Finite Group Databasebeta

← C22×C3×Q8×D5 #11757100

Subgroups — C22×C3×Q8×D5 #11757100

Order 960.

1700 conjugacy classes of subgroups; only the 1006 normal subgroups are shown.

normal subgroups only

This group has 1700 conjugacy classes of subgroups — too many to draw. Only its 1006 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×C3×C5×Q8C211yesmaximal, characteristic, complemented
2C2×C3×Q8×D5C2124yesmaximal, direct product factor
3C22×C3×C4×D5C213yesmaximal
4C22×C3×Dic10C213yesmaximal, complemented
5C22×Q8×D5C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×D5C2211yescharacteristic
7C2×C3×C5×Q8C22112yescomplemented
8C22×C3×C4×C5C2213yes—
9C22×C3×Dic5C2213yes—
10C3×Q8×D5C22164yesdirect product factor
11C2×C3×C4×D5C22136yes—
12C2×C3×Dic10C22136yescomplemented
13C23×C3×Q8—51nomaximal, Hall
14C22×C5×Q8C2×C311yescharacteristic, complemented
15C2×Q8×D5C2×C3124yesdirect product factor
16C22×C4×D5C2×C313yes—
17C22×Dic10C2×C313yescomplemented
18C23×C3×C5C2311yescharacteristic
19C22×C3×D5Q818yesdirect product factor
20C22×C3×D5C2316yes—
21C3×C5×Q8C23116yescomplemented
22C2×C3×C4×C5C23118yes—
23C2×C3×Dic5C23118yes—
24C3×C4×D5C23148yes—
25C3×Dic10C23148yescomplemented
26C22×C3×Q8—524no—
27C22×C3×Q8—53no—
28C22×C3×Q8D511yescharacteristic, direct product factor
29C23×C3×C4—53no—
30C23×D5C22×C311yescharacteristic
31C2×C5×Q8C22×C3112yescomplemented
32C22×C4×C5C22×C313yes—
33C22×Dic5C22×C313yes—
34Q8×D5C22×C3164yesdirect product factor
35C2×C4×D5C22×C3136yes—
36C2×Dic10C22×C3136yescomplemented
37C23×Q8—51noSylow
38C22×C3×C5C2×Q814yescomplemented
39C22×C3×C5C2413yes—
40C2×C3×D5C2×Q8124yesdirect product factor
41C2×C3×D5C2414yes—
42C3×C4×C5C24112yes—
43C3×Dic5C24112yes—
44C24×C3—51no—
45C2×C3×Q8—564no—
46C2×C3×Q8—536no—
47C2×C3×Q8C2×D5112yesdirect product factor
48C22×C3×C4—53no—
49C22×C3×C4—536no—
50C22×C3×C4C2×D513yes—
51C23×C5C23×C311yescharacteristic
52C22×D5C3×Q818yesdirect product factor
53C22×D5C23×C316yes—
54C5×Q8C23×C3116yescomplemented
55C2×C4×C5C23×C3118yes—
56C2×Dic5C23×C3118yes—
57C4×D5C23×C3148yes—
58Dic10C23×C3148yescomplemented
59C22×Q8—524no—
60C22×Q8—53no—
61C22×Q8C3×D511yescharacteristic, direct product factor
62C23×C4—53no—
63C2×C3×C5C22×Q816yescomplemented
64C2×C3×C5C2511yescharacteristic
65C3×D5C22×Q818yesdirect product factor
66C23×C3—58no—
67C23×C3—56no—
68C23×C3C22×D511yescharacteristic
69C3×Q8—548no—
70C3×Q8C22×D5116yesdirect product factor
71C2×C3×C4—518no—
72C2×C3×C4—548no—
73C2×C3×C4C22×D5118yes—
74C22×C5C2×C3×Q814yescomplemented
75C22×C5C24×C313yes—
76C2×D5C2×C3×Q8124yesdirect product factor
77C2×D5C24×C314yes—
