Finite Group Databasebeta

← #92018

Subgroups — #92018

Order 480.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#6817C211yesmaximal, characteristic, complemented
2C2×C5×D12C211yesmaximal, characteristic, complemented
3C3×#709C211yesmaximal, characteristic, complemented
4D3×C22⋊D5C214yesmaximal, complemented
5#6777C212yesmaximal, complemented
6D5×D12C212yesmaximal, complemented
7#6772C212yesmaximal, complemented
8#6768C212yesmaximal, complemented
9#4144—31nomaximal, Hall
10C22×C5×D3C2212yescomplemented
11C2×D3×D5C2214yescomplemented
12C2×C3×C4×C5C2211yescharacteristic, complemented
13#1220C2212yescomplemented
14D60C2211yescharacteristic, complemented
15C4×D15C2212yescomplemented
16Dic30C2211yescharacteristic, complemented
17C5×D12C2212yescomplemented
18C5×D12C2212yescomplemented
19C3×C22⋊D5C2212yescomplemented
20C3×D20C2211yescharacteristic, complemented
21C3×C4×D5C2212yescomplemented
22C3×Dic10C2211yescharacteristic, complemented
23#1203C2214yescomplemented
24#1201C2214yescomplemented
25D3×Dic5C2214yescomplemented
26#1009—51nomaximal, Hall
27C2×C5×D4—31no—
28C2×C22⋊D5—34no—
29#711—32no—
30#711—32no—
31D4×D5—32no—
32D4×D5—32no—
33#709—31no—
34#709D311yescharacteristic, complemented
35C22×C3×C5C2311yescharacteristic
36C2×D15C2312yes—
37C2×C5×D3—42no—
38C2×C5×D3C2314yes—
39C2×C3×D5C2312yes—
40D3×D5—44no—
41C3×C4×C5C2311yescharacteristic
42C3×C4×C5C2311yescharacteristic
43Dic15C2312yes—
44C3×Dic5C2312yes—
45C3×#41—51no—
46#239—52no—
47D3×D4—54no—
48D3×D4—52no—
49#235—51no—
50#235—52no—
51C2×D12—52no—
52C2×D12D511yescharacteristic, complemented
53C23×C5—32no—
54C22×D5—34no—
55C5×D4—32no—
56C5×D4—32no—
57C2×C4×C5C2×D311yescharacteristic, complemented
58C22⋊D5—32no—
59C22⋊D5—34no—
60C22⋊D5—34no—
61C22⋊D5C2×D312yescomplemented
62C2×Dic5—34no—
63D20—31no—
64D20C2×D311yescharacteristic, complemented
65C4×D5—32no—
66C4×D5C2×D312yescomplemented
67Dic10—31no—
68Dic10C2×D311yescharacteristic, complemented
69H(5,𝔽2)—151noSylow
70C2×C3×C5—21no—
71C2×C3×C5C2411yescharacteristic
72D15—22no—
73C3×D5—22no—
74C5×D3—24no—
75C22×D3—54no—
76C22×D3C2×D512yescomplemented
77C3×Q8—51no—
78C3×D4—52no—
79C3×D4—51no—
80C2×C3×C4—52no—
81C2×C3×C4C2×D511yescharacteristic, complemented
82#67—52no—
83#67—54no—
84D12—54no—
85D12—51no—
86D12C2×D512yescomplemented
87D12C2×D512yescomplemented
88C4×D3—54no—
89C4×D3—52no—
90Dic6—51no—
91C22×C5—34no—
92C22×C5—122no—
93C22×C5C22×D311yescharacteristic
94C2×D5—32no—
95C2×D5—124no—
96C2×D5C22×D312yes—
97C4×C5C22×D311yescharacteristic
98C4×C5C22×D311yescharacteristic
99Dic5—32no—
100Dic5C22×D312yes—
101#41—51no—
102#41—152no—
103#41—152no—
104#41—151no—
105C2×D4—31no—
106C2×D4—152no—
107C2×D4—152no—
108C2×D4—154no—
109C3×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
110C22×C3—52no—
111C22×C3C22×D511yescharacteristic
112C2×D3—42no—
113C2×D3—52no—
114C2×D3—204no—
115C2×D3C22×D514yes—
116C3×C4—52no—
117C3×C4C22×D511yescharacteristic
118C3×C4C22×D511yescharacteristic
119Dic3—52no—
120C2×C5—21no—
121C2×C5—64no—
122C2×C5C23×D311yescharacteristic
123D5—22no—
124D5—62no—
125C23—32no—
126C23—154no—
127Q8—51no—
128Q8—151no—
129D4—32no—
130D4—32no—
131D4—52no—
132D4—51no—
133D4—154no—
134D4—154no—
135D4—152no—
136D4—151no—
137C2×C4—52no—
138C2×C4—154no—
139C2×C4—152no—
140C2×C4D3×D511yescharacteristic, complemented
141C2×C3—21no—
142C2×C3—102no—
143C2×C3C23×D511yescharacteristic
144D3—24no—
145D3—102no—
146C5#100911yescharacteristic, complemented, Sylow
147C22—34no—
148C22—52no—
149C22—122no—
150C22—152no—
151C22—604no—
152C22C2×D3×D511yescharacteristic
153C4—52no—
154C4—152no—
155C4C2×D3×D511yescharacteristic
156C4C2×D3×D511yescharacteristic
157C3#414411yescharacteristic, complemented, Sylow
158C2—21no—
159C2—64no—
160C2—102no—
161C2—302no—
162C2C22×D3×D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D5
commutator, socle, cosocleC2×C3×C5C24
FittingC2×C3×C4×C5C22
hypercenterC2×C4D3×D5
hypocenterC3×C5H(5,𝔽2)
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #6817C2semidirect
2. C2×C5×D12C2semidirect
3. C3×#709C2semidirect
4. D3×C22⋊D5C2semidirect
5. #6777C2semidirect
6. D5×D12C2semidirect
7. #6772C2semidirect
8. #6768C2semidirect
10. C22×C5×D3C22semidirect
11. C2×D3×D5C22semidirect
12. C2×C3×C4×C5C22semidirect
13. #1220C22semidirect
14. D60C22semidirect
15. C4×D15C22semidirect
16. Dic30C22semidirect
17. C5×D12C22semidirect
18. C5×D12C22semidirect
19. C3×C22⋊D5C22semidirect
20. C3×D20C22semidirect
21. C3×C4×D5C22semidirect
22. C3×Dic10C22semidirect
23. #1203C22semidirect
24. #1201C22semidirect
25. D3×Dic5C22semidirect
34. #709D3semidirect
52. C2×D12D5semidirect
57. C2×C4×C5C2×D3semidirect
61. C22⋊D5C2×D3semidirect
64. D20C2×D3semidirect
66. C4×D5C2×D3semidirect
68. Dic10C2×D3semidirect
76. C22×D3C2×D5semidirect
81. C2×C3×C4C2×D5semidirect
86. D12C2×D5semidirect
87. D12C2×D5semidirect
109. C3×C5H(5,𝔽2)semidirect
140. C2×C4D3×D5semidirect
146. C5#1009semidirect
157. C3#4144semidirect

Maximal subgroups

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

subgroupindex
#68172
C2×C5×D122
C3×#7092
D3×C22⋊D52
#67772
D5×D122
#67722
#67682
#41443
#10095