Finite Group Databasebeta

← C2×#11716563 #13099688

Subgroups — C2×#11716563 #13099688

Order 1600.

1347 conjugacy classes of subgroups; only the 517 normal subgroups are shown.

normal subgroups only

This group has 1347 conjugacy classes of subgroups — too many to draw. Only its 517 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
1C22×D4×C25C211yesmaximal, characteristic, complemented
2C22×C22⋊D25C214yesmaximal, complemented
3#11716563C2116yesmaximal, direct product factor
4C2×#87746C214yesmaximal, complemented
5C2×D4×D25C214yesmaximal, complemented
6C2×#87744C212yesmaximal, complemented
7C24×C25C2212yescomplemented
8C23×D25C2214yescomplemented
9C2×D4×C25C2214yescomplemented
10C2×D4×C25C2218yescomplemented
11C22×C4×C25C2211yescharacteristic, complemented
12C2×C22⋊D25C2214yescomplemented
13C2×C22⋊D25C2218yescomplemented
14C2×C22⋊D25C22132yescomplemented
15C22×Dic25C2214yescomplemented
16#87746C22132yescomplemented
17D4×D25C22132yescomplemented
18#87744C22116yescomplemented
19C2×D100C2212yescomplemented
20C2×C4×D25C2214yescomplemented
21C2×Dic50C2212yescomplemented
22C2×#4144—51nomaximal
23C23×C25—44no—
24C23×C25C2314yes—
25C23×C25C2311yescharacteristic
26C23×C25C2318yescomplemented
27C22×D25—48no—
28C22×D25C2314yes—
29C22×D25C23116yescomplemented
30D4×C25C23116yescomplemented
31C2×C4×C25C2312yes—
32C2×C4×C25C2314yescomplemented
33C22⋊D25C23116yescomplemented
34C22⋊D25C23132yescomplemented
35C2×Dic25C2314yes—
36C2×Dic25C23116yescomplemented
37D100C2318yescomplemented
38C4×D25C23116yescomplemented
39Dic50C2318yescomplemented
40C22×C5×D4D511yescharacteristic
41C22×C22⋊D5—54no—
42#4144—516no—
43C2×#711—54no—
44C2×D4×D5—54no—
45C2×#709—52no—
46C22×C25—28no—
47C22×C25—22no—
48C22×C25—48no—
49C22×C25C2418yes—
50C22×C25C2412yes—
51C22×C25C2411yescharacteristic
52C2×D25—28no—
53C2×D25—416no—
54C2×D25C2418yes—
55C4×C25C2414yes—
56Dic25C2418yes—
57C24×C5C2×D512yes—
58C23×D5—54no—
59C2×C5×D4C2×D514yes—
60C2×C5×D4C2×D518yes—
61C22×C4×C5C2×D511yescharacteristic
62C2×C22⋊D5—54no—
63C2×C22⋊D5—58no—
64C2×C22⋊D5—532no—
65C22×Dic5—54no—
66#711—532no—
67D4×D5—532no—
68#709—516no—
69C2×D20—52no—
70C2×C4×D5—54no—
71C2×Dic10—52no—
72C2×H(5,𝔽2)—251noSylow
73C2×C25—28no—
74C2×C25—22no—
75C2×C25H(5,𝔽2)12yescomplemented
76C2×C25C2511yescharacteristic
77D25—28no—
78C23×C5—44no—
79C23×C5C22×D514yes—
80C23×C5C22×D511yescharacteristic
81C23×C5C22×D518yes—
82C22×D5—54no—
83C22×D5—516no—
84C22×D5—208no—
85C5×D4C22×D5116yes—
86C2×C4×C5C22×D512yes—
87C2×C4×C5C22×D514yes—
88C22⋊D5—516no—
89C22⋊D5—532no—
90C2×Dic5—54no—
91C2×Dic5—516no—
92D20—58no—
93C4×D5—516no—
94Dic10—58no—
95H(5,𝔽2)—2516no—
96C2×#41—254no—
97C2×#41—252no—
98C22×D4—254no—
99C22×D4—254no—
100C22×D4D2511yescharacteristic, complemented
