—
142C25—1330no—
1432−1+4—13320no—
1442−1+4—13480no—
1452−1+4C22×D13196yescomplemented
146H(5,𝔽2)—131920no—
147H(5,𝔽2)—13960no—
148H(5,𝔽2)—131440no—
149H(5,𝔽2)C22×D131160yescomplemented
150C2×#41—131920no—
151C2×#41—13120no—
152C2×#41—13480no—
153C2×#41—13120no—
154C2×#41—13180no—
155C2×#41—1360no—
156C2×#41—13720no—
157C2×#41C22×D13160yescomplemented
158C2×#41C22×D13120yescomplemented
159C2×#41C22×D131240yescomplemented
160C22×Q8—1340no—
161C22×Q8—1315no—
162C22×Q8C22×D13115yescomplemented
163C22×D4—1390no—
164C22×D4—13360no—
165C22×D4—131440no—
166C22×D4—1390no—
167C22×D4—1345no—
168C22×D4—13240no—
169C22×D4C22×D13145yescomplemented
170C23×C4—1390no—
171C23×C4C22×D13115yescomplemented
172C2×C13—230no—
173C2×C13H(7,𝔽2)12yescomplemented
174C2×C13C2711yescharacteristic
175D13—240no—
176C24—1390no—
177C24—13240no—
178C24—10460no—
179C24C23×D13115yes—
180#41—13960no—
181#41—13960no—
182#41—131440no—
183#41—13480no—
184#41C23×D131480yescomplemented
185#41C23×D131160yescomplemented
186C2×Q8—13320no—
187C2×Q8—1330no—
188C2×Q8—136no—
189C2×Q8—13120no—
190C2×Q8C23×D13120yes—
191C2×Q8C23×D131120yescomplemented
192C2×D4—13120no—
193C2×D4—13720no—
194C2×D4—132880no—
195C2×D4—1390no—
196C2×D4—1310no—
197C2×D4—13720no—
198C2×D4—13360no—
199C2×D4C23×D13160yes—
200C2×D4C23×D131360yescomplemented
201C22×C4—1330no—
202C22×C4—13120no—
203C22×C4—13720no—
204C22×C4C23×D13145yes—
205C22×C4C23×D13115yes—
206C22×C4C23×D131120yescomplemented
207C13C2×H(7,𝔽2)11yescharacteristic, complemented, Sylow
208C23—430no—
209C23—1320no—
210C23—13360no—
211C23—52180no—
212C23—104240no—
213C23C24×D13115yes—
214C23C24×D13160yes—
215Q8—13120no—
216Q8—1324no—
217Q8C24×D13180yes—
218D4—13480no—
219D4—13360no—
220D4—1340no—
221D4C24×D131240yes—
222C2×C4—13120no—
223C2×C4—1312no—
224C2×C4—13480no—
225C2×C4C24×D131180yes—
226C2×C4C24×D13160yes—
227C2×C4C24×D13115yes—
228C2×C4C24×D1311yescharacteristic
229C22—230no—
230C22—460no—
231C22—1340no—
232C22—2640no—
233C22—52360no—
234C22C25×D13130yes—
235C22C25×D1311yescharacteristic
236C4—1324no—
237C4C25×D13130yes—
238C4C25×D1312yes—
239C2—230no—
240C2—2640no—
241C2#1312964712yesdirect product factor
242C2C26×D1311yescharacteristic
subgroupG/H
centerC22C25×D13
commutator, cosocleC2×C13C27
FrattiniC2C26×D13
FittingC2×C13×#585C2
socleC22×C13C26
hypercenterC2×#585D13
hypocenterC13C2×H(7,𝔽2)
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. #13129647C2direct (N × H)
2. C2×#11719652C2semidirect
3. C2×#11719648C2semidirect
4. C22×#88256C2semidirect
5. C2×D13×H(5,𝔽2)C2semidirect
6. C2×C13×#585C2semidirect
7. C13×#585C22semidirect
8. C2×C13×2−1+4C22semidirect
9. C2×C13×H(5,𝔽2)C22semidirect
10. C22×C13×#41C22semidirect
11. #11719652C22semidirect
12. D13×H(5,𝔽2)C22semidirect
13. #11719648C22semidirect
14. C2×#88257C22semidirect
15. C2×#88256C22semidirect
16. C2×#88256C22semidirect
17. C2×#88256C22semidirect
18. C2×#41×D13C22semidirect
19. C2×#88254C22semidirect
20. C22×#6131C22semidirect
21. C2×#88251C22semidirect
22. C22×D4×D13C22semidirect
23. C22×#6127C22semidirect
24. C23×D52C22semidirect
25. C24×D13C23semidirect
26. C13×2−1+4C23semidirect
27. C13×H(5,𝔽2)C23semidirect
28. C2×C13×#41C23semidirect
29. C2×C13×#41C23semidirect
30. C2×C13×#41C23semidirect
31. C22×Q8×C13C23semidirect
32. C22×D4×C13C23semidirect
33. C23×C4×C13C23semidirect
34. C22×C22⋊D13C23semidirect
35. #88257C23semidirect
36. #88256C23semidirect
37. #88256C23semidirect
38. #41×D13C23semidirect
39. #88254C23semidirect
40. C2×#6131C23semidirect
41. C2×#6131C23semidirect
42. C2×Q8×D13C23semidirect
43. #88251C23semidirect
44. C2×#6129C23semidirect
45. C2×D4×D13C23semidirect
46. C2×D4×D13C23semidirect
47. C2×#6127C23semidirect
48. C2×#6127C23semidirect
49. C2×#6127C23semidirect
50. C22×D52C23semidirect
51. C22×D52C23semidirect
52. C22×D52C23semidirect
53. C22×C4×D13C23semidirect
54. C22×Dic26C23semidirect
59. C23×D13C24semidirect
60. C13×#41C24semidirect
61. C13×#41C24semidirect
63. C2×Q8×C13C24semidirect
65. C2×D4×C13C24semidirect
68. C22×C4×C13C24semidirect
70. C2×C22⋊D13C24semidirect
72. #6131C24semidirect
73. Q8×D13C24semidirect
74. #6129C24semidirect
75. D4×D13C24semidirect
76. #6127C24semidirect
77. #6127C24semidirect
80. C2×D52C24semidirect
81. C2×D52C24semidirect
83. C2×C4×D13C24semidirect
86. C2×Dic26C24semidirect
90. C2×#585D13semidirect
116. #585C2×D13semidirect
119. C2×2−1+4C2×D13semidirect
125. C2×H(5,𝔽2)C2×D13semidirect
129. C22×#41C2×D13semidirect
145. 2−1+4C22×D13semidirect
149. H(5,𝔽2)C22×D13semidirect
157. C2×#41C22×D13semidirect
158. C2×#41C22×D13semidirect
159. C2×#41C22×D13semidirect
162. C22×Q8C22×D13semidirect
169. C22×D4C22×D13semidirect
171. C23×C4C22×D13semidirect
173. C2×C13H(7,𝔽2)semidirect
184. #41C23×D13semidirect
185. #41C23×D13semidirect
191. C2×Q8C23×D13semidirect
200. C2×D4C23×D13semidirect
206. C22×C4C23×D13semidirect
207. C13C2×H(7,𝔽2)semidirect
241. C2#13129647direct (N × H)

Maximal subgroups

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

subgroupindex
#131296472
C2×#117196522
C2×#117196482
C22×#882562
C2×D13×H(5,𝔽2)2
C2×C13×#5852
C2×H(7,𝔽2)13