Finite Group Databasebeta

← C22×D4×D25 #13099686

Subgroups — C22×D4×D25 #13099686

Order 1600.

2043 conjugacy classes of subgroups; only the 581 normal subgroups are shown.

normal subgroups only

This group has 2043 conjugacy classes of subgroups — too many to draw. Only its 581 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
1C24×D25C212yesmaximal, complemented
2C22×D4×C25C211yesmaximal, characteristic, complemented
3C22×C22⋊D25C212yesmaximal, complemented
4C2×D4×D25C2124yesmaximal, direct product factor
5C22×D100C211yesmaximal, characteristic, complemented
6C22×C4×D25C211yesmaximal, characteristic, complemented
7C24×C25C2212yescomplemented
8C23×D25—216no—
9C23×D25C2211yescharacteristic
10C23×D25C22124yescomplemented
11C23×D25C2212yescomplemented
12C2×D4×C25C22112yescomplemented
13C22×C4×C25C2211yescharacteristic, complemented
14C2×C22⋊D25C22124yescomplemented
15C22×Dic25C2211yescharacteristic, complemented
16D4×D25C22164yesdirect product factor
17C2×D100C22112yescomplemented
18C2×C4×D25C22112yescomplemented
19C22×D4×D5—51nomaximal
20C23×C25—28no—
21C23×C25C2311yescharacteristic
22C23×C25C23112yescomplemented
23C22×D25—28no—
24C22×D25—296no—
25C22×D25D418yesdirect product factor
26C22×D25C2316yes—
27C22×D25C23132yescomplemented
28C22×D25C23112yescomplemented
29D4×C25C23116yescomplemented
30C2×C4×C25C2316yescomplemented
31C22⋊D25C23132yescomplemented
32C2×Dic25C2316yescomplemented
33D100C23116yescomplemented
34C4×D25C23116yescomplemented
35C24×D5—52no—
36C22×C5×D4D511yescharacteristic
37C22×C22⋊D5—52no—
38C2×D4×D5—524no—
39C22×D20—51no—
40C22×C4×D5—51no—
41C22×C25—224no—
42C22×C25C2×D414yescomplemented
43C22×C25C2413yes—
44C22×C25C2418yescomplemented
45C2×D25—224no—
46C2×D25—264no—
47C2×D25C2×D4124yesdirect product factor
48C2×D25C2414yes—
49C2×D25C2418yescomplemented
50C4×C25C2414yescomplemented
51Dic25C2414yescomplemented
52C24×C5C2×D512yes—
53C23×D5—51no—
54C23×D5—52no—
55C23×D5—524no—
56C23×D5—1016no—
57C2×C5×D4C2×D5112yes—
58C22×C4×C5C2×D511yescharacteristic
59C2×C22⋊D5—524no—
60C22×Dic5—51no—
61D4×D5—564no—
62C2×D20—512no—
63C2×C4×D5—512no—
64C23×D4—251noSylow
65C2×C25—28no—
66C2×C25C22×D416yescomplemented
67C2×C25C2511yescharacteristic
68D25—28no—
69D25C22×D418yesdirect product factor
70C23×C5—28no—
71C23×C5C22×D511yescharacteristic
72C23×C5C22×D5112yes—
73C22×D5—58no—
74C22×D5—56no—
75C22×D5—512no—
76C22×D5—532no—
77C22×D5—1096no—
78C22×D5—108no—
79C5×D4C22×D5116yes—
80C2×C4×C5C22×D516yes—
81C22⋊D5—532no—
82C2×Dic5—56no—
83D20—516no—
84C4×D5—516no—
85C25—252no—
86C22×D4—252no—
87C22×D4—2524no—
88C22×D4—251no—
89C22×D4D2511yescharacteristic, direct product factor
90C23×C4—251no—
91C25C23×D411yescharacteristic, complemented, Sylow
92C22×C5—224no—