101C25C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
102C22×C5—28no—
103C22×C5—22no—
104C22×C5—48no—
105C22×C5C23×D518yes—
106C22×C5C23×D512yes—
107C22×C5C23×D511yescharacteristic
108C2×D5—58no—
109C2×D5—108no—
110C2×D5—2016no—
111C4×C5C23×D514yes—
112Dic5—58no—
113C24—254no—
114C24C2×D2512yescomplemented
115#41—2532no—
116#41—2516no—
117C2×Q8—252no—
118C2×D4—258no—
119C2×D4—254no—
120C2×D4—2532no—
121C2×D4—2532no—
122C2×D4—252no—
123C2×D4C2×D2514yescomplemented
124C2×D4C2×D2518yescomplemented
125C22×C4—254no—
126C22×C4—254no—
127C22×C4C2×D2511yescharacteristic, complemented
128C2×C5—28no—
129C2×C5—22no—
130C2×C5#414412yes—
131C2×C5C24×D511yescharacteristic
132D5—108no—
133C23—44no—
134C23—254no—
135C23—2516no—
136C23—1008no—
137C23C22×D2514yes—
138C23C22×D2511yescharacteristic
139C23C22×D2518yescomplemented
140Q8—258no—
141D4—2532no—
142D4—2516no—
143D4—258no—
144D4C22×D25116yescomplemented
145C2×C4—2516no—
146C2×C4—254no—
147C2×C4—2516no—
148C2×C4C22×D2512yes—
149C2×C4C22×D2514yescomplemented
150C5C2×#414411yescharacteristic
151C22—22no—
152C22—28no—
153C22—48no—
154C22—258no—
155C22—508no—
156C22—10016no—
157C22C23×D2518yes—
158C22C23×D2512yes—
159C22C23×D2511yescharacteristic
160C4—258no—
161C4C23×D2514yes—
162C2—22no—
163C2—28no—
164C2—508no—
165C2#1171656312yesdirect product factor
166C2C24×D2511yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC2×C25C25
FrattiniC2×C5C24×D5
FittingC22×D4×C25C2
socleC22×C5C23×D5
hypercenterC22×D4D25
hypocenterC25C2×H(5,𝔽2)
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C25C2semidirect
2. C22×C22⋊D25C2semidirect
3. #11716563C2direct (N × H)
4. C2×#87746C2semidirect
5. C2×D4×D25C2semidirect
6. C2×#87744C2semidirect
7. C24×C25C22semidirect
8. C23×D25C22semidirect
9. C2×D4×C25C22semidirect
10. C2×D4×C25C22semidirect
11. C22×C4×C25C22semidirect
12. C2×C22⋊D25C22semidirect
13. C2×C22⋊D25C22semidirect
14. C2×C22⋊D25C22semidirect
15. C22×Dic25C22semidirect
16. #87746C22semidirect
17. D4×D25C22semidirect
18. #87744C22semidirect
19. C2×D100C22semidirect
20. C2×C4×D25C22semidirect
21. C2×Dic50C22semidirect
26. C23×C25C23semidirect
29. C22×D25C23semidirect
30. D4×C25C23semidirect
32. C2×C4×C25C23semidirect
33. C22⋊D25C23semidirect
34. C22⋊D25C23semidirect
36. C2×Dic25C23semidirect
37. D100C23semidirect
38. C4×D25C23semidirect
39. Dic50C23semidirect
75. C2×C25H(5,𝔽2)semidirect
100. C22×D4D25semidirect
101. C25C2×H(5,𝔽2)semidirect
114. C24C2×D25semidirect
123. C2×D4C2×D25semidirect
124. C2×D4C2×D25semidirect
127. C22×C4C2×D25semidirect
139. C23C22×D25semidirect
144. D4C22×D25semidirect
149. C2×C4C22×D25semidirect
165. C2#11716563direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C252
C22×C22⋊D252
#117165632
C2×#877462
C2×D4×D252
C2×#877442
C2×#41445