Finite Group Databasebeta

← C2×#10619442 #13013197

Subgroups — C2×#10619442 #13013197

Order 1280.

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
1C2×C5×#585C211yesmaximal, characteristic, complemented
2#10619442C2164yesmaximal, direct product factor
3C2×#66287C2112yesmaximal, complemented
4C2×D5×H(5,𝔽2)C2120yesmaximal, complemented
5C2×#66283C2115yesmaximal, complemented
6C22×#4149C2115yesmaximal, complemented
7C5×#585C22132yescomplemented
8C2×C5×2−1+4C2216yescomplemented
9C2×C5×H(5,𝔽2)C22110yescomplemented
10C22×C5×#41C22115yescomplemented
11#66287C221384yescomplemented
12D5×H(5,𝔽2)C221640yescomplemented
13#66283C221480yescomplemented
14C2×#4150C22120yescomplemented
15C2×#4149C22160yescomplemented
16C2×#4149C221120yescomplemented
17C2×#4149C221480yescomplemented
18C2×D5×#41C221120yescomplemented
19C2×#4147C22130yescomplemented
20C22×#713C22130yescomplemented
21C2×#4144C22190yescomplemented
22C22×D4×D5C22190yescomplemented
23C22×#709C22145yescomplemented
24C23×D20C22115yescomplemented
25C2×H(7,𝔽2)—51nomaximal, Sylow
26C24×D5C23130yescomplemented
27C5×2−1+4C23196yescomplemented
28C5×H(5,𝔽2)C231160yescomplemented
29C2×C5×#41C23160yescomplemented
30C2×C5×#41C23120yescomplemented
31C2×C5×#41C231240yescomplemented
32C22×C5×Q8C23115yescomplemented
33C22×C5×D4C23145yescomplemented
34C23×C4×C5C23115yescomplemented
35C22×C22⋊D5C23190yescomplemented
36#4150C231320yescomplemented
37#4149C231960yescomplemented
38#4149C2311920yescomplemented
39D5×#41C2311920yescomplemented
40#4147C231480yescomplemented
41C2×#713C231120yescomplemented
42C2×#713C231480yescomplemented
43C2×Q8×D5C23140yescomplemented
44#4144C2311440yescomplemented
45C2×#711C231120yescomplemented
46C2×D4×D5C231360yescomplemented
47C2×D4×D5C2311440yescomplemented
48C2×#709C23160yescomplemented
49C2×#709C231180yescomplemented
50C2×#709C231720yescomplemented
51C22×D20C23145yescomplemented
52C22×D20C23190yescomplemented
53C22×D20C231240yescomplemented
54C22×C4×D5C23190yescomplemented
55C22×Dic10C23115yescomplemented
56H(7,𝔽2)—564no—
57C2×#585—512no—
58C2×#585—515no—
59C2×#585D511yescharacteristic, complemented
60C22×H(5,𝔽2)—520no—
61C22×H(5,𝔽2)—515no—
62C24×C5C24115yes—
63C23×D5—860no—
64C23×D5C24190yes—
65C23×D5C241240yescomplemented
66C5×#41C241480yescomplemented
67C5×#41C241160yescomplemented
68C2×C5×Q8C24120yes—
69C2×C5×Q8C241120yescomplemented
70C2×C5×D4C24160yes—
71C2×C5×D4C241360yescomplemented
72C22×C4×C5C24115yes—
73C22×C4×C5C24145yes—
74C22×C4×C5C241120yescomplemented
75C2×C22⋊D5C241120yes—
76C2×C22⋊D5C241720yescomplemented
77C22×Dic5C24130yes—
78#713C241960yescomplemented
79Q8×D5C241320yescomplemented
80#711C241960yescomplemented
81D4×D5C2412880yescomplemented
82#709C241480yescomplemented
83#709C2411440yescomplemented
84C2×D20C24110yes—
85C2×D20C24190yes—
86C2×D20C241360yescomplemented
87C2×D20C241720yescomplemented
88C2×C4×D5C241120yes—
89C2×C4×D5C241720yescomplemented
90C2×Dic10C2416yes—
91C2×Dic10C24130yes—
