Finite Group Databasebeta

← #92017

Subgroups — #92017

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
2C5×#235C211yesmaximal, characteristic, complemented
3C2×C3×D20C211yesmaximal, characteristic, complemented
4D5×#67C214yesmaximal, complemented
5#6777C212yesmaximal, complemented
6D3×D20C212yesmaximal, complemented
7#6766C212yesmaximal, complemented
8#6765C212yesmaximal, complemented
9#4149—31nomaximal, Hall
10C22×C3×D5C2212yescomplemented
11C2×D3×D5C2214yescomplemented
12C2×C3×C4×C5C2211yescharacteristic, complemented
13#1220C2212yescomplemented
14D60C2211yescharacteristic, complemented
15C4×D15C2212yescomplemented
16Dic30C2211yescharacteristic, complemented
17C5×#67C2212yescomplemented
18C5×D12C2211yescharacteristic, complemented
19C4×C5×D3C2212yescomplemented
20C5×Dic6C2211yescharacteristic, complemented
21C3×D20C2212yescomplemented
22C3×D20C2212yescomplemented
23#1202C2214yescomplemented
24#1201C2214yescomplemented
25D5×Dic3C2214yescomplemented
26#1004—51nomaximal, Hall
27C5×#41—31no—
28#713—32no—
29D4×D5—34no—
30D4×D5—32no—
31#709—31no—
32#709—32no—
33C2×D20—32no—
34C2×D20D311yescharacteristic, complemented
35C22×C3×C5C2311yescharacteristic
36C2×D15C2312yes—
37C2×C5×D3C2312yes—
38C2×C3×D5—42no—
39C2×C3×D5C2314yes—
40D3×D5—44no—
41C3×C4×C5C2311yescharacteristic
42C3×C4×C5C2311yescharacteristic
43Dic15C2312yes—
44C5×Dic3C2312yes—
45C2×C3×D4—51no—
46C2×#67—54no—
47#237—52no—
48#237—52no—
49D3×D4—52no—
50D3×D4—52no—
51#235—51no—
52#235D511yescharacteristic, complemented
53C22×D5—34no—
54C22×D5C2×D312yescomplemented
55C5×Q8—31no—
56C5×D4—32no—
57C5×D4—31no—
58C2×C4×C5—32no—
59C2×C4×C5C2×D311yescharacteristic, complemented
60C22⋊D5—32no—
61C22⋊D5—34no—
62D20—34no—
63D20—31no—
64D20C2×D312yescomplemented
65D20C2×D312yescomplemented
66C4×D5—34no—
67C4×D5—32no—
68Dic10—31no—
69H(5,𝔽2)—151noSylow
70C2×C3×C5—21no—
71C2×C3×C5C2411yescharacteristic
72D15—22no—
73C3×D5—24no—
74C5×D3—22no—
75C23×C3—52no—
76C22×D3—54no—
77C3×D4—52no—
78C3×D4—52no—
79C2×C3×C4C2×D511yescharacteristic, complemented
80#67—52no—
81#67—54no—
82#67—54no—
83#67C2×D512yescomplemented
84C2×Dic3—54no—
85D12—51no—
86D12C2×D511yescharacteristic, complemented
87C4×D3—52no—
88C4×D3C2×D512yescomplemented
89Dic6—51no—
90Dic6C2×D511yescharacteristic, complemented
91C22×C5—32no—
92C22×C5C22×D311yescharacteristic
93C2×D5—32no—
94C2×D5—42no—
95C2×D5—124no—
96C2×D5C22×D314yes—
97C4×C5—32no—
98C4×C5C22×D311yescharacteristic
99C4×C5C22×D311yescharacteristic
100Dic5—32no—
101#41—31no—
102#41—152no—
103#41—152no—
104#41—151no—
105C2×D4—51no—
106C2×D4—152no—
107C2×D4—152no—
108C2×D4—154no—
109C3×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
110C22×C3—54no—
111C22×C3—202no—
112C22×C3C22×D511yescharacteristic
113C2×D3—52no—
114C2×D3—204no—
115C2×D3C22×D512yes—
116C3×C4C22×D511yescharacteristic
117C3×C4C22×D511yescharacteristic
118Dic3—52no—
119Dic3C22×D512yes—
120C2×C5—21no—
121C2×C5—62no—
122C2×C5C23×D311yescharacteristic
123D5—24no—
124D5—62no—
125C23—52no—
126C23—154no—
127Q8—31no—
128Q8—151no—
129D4—32no—
130D4—31no—
131D4—52no—
132D4—52no—
133D4—154no—
134D4—154no—
135D4—152no—
136D4—151no—
137C2×C4—32no—
138C2×C4—154no—
139C2×C4—152no—
140C2×C4D3×D511yescharacteristic, complemented
141C2×C3—21no—
142C2×C3—104no—
143C2×C3C23×D511yescharacteristic
144D3—22no—
145D3—102no—
146C5#100411yescharacteristic, complemented, Sylow
147C22—32no—
148C22—54no—
149C22—152no—
150C22—202no—
151C22—604no—
152C22C2×D3×D511yescharacteristic
153C4—32no—
154C4—152no—
155C4C2×D3×D511yescharacteristic
156C4C2×D3×D511yescharacteristic
157C3#414911yescharacteristic, complemented, Sylow
158C2—21no—
159C2—62no—
160C2—104no—
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. C5×#235C2semidirect
3. C2×C3×D20C2semidirect
4. D5×#67C2semidirect
5. #6777C2semidirect
6. D3×D20C2semidirect
7. #6766C2semidirect
8. #6765C2semidirect
10. C22×C3×D5C22semidirect
11. C2×D3×D5C22semidirect
12. C2×C3×C4×C5C22semidirect
13. #1220C22semidirect
14. D60C22semidirect
15. C4×D15C22semidirect
16. Dic30C22semidirect
17. C5×#67C22semidirect
18. C5×D12C22semidirect
19. C4×C5×D3C22semidirect
20. C5×Dic6C22semidirect
21. C3×D20C22semidirect
22. C3×D20C22semidirect
23. #1202C22semidirect
24. #1201C22semidirect
25. D5×Dic3C22semidirect
34. C2×D20D3semidirect
52. #235D5semidirect
54. C22×D5C2×D3semidirect
59. C2×C4×C5C2×D3semidirect
64. D20C2×D3semidirect
65. D20C2×D3semidirect
79. C2×C3×C4C2×D5semidirect
83. #67C2×D5semidirect
86. D12C2×D5semidirect
88. C4×D3C2×D5semidirect
90. Dic6C2×D5semidirect
109. C3×C5H(5,𝔽2)semidirect
140. C2×C4D3×D5semidirect
146. C5#1004semidirect
157. C3#4149semidirect

Maximal subgroups

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

subgroupindex
#68172
C5×#2352
C2×C3×D202
D5×#672
#67772
D3×D202
#67662
#67652
#41493
#10045