Finite Group Databasebeta

← C2×D4×#1035 #13099669

Subgroups — C2×D4×#1035 #13099669

Order 1600.

639 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 639 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1035C212yesmaximal, complemented
2C2×D4×D25C211yesmaximal, characteristic
3C2×C22⋊#1035C212yesmaximal, complemented
4D4×#1035C218yesmaximal, direct product factor
5C2×C4⋊#1035C211yesmaximal, characteristic, complemented
6C2×C4×#1035C211yesmaximal, characteristic, complemented
7C23×D25C2212yes—
8C22×#1035—28no—
9C22×#1035C2212yes—
10C22×#1035C2211yescharacteristic
11C22×#1035C2211yescharacteristic
12C22×#1035C2218yescomplemented
13C2×D4×C25C411yescharacteristic, complemented
14C2×C22⋊D25C412yescomplemented
15D4×D25C414yescomplemented
16D4×D25C2214yes—
17C2×D100C411yescharacteristic, complemented
18C2×C4×D25C2211yescharacteristic
19C22⋊#1035C2218yescomplemented
20C4⋊#1035C2214yescomplemented
21C4×#1035C2214yescomplemented
22C2×D4×AGL(1,𝔽5)—51nomaximal
23C23×C25C2×C412yescomplemented
24C22×D25—24no—
25C22×D25—24no—
26C22×D25C2×C414yescomplemented
27C22×D25C2×C412yescomplemented
28C22×D25C2314yes—
29C22×D25C2311yescharacteristic
30C2×#1035—24no—
31C2×#1035—22no—
32C2×#1035—216no—
33C2×#1035D414yesdirect product factor
34C2×#1035C2312yes—
35C2×#1035C2314yes—
36C2×#1035C2312yes—
37D4×C25C2×C414yescomplemented
38C2×C4×C25C2×C411yescharacteristic, complemented
39C22⋊D25C2×C418yescomplemented
40C2×Dic25C2×C411yescharacteristic, complemented
41D100C2×C414yescomplemented
42C4×D25C2×C412yescomplemented
43C4×D25C2312yes—
44C23×AGL(1,𝔽5)—52no—
45C2×D4×D5—51no—
46C2×C22⋊AGL(1,𝔽5)—52no—
47D4×AGL(1,𝔽5)—58no—
48C2×C4⋊AGL(1,𝔽5)—51no—
49C2×C4×AGL(1,𝔽5)—51no—
50C22×C25—24no—
51C22×C25C22×C411yescharacteristic
52C22×C25C22×C414yescomplemented
53C2×D25—24no—
54C2×D25—28no—
55C2×D25—24no—
56C2×D25—24no—
57C2×D25C22×C411yescharacteristic
58C2×D25C22×C414yescomplemented
59C2×D25C2×D412yes—
60C2×D25#4112yes—
61C2×D25C2411yescharacteristic
62#1035—24no—
63#1035—22no—
64#1035C2×D414yesdirect product factor
65C4×C25C22×C412yescomplemented
66Dic25C22×C412yescomplemented
67C23×D5—52no—
68C22×AGL(1,𝔽5)—51no—
69C22×AGL(1,𝔽5)—51no—
70C22×AGL(1,𝔽5)—52no—
71C22×AGL(1,𝔽5)—58no—
72C22×AGL(1,𝔽5)—108no—
73C2×C5×D4AGL(1,𝔽5)11yescharacteristic
74C2×C22⋊D5—52no—
75D4×D5—54no—
76D4×D5—54no—
77C2×D20—51no—
78C2×C4×D5—51no—
79C22⋊AGL(1,𝔽5)—58no—
80C4⋊AGL(1,𝔽5)—54no—
81C4×AGL(1,𝔽5)—54no—
82C2×C4×D4—251noSylow
83C2×C25—24no—
84C2×C25C4×D412yescomplemented
85C2×C25C23×C411yescharacteristic
86D25—24no—
87D25C4×D412yescomplemented
88D25C22×D411yescharacteristic
89D25C2×#4111yescharacteristic
90C23×C5C2×AGL(1,𝔽5)12yes—
91C22×D5—51no—
92C22×D5—52no—
93C22×D5—54no—
94C22×D5—54no—
95C22×D5—104no—
96C22×D5—104no—
97C2×AGL(1,𝔽5)—54no—
98C2×AGL(1,𝔽5)—52no—
99C2×AGL(1,𝔽5)—52no—
100C2×AGL(1,𝔽5)—54no—
101C2×AGL(1,𝔽5)—1016no—
102C2×AGL(1,𝔽5)—102no—
103C2×AGL(1,𝔽5)—104no—
104C5×D4C2×AGL(1,𝔽5)14yes—
105C2×C4×C5C2×AGL(1,𝔽5)11yescharacteristic
106C22⋊D5—58no—
107C2×Dic5—51no—
108D20—54no—
109C4×D5—52no—
110C4×D5—52no—
111C22×D4—251no—
112C23×C4—252no—
113C4×D4—258no—
114C2×C4⋊C4—251no—
