Finite Group Databasebeta

← C23×#4149 #13013187

Subgroups — C23×#4149 #13013187

Order 1280.

65726 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×#41C211yesmaximal, characteristic, complemented
2C22×#4149C21112yesmaximal, direct product factor
3C23×#713C212yesmaximal, complemented
4C23×D4×D5C216yesmaximal, complemented
5C23×#709C213yesmaximal, complemented
6C24×D20C213yesmaximal, complemented
7C25×D5C2216yescomplemented
8C22×C5×#41C22156yescomplemented
9C23×C5×Q8C2211yescharacteristic, complemented
10C23×C5×D4C2213yescomplemented
11C24×C4×C5C2213yescomplemented
12C23×C22⋊D5C2216yescomplemented
13C2×#4149C2211792yesdirect product factor
14C22×#713C221112yescomplemented
15C22×D4×D5C221336yescomplemented
16C22×#709C221168yescomplemented
17C23×D20C2213yescomplemented
18C23×D20C2216yescomplemented
19C23×D20C221168yescomplemented
20C23×C4×D5C2216yescomplemented
21C23×Dic10C2211yescharacteristic, complemented
22C23×H(5,𝔽2)—51nomaximal, Sylow
23C25×C5C2313yes—
24C24×D5—448no—
25C24×D5C2316yes—
26C24×D5C231168yescomplemented
27C2×C5×#41C231448yescomplemented
28C22×C5×Q8C23128yescomplemented
29C22×C5×D4C23184yescomplemented
30C23×C4×C5C2311yescharacteristic
31C23×C4×C5C2313yes—
32C23×C4×C5C23184yescomplemented
33C22×C22⋊D5C231168yescomplemented
34C23×Dic5C2312yes—
35#4149C2314096yesdirect product factor
36C2×#713C231896yescomplemented
37C2×D4×D5C2312688yescomplemented
38C2×#709C2311344yescomplemented
39C22×D20C23184yescomplemented
40C22×D20C231168yescomplemented
41C22×D20C2311344yescomplemented
42C22×C4×D5C231168yescomplemented
43C22×Dic10C23128yescomplemented
44C22×H(5,𝔽2)—5112no—
45C23×#41—52no—
46C23×#41—53no—
47C23×#41D511yescharacteristic, complemented
48C24×D4—56no—
49C24×D4—53no—
50C24×C5—224no—
51C24×C5C24142yes—
52C24×C5C2411yescharacteristic
53C23×D5—248no—
54C23×D5—4672no—
55C23×D5C24184yes—
56C23×D5C241672yescomplemented
57C5×#41C241512yescomplemented
58C2×C5×Q8C241112yescomplemented
59C2×C5×D4C241336yescomplemented
60C22×C4×C5C24114yes—
61C22×C4×C5C24142yes—
62C22×C4×C5C241336yescomplemented
63C2×C22⋊D5C241672yescomplemented
64C22×Dic5C24128yes—
65#713C2411024yescomplemented
66D4×D5C2413072yescomplemented
67#709C2411536yescomplemented
68C2×D20C241336yescomplemented
69C2×D20C241672yescomplemented
70C2×D20C2411536yescomplemented
71C2×C4×D5C241672yescomplemented
72C2×Dic10C241112yescomplemented
73C26—56no—
74C2×H(5,𝔽2)—51792no—
75C22×#41—5112no—
76C22×#41—5168no—
77C22×#41C2×D5156yescomplemented
78C23×Q8—51no—
79C23×Q8C2×D511yescharacteristic, complemented
80C23×D4—56no—
81C23×D4—5336no—
82C23×D4—56no—
83C23×D4—53no—
84C23×D4—5168no—
85C23×D4C2×D513yescomplemented
86C24×C4—56no—
87C24×C4C2×D513yescomplemented
88C23×C5—2168no—
89C23×C5H(5,𝔽2)18yescomplemented
90C23×C5C25184yes—
91C23×C5C2517yes—
92C22×D5—2336no—
93C22×D5—41344no—
94C22×D5C251168yes—
95C22×D5C251384yescomplemented
96C5×Q8C25164yescomplemented
97C5×D4C251192yescomplemented
98C2×C4×C5C25128yes—
99C2×C4×C5C25184yes—
100C2×C4×C5C251192yescomplemented
101C22⋊D5C251384yescomplemented
102C2×Dic5C25156yes—
103D20C251192yescomplemented
104D20C251384yescomplemented
105C4×D5C251384yescomplemented
106Dic10C25164yescomplemented
107C25—56no—
108C25—5168no—
109C25—2048no—
110C25C22×D513yes—
111H(5,𝔽2)—54096no—
112C2×#41—5896no—
113C2×#41—51344no—
114C2×#41C22×D51448yescomplemented
115C22×Q8—528no—
116C22×Q8C22×D5128yescomplemented
117C22×D4—5168no—
118C22×D4—52688no—
119C22×D4—5168no—
120C22×D4—584no—
121C22×D4—51344no—
122C22×D4C22×D5184yescomplemented
123C23×C4—52no—
124C23×C4—5168no—
125C23×C4C22×D513yes—
126C23×C4C22×D511yescharacteristic
127C23×C4C22×D5184yescomplemented
128C22×C5—2168no—
129C22×C5C2×H(5,𝔽2)128yescomplemented
130C22×C5C26124yes—
131C22×C5C2617yes—
132C2×D5—2336no—
133C2×D5—4384no—
134C2×D5C26148yes—
135C4×C5C2618yes—
