Finite Group Databasebeta

← #92019

Subgroups — #92019

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
1C2×D60C211yesmaximal, characteristic, complemented
2C5×#235C211yesmaximal, characteristic, complemented
3C3×#709C211yesmaximal, characteristic, complemented
4#6790C214yesmaximal, complemented
5D3×D20C212yesmaximal, complemented
6D5×D12C212yesmaximal, complemented
7#6773C212yesmaximal, complemented
8#6769C212yesmaximal, complemented
9#4149—31nomaximal, Hall
10C22×D15C2212yescomplemented
11C2×D3×D5C2214yescomplemented
12C2×C3×C4×C5C2211yescharacteristic, complemented
13D60C2212yescomplemented
14D60C2212yescomplemented
15C5×#67C2212yescomplemented
16C5×D12C2211yescharacteristic, complemented
17C4×C5×D3C2212yescomplemented
18C5×Dic6C2211yescharacteristic, complemented
19C3×C22⋊D5C2212yescomplemented
20C3×D20C2211yescharacteristic, complemented
21C3×C4×D5C2212yescomplemented
22C3×Dic10C2211yescharacteristic, complemented
23#1203C2214yescomplemented
24#1202C2214yescomplemented
25#1200C2214yescomplemented
26#1009—51nomaximal, Hall
27C5×#41—31no—
28#713—32no—
29D4×D5—34no—
30D4×D5—32no—
31#709—32no—
32#709D311yescharacteristic, complemented
33C2×D20—31no—
34C2×D20—32no—
35C22×C3×C5C2311yescharacteristic
36C2×D15—42no—
37C2×D15C2314yes—
38C2×C5×D3C2312yes—
39C2×C3×D5C2312yes—
40D3×D5—44no—
41C3×C4×C5C2311yescharacteristic
42C3×C4×C5C2311yescharacteristic
43C3×Dic5C2312yes—
44C5×Dic3C2312yes—
45C3×#41—51no—
46#239—52no—
47D3×D4—54no—
48D3×D4—52no—
49#235—52no—
50#235D511yescharacteristic, complemented
51C2×D12—51no—
52C2×D12—52no—
53C22×D5—32no—
54C22×D5—34no—
55C5×Q8—31no—
56C5×D4—32no—
57C5×D4—31no—
58C2×C4×C5—32no—
59C2×C4×C5C2×D311yescharacteristic, complemented
60C22⋊D5—34no—
61C22⋊D5C2×D312yescomplemented
62D20—34no—
63D20—32no—
64D20—32no—
65D20C2×D311yescharacteristic, complemented
66C4×D5—34no—
67C4×D5C2×D312yescomplemented
68Dic10C2×D311yescharacteristic, complemented
69H(5,𝔽2)—151noSylow
70C2×C3×C5—21no—
71C2×C3×C5C2411yescharacteristic
72D15—24no—
73C3×D5—22no—
74C5×D3—22no—
75C22×D3—52no—
76C22×D3—54no—
77C3×Q8—51no—
78C3×D4—52no—
79C3×D4—51no—
80C2×C3×C4—52no—
81C2×C3×C4C2×D511yescharacteristic, complemented
82#67—54no—
83#67C2×D512yescomplemented
84D12—54no—
85D12—52no—
86D12—52no—
87D12C2×D511yescharacteristic, complemented
88C4×D3—54no—
89C4×D3C2×D512yescomplemented
90Dic6C2×D511yescharacteristic, complemented
91C22×C5—32no—
92C22×C5C22×D311yescharacteristic
93C2×D5—34no—
94C2×D5—124no—
95C2×D5—122no—
96C2×D5C22×D312yes—
97C4×C5—32no—
98C4×C5C22×D311yescharacteristic
99C4×C5C22×D311yescharacteristic
100Dic5C22×D312yes—
101#41—31no—
102#41—51no—
103#41—152no—
104#41—152no—
105C2×D4—152no—
106C2×D4—152no—
107C2×D4—154no—
108C2×D4—151no—
109C3×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
110C22×C3—52no—
111C22×C3C22×D511yescharacteristic
112C2×D3—54no—
113C2×D3—204no—
114C2×D3—202no—
115C2×D3C22×D512yes—
116C3×C4—52no—
117C3×C4C22×D511yescharacteristic
118C3×C4C22×D511yescharacteristic
119Dic3C22×D512yes—
120C2×C5—21no—
121C2×C5—62no—
122C2×C5C23×D311yescharacteristic
123D5—22no—
124D5—64no—
125C23—154no—
126C23—152no—
127Q8—31no—
128Q8—51no—
129D4—32no—
130D4—31no—
131D4—52no—
132D4—51no—
133D4—154no—
134D4—154no—
135D4—152no—
136D4—152no—
137C2×C4—32no—
138C2×C4—52no—
139C2×C4—154no—
140C2×C4D3×D511yescharacteristic, complemented
141C2×C3—21no—
142C2×C3—102no—
143C2×C3C23×D511yescharacteristic
144D3—22no—
145D3—104no—
146C5#100911yescharacteristic, complemented, Sylow
147C22—32no—
148C22—52no—
149C22—154no—
150C22—602no—
151C22—604no—
152C22C2×D3×D511yescharacteristic
153C4—32no—
154C4—52no—
155C4C2×D3×D511yescharacteristic
156C4C2×D3×D511yescharacteristic
157C3#414911yescharacteristic, complemented, Sylow
158C2—21no—
159C2—62no—
160C2—102no—
161C2—304no—
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. C2×D60C2semidirect
2. C5×#235C2semidirect
3. C3×#709C2semidirect
4. #6790C2semidirect
5. D3×D20C2semidirect
6. D5×D12C2semidirect
7. #6773C2semidirect
8. #6769C2semidirect
10. C22×D15C22semidirect
11. C2×D3×D5C22semidirect
12. C2×C3×C4×C5C22semidirect
13. D60C22semidirect
14. D60C22semidirect
15. C5×#67C22semidirect
16. C5×D12C22semidirect
17. C4×C5×D3C22semidirect
18. C5×Dic6C22semidirect
19. C3×C22⋊D5C22semidirect
20. C3×D20C22semidirect
21. C3×C4×D5C22semidirect
22. C3×Dic10C22semidirect
23. #1203C22semidirect
24. #1202C22semidirect
25. #1200C22semidirect
32. #709D3semidirect
50. #235D5semidirect
59. C2×C4×C5C2×D3semidirect
61. C22⋊D5C2×D3semidirect
65. D20C2×D3semidirect
67. C4×D5C2×D3semidirect
68. Dic10C2×D3semidirect
81. C2×C3×C4C2×D5semidirect
83. #67C2×D5semidirect
87. D12C2×D5semidirect
89. C4×D3C2×D5semidirect
90. Dic6C2×D5semidirect
109. C3×C5H(5,𝔽2)semidirect
140. C2×C4D3×D5semidirect
146. C5#1009semidirect
157. C3#4149semidirect

Maximal subgroups

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

subgroupindex
C2×D602
C5×#2352
C3×#7092
#67902
D3×D202
D5×D122
#67732
#67692
#41493
#10095