92C2×Dic10C241120yescomplemented
93#585—5384no—
94#585—5480no—
95#585C2×D5132yescomplemented
96C2×2−1+4—520no—
97C2×2−1+4—530no—
98C2×2−1+4C2×D516yescomplemented
99C2×H(5,𝔽2)—5640no—
100C2×H(5,𝔽2)—5120no—
101C2×H(5,𝔽2)—560no—
102C2×H(5,𝔽2)—5480no—
103C2×H(5,𝔽2)—590no—
104C2×H(5,𝔽2)C2×D5110yescomplemented
105C22×#41—5120no—
106C22×#41—530no—
107C22×#41—545no—
108C22×#41C2×D5115yescomplemented
109C23×D4—590no—
110C23×D4—515no—
111C23×C5—430no—
112C23×C5C25115yes—
113C23×C5C25160yes—
114C22×D5—4180no—
115C22×D5—8240no—
116C22×D5C25120yes—
117C22×D5C251360yes—
118C5×Q8C25180yes—
119C5×D4C251240yes—
120C2×C4×C5C2511yescharacteristic
121C2×C4×C5C25115yes—
122C2×C4×C5C25160yes—
123C2×C4×C5C251180yes—
124C22⋊D5C251480yes—
125C2×Dic5C25112yes—
126C2×Dic5C251120yes—
127D20C25140yes—
128D20C251360yes—
129C4×D5C251480yes—
130Dic10C25124yes—
131Dic10C251120yes—
132C25—530no—
1332−1+4—5320no—
1342−1+4—5480no—
1352−1+4C22×D5196yescomplemented
136H(5,𝔽2)—51920no—
137H(5,𝔽2)—5960no—
138H(5,𝔽2)—51440no—
139H(5,𝔽2)C22×D51160yescomplemented
140C2×#41—51920no—
141C2×#41—5120no—
142C2×#41—5480no—
143C2×#41—5120no—
144C2×#41—5180no—
145C2×#41—560no—
146C2×#41—5720no—
147C2×#41C22×D5160yescomplemented
148C2×#41C22×D5120yescomplemented
149C2×#41C22×D51240yescomplemented
150C22×Q8—540no—
151C22×Q8—515no—
152C22×Q8C22×D5115yescomplemented
153C22×D4—590no—
154C22×D4—5360no—
155C22×D4—51440no—
156C22×D4—590no—
157C22×D4—545no—
158C22×D4—5240no—
159C22×D4C22×D5145yescomplemented
160C23×C4—590no—
161C23×C4C22×D5115yescomplemented
162C22×C5—230no—
163C22×C5—460no—
164C22×C5C26130yes—
165C22×C5C2611yescharacteristic
166C2×D5—240no—
167C2×D5—4360no—
168C2×D5C26140yes—
169C4×C5C2612yes—
170C4×C5C26130yes—
171Dic5C26124yes—
172C24—590no—
173C24—5240no—
174C24—4060no—
175C24C23×D5115yes—
176#41—5960no—
177#41—5960no—
178#41—51440no—
179#41—5480no—
180#41C23×D51480yescomplemented
181#41C23×D51160yescomplemented
182C2×Q8—5320no—
183C2×Q8—530no—
184C2×Q8—56no—
185C2×Q8—5120no—
186C2×Q8C23×D5120yes—
187C2×Q8C23×D51120yescomplemented
188C2×D4—5120no—
189C2×D4—5720no—
190C2×D4—52880no—
191C2×D4—590no—
192C2×D4—510no—
193C2×D4—5720no—
194C2×D4—5360no—
195C2×D4C23×D5160yes—
196C2×D4C23×D51360yescomplemented
197C22×C4—530no—
198C22×C4—5120no—
199C22×C4—5720no—
200C22×C4C23×D5145yes—
201C22×C4C23×D5115yes—
202C22×C4C23×D51120yescomplemented
203C2×C5—230no—
204C2×C5H(7,𝔽2)12yescomplemented
205C2×C5C2711yescharacteristic
206D5—240no—
207C23—430no—
208C23—520no—
209C23—5360no—
210C23—20180no—
211C23—40240no—
212C23C24×D5115yes—
213C23C24×D5160yes—
214Q8—5120no—
215Q8—524no—
216Q8C24×D5180yes—
217D4—5480no—
218D4—5360no—
219D4—540no—
220D4C24×D51240yes—
221C2×C4—5120no—
222C2×C4—512no—
223C2×C4—5480no—
224C2×C4C24×D51180yes—
225C2×C4C24×D5160yes—
226C2×C4C24×D5115yes—
227C2×C4C24×D511yescharacteristic
228C5C2×H(7,𝔽2)11yescharacteristic, complemented, Sylow
229C22—230no—
230C22—460no—
231C22—540no—
232C22—1040no—