93C22×C5D4×D514yes—
94C22×C5C23×D513yes—
95C22×C5C23×D518yes—
96C2×D5—524no—
97C2×D5—54no—
98C2×D5—58no—
99C2×D5—1064no—
100C2×D5—1024no—
101C4×C5C23×D514yes—
102Dic5—54no—
103C24—251no—
104C24—252no—
105C24—2524no—
106C24—5016no—
107C24C2×D2512yescomplemented
108C2×D4—2524no—
109C2×D4—2564no—
110C2×D4—2512no—
111C2×D4C2×D25112yesdirect product factor
112C22×C4—251no—
113C22×C4—2512no—
114C22×C4C2×D2511yescharacteristic, complemented
115C2×C5—28no—
116C2×C5C2×D4×D516yes—
117C2×C5C24×D511yescharacteristic
118D5—58no—
119D5—108no—
120C23—28no—
121C23—258no—
122C23—256no—
123C23—2512no—
124C23—2532no—
125C23—5096no—
126C23—508no—
127C23C22×D2511yescharacteristic
128C23C22×D25112yescomplemented
129D4—2532no—
130D4—2516no—
131D4C22×D25116yesdirect product factor
132C2×C4—256no—
133C2×C4—2516no—
134C2×C4C22×D2516yescomplemented
135C5C22×D4×D511yescharacteristic
136C22—224no—
137C22—254no—
138C22—2524no—
139C22—258no—
140C22—5064no—
141C22—5024no—
142C22D4×D2514yesdirect product factor
143C22C23×D2513yes—
144C22C23×D2518yescomplemented
145C4—254no—
146C4C23×D2514yescomplemented
147C2—28no—
148C2—258no—
149C2—508no—
150C2C2×D4×D2516yesdirect product factor
151C2C24×D2511yescharacteristic
subgroupG/H
centerC23C22×D25
commutator, cosocleC2×C25C25
FrattiniC2×C5C24×D5
FittingC22×D4×C25C2
socleC23×C5C22×D5
hypercenterC22×D4D25
hypocenterC25C23×D4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D25C2semidirect
2. C22×D4×C25C2semidirect
3. C22×C22⋊D25C2semidirect
4. C2×D4×D25C2direct (N × H)
5. C22×D100C2semidirect
6. C22×C4×D25C2semidirect
7. C24×C25C22semidirect
10. C23×D25C22semidirect
11. C23×D25C22semidirect
12. C2×D4×C25C22semidirect
13. C22×C4×C25C22semidirect
14. C2×C22⋊D25C22semidirect
15. C22×Dic25C22semidirect
16. D4×D25C22direct (N × H)
17. C2×D100C22semidirect
18. C2×C4×D25C22semidirect
22. C23×C25C23semidirect
25. C22×D25D4direct (N × H)
27. C22×D25C23semidirect
28. C22×D25C23semidirect
29. D4×C25C23semidirect
30. C2×C4×C25C23semidirect
31. C22⋊D25C23semidirect
32. C2×Dic25C23semidirect
33. D100C23semidirect
34. C4×D25C23semidirect
42. C22×C25C2×D4semidirect
44. C22×C25C24semidirect
47. C2×D25C2×D4direct (N × H)
49. C2×D25C24semidirect
50. C4×C25C24semidirect
51. Dic25C24semidirect
66. C2×C25C22×D4semidirect
69. D25C22×D4direct (N × H)
89. C22×D4D25direct (N × H)
91. C25C23×D4semidirect
107. C24C2×D25semidirect
111. C2×D4C2×D25direct (N × H)
114. C22×C4C2×D25semidirect
128. C23C22×D25semidirect
131. D4C22×D25direct (N × H)
134. C2×C4C22×D25semidirect
142. C22D4×D25direct (N × H)
144. C22C23×D25semidirect
146. C4C23×D25semidirect
150. C2C2×D4×D25direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D252
C22×D4×C252
C22×C22⋊D252
C2×D4×D252
C22×D1002
C22×C4×D252
C22×D4×D55