115C2×C22⋊C4—252no—
116C2×C42—251no—
117C25C2×C4×D411yescharacteristic, complemented, Sylow
118C22×C5—24no—
119C22×C5C22×AGL(1,𝔽5)11yescharacteristic
120C22×C5C22×AGL(1,𝔽5)14yes—
121C2×D5—52no—
122C2×D5—52no—
123C2×D5—51no—
124C2×D5—51no—
125C2×D5—54no—
126C2×D5—104no—
127C2×D5—104no—
128C2×D5—108no—
129C2×D5—104no—
130AGL(1,𝔽5)—54no—
131AGL(1,𝔽5)—102no—
132AGL(1,𝔽5)—104no—
133C4×C5C22×AGL(1,𝔽5)12yes—
134Dic5—52no—
135C24—252no—
136C2×D4—252no—
137C2×D4—254no—
138C2×D4—254no—
139C2×D4—251no—
140C2×D4#103511yescharacteristic, direct product factor
141C22×C4—251no—
142C22×C4—251no—
143C22×C4—251no—
144C22×C4—252no—
145C22×C4—258no—
146C22×C4—508no—
147C4⋊C4—254no—
148C22⋊C4—258no—
149C42—254no—
150C2×C5—24no—
151C2×C5D4×AGL(1,𝔽5)12yes—
152C2×C5C23×AGL(1,𝔽5)11yescharacteristic
153D5—51no—
154D5—51no—
155D5—52no—
156D5—104no—
157C23—251no—
158C23—252no—
159C23—254no—
160C23—254no—
161C23—504no—
162C23—504no—
163C23C2×#103512yescomplemented
164D4—258no—
165D4—254no—
166D4C2×#103514yesdirect product factor
167C2×C4—252no—
168C2×C4—254no—
169C2×C4—251no—
170C2×C4—252no—
171C2×C4—252no—
172C2×C4—252no—
173C2×C4—254no—
174C2×C4—5016no—
175C2×C4—504no—
176C2×C4—502no—
177C2×C4C2×#103511yescharacteristic, complemented
178C5C2×D4×AGL(1,𝔽5)11yescharacteristic
179C22—24no—
180C22—251no—
181C22—251no—
182C22—252no—
183C22—252no—
184C22—254no—
185C22—504no—
186C22—504no—
187C22—508no—
188C22—504no—
189C22C22×#103511yescharacteristic
190C22C22×#103514yescomplemented
191C4—254no—
192C4—252no—
193C4—504no—
194C4—502no—
195C4C22×#103512yescomplemented
196C2—24no—
197C2—251no—
198C2—251no—
199C2—252no—
200C2—504no—
201C2D4×#103512yesdirect product factor
202C2C23×#103511yescharacteristic
subgroupG/H
centerC22C22×#1035
commutatorC2×C25C23×C4
FrattiniC2×C5C23×AGL(1,𝔽5)
FittingC2×D4×C25C4
socleC22×C5C22×AGL(1,𝔽5)
prime radicalC2×D4×D25C2
cosocleC2×D25C24
hypercenterC2×D4#1035
hypocenterC25C2×C4×D4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#1035C2semidirect
3. C2×C22⋊#1035C2semidirect
4. D4×#1035C2direct (N × H)
5. C2×C4⋊#1035C2semidirect
6. C2×C4×#1035C2semidirect
12. C22×#1035C22semidirect
13. C2×D4×C25C4semidirect
14. C2×C22⋊D25C4semidirect
15. D4×D25C4semidirect
17. C2×D100C4semidirect
19. C22⋊#1035C22semidirect
20. C4⋊#1035C22semidirect
21. C4×#1035C22semidirect
23. C23×C25C2×C4semidirect
26. C22×D25C2×C4semidirect
27. C22×D25C2×C4semidirect
33. C2×#1035D4direct (N × H)
37. D4×C25C2×C4semidirect
38. C2×C4×C25C2×C4semidirect
39. C22⋊D25C2×C4semidirect
40. C2×Dic25C2×C4semidirect
41. D100C2×C4semidirect
42. C4×D25C2×C4semidirect
52. C22×C25C22×C4semidirect
58. C2×D25C22×C4semidirect
64. #1035C2×D4direct (N × H)
65. C4×C25C22×C4semidirect
66. Dic25C22×C4semidirect
84. C2×C25C4×D4semidirect
87. D25C4×D4semidirect
117. C25C2×C4×D4semidirect
140. C2×D4#1035direct (N × H)
163. C23C2×#1035semidirect
166. D4C2×#1035direct (N × H)
177. C2×C4C2×#1035semidirect
190. C22C22×#1035semidirect
195. C4C22×#1035semidirect
201. C2D4×#1035direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#10352
C2×D4×D252
C2×C22⋊#10352
D4×#10352
C2×C4⋊#10352
C2×C4×#10352
C2×D4×AGL(1,𝔽5)5