78C4×C5C24×C3112yes—
79Dic5C24×C3112yes—
80C24—51no—
81C2×Q8—564no—
82C2×Q8—536no—
83C2×Q8C2×C3×D5112yesdirect product factor
84C22×C4—53no—
85C22×C4—536no—
86C22×C4C2×C3×D513yes—
87C3×C5C23×Q811yescharacteristic, complemented, Hall
88C22×C3—524no—
89C22×C3—54no—
90C22×C3Q8×D514yesdirect product factor
91C22×C3C23×D513yes—
92C3×C4—512no—
93C3×C4C23×D5112yes—
94C2×C5C22×C3×Q816yescomplemented
95C2×C5C25×C311yescharacteristic
96D5C22×C3×Q818yesdirect product factor
97C23—58no—
98C23—56no—
99C23C22×C3×D511yescharacteristic
100Q8—548no—
101Q8C22×C3×D5116yesdirect product factor
102C2×C4—518no—
103C2×C4—548no—
104C2×C4C22×C3×D5118yes—
105C2×C3—58no—
106C2×C3C2×Q8×D516yesdirect product factor
107C2×C3C24×D511yescharacteristic
108C5C23×C3×Q811yescharacteristic, complemented, Sylow
109C22—524no—
110C22—54no—
111C22C3×Q8×D514yesdirect product factor
112C22C23×C3×D513yes—
113C4—512no—
114C4C23×C3×D5112yes—
115C3C22×Q8×D511yescharacteristic, direct product factor, Sylow
116C2—58no—
117C2C2×C3×Q8×D516yesdirect product factor
118C2C24×C3×D511yescharacteristic
subgroupG/H
centerC23×C3C22×D5
commutator, cosocleC2×C5C25×C3
FrattiniC2C24×C3×D5
FittingC22×C3×C5×Q8C2
socleC23×C3×C5C23
prime radicalC23×C3×D5C22
hypercenterC22×C3×Q8D5
hypocenterC5C23×C3×Q8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×Q8C2semidirect
2. C2×C3×Q8×D5C2direct (N × H)
4. C22×C3×Dic10C2semidirect
5. C22×Q8×D5C3direct (N × H)
7. C2×C3×C5×Q8C22semidirect
10. C3×Q8×D5C22direct (N × H)
12. C2×C3×Dic10C22semidirect
14. C22×C5×Q8C2×C3semidirect
15. C2×Q8×D5C2×C3direct (N × H)
17. C22×Dic10C2×C3semidirect
19. C22×C3×D5Q8direct (N × H)
21. C3×C5×Q8C23semidirect
25. C3×Dic10C23semidirect
28. C22×C3×Q8D5direct (N × H)
31. C2×C5×Q8C22×C3semidirect
34. Q8×D5C22×C3direct (N × H)
36. C2×Dic10C22×C3semidirect
38. C22×C3×C5C2×Q8semidirect
40. C2×C3×D5C2×Q8direct (N × H)
47. C2×C3×Q8C2×D5direct (N × H)
52. C22×D5C3×Q8direct (N × H)
54. C5×Q8C23×C3semidirect
58. Dic10C23×C3semidirect
61. C22×Q8C3×D5direct (N × H)
63. C2×C3×C5C22×Q8semidirect
65. C3×D5C22×Q8direct (N × H)
70. C3×Q8C22×D5direct (N × H)
74. C22×C5C2×C3×Q8semidirect
76. C2×D5C2×C3×Q8direct (N × H)
83. C2×Q8C2×C3×D5direct (N × H)
87. C3×C5C23×Q8semidirect
90. C22×C3Q8×D5direct (N × H)
94. C2×C5C22×C3×Q8semidirect
96. D5C22×C3×Q8direct (N × H)
101. Q8C22×C3×D5direct (N × H)
106. C2×C3C2×Q8×D5direct (N × H)
108. C5C23×C3×Q8semidirect
111. C22C3×Q8×D5direct (N × H)
115. C3C22×Q8×D5direct (N × H)
117. C2C2×C3×Q8×D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×Q82
C2×C3×Q8×D52
C22×C3×C4×D52
C22×C3×Dic102
C22×Q8×D53
C23×C3×Q85