Finite Group Databasebeta

← C23×C5×C22⋊D5 #13107874

Subgroups — C23×C5×C22⋊D5 #13107874

Order 1600.

3472 conjugacy classes of subgroups; only the 1086 normal subgroups are shown.

normal subgroups only

This group has 3472 conjugacy classes of subgroups — too many to draw. Only its 1086 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
1C25×C52C211yesmaximal, characteristic, complemented
2C24×C5×D5C211yesmaximal, characteristic, complemented
3C22×C5×C22⋊D5C2128yesmaximal, direct product factor
4C23×C5×Dic5C211yesmaximal, characteristic, complemented
5C24×C52—28no—
6C24×C52C2211yescharacteristic
7C24×C52C22114yescomplemented
8C23×C5×D5—28no—
9C23×C5×D5C22114yescomplemented
10C2×C5×C22⋊D5C221112yesdirect product factor
11C22×C5×Dic5C22114yescomplemented
12C23×C5×D4—51nomaximal
13C23×C22⋊D5C511yesmaximal, characteristic, direct product factor
14C23×C52—256no—
15C23×C52D418yescomplemented
16C23×C52C2317yes—
17C23×C52C23128yescomplemented
18C22×C5×D5—256no—
19C22×C5×D5C23128yescomplemented
20C5×C22⋊D5C23164yesdirect product factor
21C2×C5×Dic5C23128yescomplemented
22C25×C5—22no—
23C25×C5—51no—
24C25×C5D511yescharacteristic, complemented
25C25×C5C2×C511yescharacteristic, complemented
26C24×D5C2×C511yescharacteristic, complemented
27C22×C5×D4—528no—
28C23×C4×C5—51no—
29C22×C22⋊D5C2×C5128yesdirect product factor
30C23×Dic5C2×C511yescharacteristic, complemented
31C22×C52—256no—
32C22×C52C2×D4128yescomplemented
33C22×C52C2417yes—
34C22×C52C2418yescomplemented
35C2×C5×D5—256no—
36C2×C5×D5C2418yescomplemented
37C5×Dic5C2418yescomplemented
38C24×C5—232no—
39C24×C5—28no—
40C24×C5—28no—
41C24×C5—22no—
42C24×C5—228no—
43C24×C5—514no—
44C24×C5—108no—
45C24×C5C2×D511yescharacteristic
46C24×C5C2×D5114yescomplemented
47C24×C5C22×C511yescharacteristic
48C24×C5C22×C5114yescomplemented
49C23×D5—28no—
50C23×D5C22×C5114yescomplemented
51C2×C5×D4—5112no—
52C22×C4×C5—514no—
53C2×C22⋊D5C22×C51112yesdirect product factor
54C22×Dic5C22×C5114yescomplemented
55C23×D4—51noSylow
56C2×C52—28no—
57C2×C52C22×D4114yescomplemented
58C2×C52C2511yescharacteristic
59C5×D5—28no—
60C23×C5—2224no—
61C23×C5—256no—
62C23×C5—256no—
63C23×C5—216no—
64C23×C5—214no—
65C23×C5—256no—
66C23×C5—528no—
67C23×C5—1056no—
68C23×C5C22⋊D518yesdirect product factor
69C23×C5C5×D418yescomplemented
70C23×C5C22×D517yes—
71C23×C5C22×D5128yescomplemented
72C23×C5C23×C517yes—
73C23×C5C23×C5128yescomplemented
74C22×D5—256no—
75C22×D5C23×C5128yescomplemented
76C5×D4—564no—
77C2×C4×C5—528no—
78C22⋊D5C23×C5164yesdirect product factor
79C2×Dic5C23×C5128yescomplemented
80C25—51no—
81C25C5×D511yescharacteristic, complemented
82C22×D4—528no—
83C23×C4—51no—
84C52C23×D411yescharacteristic, complemented, Sylow
85C22×C5—2224no—
86C22×C5—256no—
87C22×C5—256no—
88C22×C5—256no—
89C22×C5—214no—
90C22×C5—216no—
91C22×C5—58no—
92C22×C5—1056no—
93C22×C5C2×C22⋊D5128yesdirect product factor
94C22×C5C2×C5×D4128yescomplemented
95C22×C5C23×D517yes—
96C22×C5C23×D518yescomplemented
97C22×C5C24×C517yes—
98C22×C5C24×C518yescomplemented
99C2×D5—256no—
100C2×D5C24×C518yescomplemented
101C4×C5—58no—
102Dic5C24×C518yescomplemented
103C24—28no—
104C24—514no—
105C24—108no—
106C24C2×C5×D511yescharacteristic
107C24C2×C5×D5114yescomplemented
108C2×D4—5112no—
109C22×C4—514no—
110C2×C5—232no—
111C2×C5—28no—
112C2×C5—28no—
113C2×C5—228no—
114C2×C5—22no—
115C2×C5—108no—
116C2×C5C22×C22⋊D5114yesdirect product factor
117C2×C5C22×C5×D4114yescomplemented
118C2×C5C24×D511yescharacteristic
119C2×C5C25×C511yescharacteristic
120D5—28no—
121C23—256no—
122C23—528no—
123C23—1056no—
124C23C5×C22⋊D518yesdirect product factor
125C23C22×C5×D517yes—
126C23C22×C5×D5128yescomplemented
127D4—564no—
128C2×C4—528no—
129C5—22no—
130C5C23×C22⋊D511yescharacteristic, direct product factor
131C5C23×C5×D411yescharacteristic, complemented
132C22—256no—
133C22—58no—
134C22—1056no—
135C22C2×C5×C22⋊D5128yesdirect product factor
136C22C23×C5×D517yes—
137C22C23×C5×D518yescomplemented
138C4—58no—
139C2—28no—
140C2—108no—
141C2C22×C5×C22⋊D5114yesdirect product factor
142C2C24×C5×D511yescharacteristic
subgroupG/H
centerC24×C5C2×D5
commutator, cosocleC2×C5C25×C5
FrattiniC2C24×C5×D5
FittingC25×C52C2
socleC24×C52C22
hypercenterC25×C5D5
hypocenterC5C23×C5×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C5 ◁ C25×C5

