Finite Group Databasebeta

← C3×#66054 #11755731

Subgroups — C3×#66054 #11755731

Order 960.

504 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 182 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
1C3×C5×#127C211yesmaximal, characteristic, complemented
2C3×#4085C216yesmaximal, complemented
3C3×#4083C213yesmaximal, complemented
4C3×#4081C213yesmaximal, complemented
5C3×#4022C212yesmaximal, complemented
6#66054C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×D5C2211yescharacteristic
8C2×C3×C5×D4C2213yes—
9C2×C3×C5×D4C2213yescomplemented
10C2×C3×C22⋊D5C2216yes—
11C22×C3×Dic5C2213yescomplemented
12C3×C42×C5C2211yescharacteristic, complemented
13C3×C22⋊Dic5C2213yes—
14C3×C22⋊Dic5C2213yescomplemented
15C3×#685C2216yes—
16C3×#683C2216yescomplemented
17C3×#560—51nomaximal, Hall
18C5×#127C2×C311yescharacteristic, complemented
19#4085C2×C316yescomplemented
20#4083C2×C313yescomplemented
21#4081C2×C313yescomplemented
22#4022C2×C312yescomplemented
23C23×C3×C5C2311yescharacteristic
24C23×C3×C5C2313yes—
25C22×C3×D5—43no—
26C22×C3×D5C2312yes—
27C3×C5×D4—43no—
28C3×C5×D4—43no—
29C2×C3×C4×C5C2313yes—
30C3×C22⋊D5—46no—
31C2×C3×Dic5—43no—
32C2×C3×Dic5C2316yes—
33C3×#127D511yescharacteristic, complemented
34C3×#126—52no—
35C3×#123—53no—
36C3×#121—56no—
37C3×#120—53no—
38C23×D5C22×C311yescharacteristic
39C2×C5×D4C22×C313yes—
40C2×C5×D4C22×C313yescomplemented
41C2×C22⋊D5C22×C316yes—
42C22×Dic5C22×C313yescomplemented
43C42×C5C22×C311yescharacteristic, complemented
44C22⋊Dic5C22×C313yes—
45C22⋊Dic5C22×C313yescomplemented
46#685C22×C316yes—
47#683C22×C316yescomplemented
48#560—51noSylow
49C22×C3×C5—23no—
50C22×C3×C5—26no—
51C22×C3×C5—23no—
52C22×C3×C5C2411yescharacteristic
53C2×C3×D5—26no—
54C2×C3×D5—44no—
55C3×C4×C5—23no—
56C3×Dic5—26no—
57C24×C3—51no—
58C2×C3×D4—56no—
59C2×C3×D4C2×D513yes—
60C2×C3×D4C2×D513yescomplemented
61C22×C3×C4—53no—
62C3×C4⋊C4—56no—
63C3×C22⋊C4—53no—
64C3×C22⋊C4—53no—
65C3×C22⋊C4—56no—
66C3×C42C2×D511yescharacteristic, complemented
67C23×C5C23×C311yescharacteristic
68C23×C5C23×C313yes—
69C22×D5—43no—
70C22×D5C23×C312yes—
71C5×D4—43no—
72C5×D4—43no—
73C2×C4×C5C23×C313yes—
74C22⋊D5—46no—
75C2×Dic5—43no—
76C2×Dic5C23×C316yes—
77#127C3×D511yescharacteristic, complemented
78#126—52no—
79#123—53no—
80#121—56no—
81#120—53no—
82C2×C3×C5—41no—
83C2×C3×C5—43no—
84C2×C3×C5H(5,𝔽2)13yes—
85C3×D5—42no—
86C23×C3—52no—
87C23×C3—203no—
88C23×C3C22×D511yescharacteristic
89C23×C3C22×D513yes—
90C3×D4—43no—
91C3×D4—43no—
92C3×D4—206no—
93C2×C3×C4—56no—
94C2×C3×C4—203no—
95C2×C3×C4C22×D513yes—
96C22×C5—23no—
97C22×C5—26no—
98C22×C5—23no—
99C22×C5C24×C311yescharacteristic
100C2×D5—26no—
101C2×D5—44no—
102C4×C5—23no—
103Dic5—26no—
104C24—51no—
105C2×D4—56no—
106C2×D4C2×C3×D513yes—
107C2×D4C2×C3×D513yescomplemented
108C22×C4—53no—
109C4⋊C4—56no—
110C22⋊C4—53no—
111C22⋊C4—53no—
112C22⋊C4—56no—
113C42C2×C3×D511yescharacteristic, complemented
114C3×C5#56011yescharacteristic, complemented, Hall
115C22×C3—23no—
116C22×C3—26no—
117C22×C3—23no—
118C22×C3—106no—
119C22×C3—204no—
120C22×C3C23×D511yescharacteristic
121C3×C4—23no—
122C3×C4—106no—
123C2×C5—41no—
124C2×C5—43no—
125C2×C5C3×H(5,𝔽2)13yes—
126D5—42no—
127C23—52no—
128C23—203no—
129C23C22×C3×D511yescharacteristic
130C23C22×C3×D513yes—
131D4—43no—
132D4—43no—
133D4—206no—
134C2×C4—56no—
135C2×C4—203no—
136C2×C4C22×C3×D513yes—
137C2×C3—41no—
138C2×C3—43no—
139C2×C3—202no—
140C2×C3#414413yes—
141C5C3×#56011yescharacteristic, complemented, Sylow
142C22—23no—
143C22—26no—
144C22—23no—
145C22—106no—
146C22—204no—
147C22C23×C3×D511yescharacteristic
148C4—23no—
149C4—106no—
150C3#6605411yescharacteristic, direct product factor, Sylow
151C2—41no—
152C2—43no—
153C2—202no—
154C2C3×#414413yes—
subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#127C2
socleC22×C3×C5C24
hypercenterC3×#127D5
hypocenterC5C3×#560
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#127

Complements

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

NH ≅ G/Ntype
1. C3×C5×#127C2semidirect
2. C3×#4085C2semidirect
3. C3×#4083C2semidirect
4. C3×#4081C2semidirect
5. C3×#4022C2semidirect
6. #66054C3direct (N × H)
9. C2×C3×C5×D4C22semidirect
11. C22×C3×Dic5C22semidirect
12. C3×C42×C5C22semidirect
14. C3×C22⋊Dic5C22semidirect
16. C3×#683C22semidirect
18. C5×#127C2×C3semidirect
19. #4085C2×C3semidirect
20. #4083C2×C3semidirect
21. #4081C2×C3semidirect
22. #4022C2×C3semidirect
33. C3×#127D5semidirect
40. C2×C5×D4C22×C3semidirect
42. C22×Dic5C22×C3semidirect
43. C42×C5C22×C3semidirect
45. C22⋊Dic5C22×C3semidirect
47. #683C22×C3semidirect
60. C2×C3×D4C2×D5semidirect
66. C3×C42C2×D5semidirect
77. #127C3×D5semidirect
107. C2×D4C2×C3×D5semidirect
113. C42C2×C3×D5semidirect
114. C3×C5#560semidirect
141. C5C3×#560semidirect
150. C3#66054direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#1272
C3×#40852
C3×#40832
C3×#40812
C3×#40222
#660543
C3×#5605