136C4×C5C26124yes—
137Dic5C26116yes—
138C24—224no—
139C24—584no—
140C24—5672no—
141C24—1048no—
142C24—20672no—
143C24C23×D5142yes—
144C24C23×D511yescharacteristic
145#41—51024no—
146#41—51536no—
147#41C23×D51512yescomplemented
148C2×Q8—5112no—
149C2×Q8C23×D51112yescomplemented
150C2×D4—5672no—
151C2×D4—53072no—
152C2×D4—5672no—
153C2×D4—5336no—
154C2×D4—51536no—
155C2×D4C23×D51336yescomplemented
156C22×C4—528no—
157C22×C4—5672no—
158C22×C4C23×D5142yes—
159C22×C4C23×D5114yes—
160C22×C4C23×D51336yescomplemented
161C2×C5—224no—
162C2×C5C22×H(5,𝔽2)114yescomplemented
163C2×C5C2711yescharacteristic
164D5—248no—
165C23—2168no—
166C23—5168no—
167C23—5384no—
168C23—10336no—
169C23—201344no—
170C23#414918yesdirect product factor
171C23C24×D5184yes—
172C23C24×D517yes—
173Q8—564no—
174Q8C24×D5164yescomplemented
175D4—5384no—
176D4—5384no—
177D4—5192no—
178D4C24×D51192yescomplemented
179C2×C4—556no—
180C2×C4—5384no—
181C2×C4C24×D5184yes—
182C2×C4C24×D5128yes—
183C2×C4C24×D51192yescomplemented
184C5C23×H(5,𝔽2)11yescharacteristic, complemented, Sylow
185C22—2168no—
186C22—548no—
187C22—10336no—
188C22—20384no—
189C22C2×#4149128yesdirect product factor
190C22C25×D5124yes—
191C22C25×D517yes—
192C4—516no—
193C4C25×D5124yes—
194C4C25×D518yes—
195C2—224no—
196C2—1048no—
197C2C22×#4149114yesdirect product factor
198C2C26×D511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC2×C5C27
FrattiniC2C26×D5
FittingC23×C5×#41C2
socleC24×C5C24
hypercenterC23×#41D5
hypocenterC5C23×H(5,𝔽2)
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C23×C5×#41C2semidirect
2. C22×#4149C2direct (N × H)
3. C23×#713C2semidirect
4. C23×D4×D5C2semidirect
5. C23×#709C2semidirect
6. C24×D20C2semidirect
7. C25×D5C22semidirect
8. C22×C5×#41C22semidirect
9. C23×C5×Q8C22semidirect
10. C23×C5×D4C22semidirect
11. C24×C4×C5C22semidirect
12. C23×C22⋊D5C22semidirect
13. C2×#4149C22direct (N × H)
14. C22×#713C22semidirect
15. C22×D4×D5C22semidirect
16. C22×#709C22semidirect
17. C23×D20C22semidirect
18. C23×D20C22semidirect
19. C23×D20C22semidirect
20. C23×C4×D5C22semidirect
21. C23×Dic10C22semidirect
26. C24×D5C23semidirect
27. C2×C5×#41C23semidirect
28. C22×C5×Q8C23semidirect
29. C22×C5×D4C23semidirect
32. C23×C4×C5C23semidirect
33. C22×C22⋊D5C23semidirect
35. #4149C23direct (N × H)
36. C2×#713C23semidirect
37. C2×D4×D5C23semidirect
38. C2×#709C23semidirect
39. C22×D20C23semidirect
40. C22×D20C23semidirect
41. C22×D20C23semidirect
42. C22×C4×D5C23semidirect
43. C22×Dic10C23semidirect
47. C23×#41D5semidirect
56. C23×D5C24semidirect
57. C5×#41C24semidirect
58. C2×C5×Q8C24semidirect
59. C2×C5×D4C24semidirect
62. C22×C4×C5C24semidirect
63. C2×C22⋊D5C24semidirect
65. #713C24semidirect
66. D4×D5C24semidirect
67. #709C24semidirect
68. C2×D20C24semidirect
69. C2×D20C24semidirect
70. C2×D20C24semidirect
71. C2×C4×D5C24semidirect
72. C2×Dic10C24semidirect
77. C22×#41C2×D5semidirect
79. C23×Q8C2×D5semidirect
85. C23×D4C2×D5semidirect
87. C24×C4C2×D5semidirect
89. C23×C5H(5,𝔽2)semidirect
95. C22×D5C25semidirect
96. C5×Q8C25semidirect
97. C5×D4C25semidirect
100. C2×C4×C5C25semidirect
101. C22⋊D5C25semidirect
103. D20C25semidirect
104. D20C25semidirect
105. C4×D5C25semidirect
106. Dic10C25semidirect
114. C2×#41C22×D5semidirect
116. C22×Q8C22×D5semidirect
122. C22×D4C22×D5semidirect
127. C23×C4C22×D5semidirect
129. C22×C5C2×H(5,𝔽2)semidirect
147. #41C23×D5semidirect
149. C2×Q8C23×D5semidirect
155. C2×D4C23×D5semidirect
160. C22×C4C23×D5semidirect
162. C2×C5C22×H(5,𝔽2)semidirect
170. C23#4149direct (N × H)
174. Q8C24×D5semidirect
178. D4C24×D5semidirect
183. C2×C4C24×D5semidirect
184. C5C23×H(5,𝔽2)semidirect
189. C22C2×#4149direct (N × H)
197. C2C22×#4149direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×#412
C22×#41492
C23×#7132
C23×D4×D52
C23×#7092
C24×D202
C23×H(5,𝔽2)5