Complements

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

NH ≅ G/Ntype
1. C25×C52C2semidirect
2. C24×C5×D5C2semidirect
3. C22×C5×C22⋊D5C2direct (N × H)
4. C23×C5×Dic5C2semidirect
7. C24×C52C22semidirect
9. C23×C5×D5C22semidirect
10. C2×C5×C22⋊D5C22direct (N × H)
11. C22×C5×Dic5C22semidirect
13. C23×C22⋊D5C5direct (N × H)
15. C23×C52D4semidirect
17. C23×C52C23semidirect
19. C22×C5×D5C23semidirect
20. C5×C22⋊D5C23direct (N × H)
21. C2×C5×Dic5C23semidirect
24. C25×C5D5semidirect
25. C25×C5C2×C5semidirect
26. C24×D5C2×C5semidirect
29. C22×C22⋊D5C2×C5direct (N × H)
30. C23×Dic5C2×C5semidirect
32. C22×C52C2×D4semidirect
34. C22×C52C24semidirect
36. C2×C5×D5C24semidirect
37. C5×Dic5C24semidirect
46. C24×C5C2×D5semidirect
48. C24×C5C22×C5semidirect
50. C23×D5C22×C5semidirect
53. C2×C22⋊D5C22×C5direct (N × H)
54. C22×Dic5C22×C5semidirect
57. C2×C52C22×D4semidirect
68. C23×C5C22⋊D5direct (N × H)
69. C23×C5C5×D4semidirect
71. C23×C5C22×D5semidirect
73. C23×C5C23×C5semidirect
75. C22×D5C23×C5semidirect
78. C22⋊D5C23×C5direct (N × H)
79. C2×Dic5C23×C5semidirect
81. C25C5×D5semidirect
84. C52C23×D4semidirect
93. C22×C5C2×C22⋊D5direct (N × H)
94. C22×C5C2×C5×D4semidirect
96. C22×C5C23×D5semidirect
98. C22×C5C24×C5semidirect
100. C2×D5C24×C5semidirect
102. Dic5C24×C5semidirect
107. C24C2×C5×D5semidirect
116. C2×C5C22×C22⋊D5direct (N × H)
117. C2×C5C22×C5×D4semidirect
124. C23C5×C22⋊D5direct (N × H)
126. C23C22×C5×D5semidirect
130. C5C23×C22⋊D5direct (N × H)
131. C5C23×C5×D4semidirect
135. C22C2×C5×C22⋊D5direct (N × H)
137. C22C23×C5×D5semidirect
141. C2C22×C5×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C522
C24×C5×D52
C22×C5×C22⋊D52
C23×C5×Dic52
C23×C5×D45
C23×C22⋊D55