233C22—20360no—
234C22C25×D5130yes—
235C22C25×D511yescharacteristic
236C4—524no—
237C4C25×D5130yes—
238C4C25×D512yes—
239C2—230no—
240C2—1040no—
241C2#1061944212yesdirect product factor
242C2C26×D511yescharacteristic
subgroupG/H
centerC22C25×D5
commutator, cosocleC2×C5C27
FrattiniC2C26×D5
FittingC2×C5×#585C2
socleC22×C5C26
hypercenterC2×#585D5
hypocenterC5C2×H(7,𝔽2)
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×C5×#585C2semidirect
2. #10619442C2direct (N × H)
3. C2×#66287C2semidirect
4. C2×D5×H(5,𝔽2)C2semidirect
5. C2×#66283C2semidirect
6. C22×#4149C2semidirect
7. C5×#585C22semidirect
8. C2×C5×2−1+4C22semidirect
9. C2×C5×H(5,𝔽2)C22semidirect
10. C22×C5×#41C22semidirect
11. #66287C22semidirect
12. D5×H(5,𝔽2)C22semidirect
13. #66283C22semidirect
14. C2×#4150C22semidirect
15. C2×#4149C22semidirect
16. C2×#4149C22semidirect
17. C2×#4149C22semidirect
18. C2×D5×#41C22semidirect
19. C2×#4147C22semidirect
20. C22×#713C22semidirect
21. C2×#4144C22semidirect
22. C22×D4×D5C22semidirect
23. C22×#709C22semidirect
24. C23×D20C22semidirect
26. C24×D5C23semidirect
27. C5×2−1+4C23semidirect
28. C5×H(5,𝔽2)C23semidirect
29. C2×C5×#41C23semidirect
30. C2×C5×#41C23semidirect
31. C2×C5×#41C23semidirect
32. C22×C5×Q8C23semidirect
33. C22×C5×D4C23semidirect
34. C23×C4×C5C23semidirect
35. C22×C22⋊D5C23semidirect
36. #4150C23semidirect
37. #4149C23semidirect
38. #4149C23semidirect
39. D5×#41C23semidirect
40. #4147C23semidirect
41. C2×#713C23semidirect
42. C2×#713C23semidirect
43. C2×Q8×D5C23semidirect
44. #4144C23semidirect
45. C2×#711C23semidirect
46. C2×D4×D5C23semidirect
47. C2×D4×D5C23semidirect
48. C2×#709C23semidirect
49. C2×#709C23semidirect
50. C2×#709C23semidirect
51. C22×D20C23semidirect
52. C22×D20C23semidirect
53. C22×D20C23semidirect
54. C22×C4×D5C23semidirect
55. C22×Dic10C23semidirect
59. C2×#585D5semidirect
65. C23×D5C24semidirect
66. C5×#41C24semidirect
67. C5×#41C24semidirect
69. C2×C5×Q8C24semidirect
71. C2×C5×D4C24semidirect
74. C22×C4×C5C24semidirect
76. C2×C22⋊D5C24semidirect
78. #713C24semidirect
79. Q8×D5C24semidirect
80. #711C24semidirect
81. D4×D5C24semidirect
82. #709C24semidirect
83. #709C24semidirect
86. C2×D20C24semidirect
87. C2×D20C24semidirect
89. C2×C4×D5C24semidirect
92. C2×Dic10C24semidirect
95. #585C2×D5semidirect
98. C2×2−1+4C2×D5semidirect
104. C2×H(5,𝔽2)C2×D5semidirect
108. C22×#41C2×D5semidirect
135. 2−1+4C22×D5semidirect
139. H(5,𝔽2)C22×D5semidirect
147. C2×#41C22×D5semidirect
148. C2×#41C22×D5semidirect
149. C2×#41C22×D5semidirect
152. C22×Q8C22×D5semidirect
159. C22×D4C22×D5semidirect
161. C23×C4C22×D5semidirect
180. #41C23×D5semidirect
181. #41C23×D5semidirect
187. C2×Q8C23×D5semidirect
196. C2×D4C23×D5semidirect
202. C22×C4C23×D5semidirect
204. C2×C5H(7,𝔽2)semidirect
228. C5C2×H(7,𝔽2)semidirect
241. C2#10619442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5852
#106194422
C2×#662872
C2×D5×H(5,𝔽2)2
C2×#662832
C22×#41492
C2×H(7,𝔽2)5