Finite Group Databasebeta

← #92049

Subgroups — #92049

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×#1220C211yesmaximal, characteristic, complemented
2C2×C5×#67C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊D5C211yesmaximal, characteristic, complemented
4#6790C212yesmaximal, complemented
5D3×C22⋊D5C212yesmaximal, complemented
6D5×#67C212yesmaximal, complemented
7#6782C212yesmaximal, complemented
8#6780C212yesmaximal, complemented
9#6779C212yesmaximal, complemented
10#4144—31nomaximal, Hall
11C23×C3×C5C2211yescharacteristic, complemented
12C22×D15C2211yescharacteristic, complemented
13C22×C5×D3C2211yescharacteristic, complemented
14C22×C3×D5C2211yescharacteristic, complemented
15C2×D3×D5C2212yescomplemented
16#1220C2212yescomplemented
17#1220C2212yescomplemented
18C2×Dic15C2211yescharacteristic, complemented
19C5×#67C2212yescomplemented
20C5×#67C2212yescomplemented
21C2×C5×Dic3C2211yescharacteristic, complemented
22C3×C22⋊D5C2212yescomplemented
23C3×C22⋊D5C2212yescomplemented
24C2×C3×Dic5C2211yescharacteristic, complemented
25#1204C2212yescomplemented
26#1203C2212yescomplemented
27#1202C2212yescomplemented
28#1201C2212yescomplemented
29#1200C2212yescomplemented
30D3×Dic5C2212yescomplemented
31D5×Dic3C2212yescomplemented
32#1004—51nomaximal, Hall
33C2×C5×D4—31no—
34C2×C22⋊D5—31no—
35C2×C22⋊D5—32no—
36C2×C22⋊D5D311yescharacteristic, complemented
37#711—32no—
38#711—32no—
39D4×D5—32no—
40D4×D5—32no—
41#709—32no—
42C22×C3×C5—41no—
43C22×C3×C5C2311yescharacteristic
44C22×C3×C5C2311yescharacteristic
45C22×C3×C5C2311yescharacteristic
46C2×D15—41no—
47C2×D15C2312yes—
48C2×C5×D3—41no—
49C2×C5×D3C2312yes—
50C2×C3×D5—41no—
51C2×C3×D5C2312yes—
52D3×D5—42no—
53Dic15C2312yes—
54C3×Dic5C2312yes—
55C5×Dic3C2312yes—
56C2×C3×D4—51no—
57C2×#67—51no—
58C2×#67—52no—
59C2×#67D511yescharacteristic, complemented
60#237—52no—
61#237—52no—
62D3×D4—52no—
63D3×D4—52no—
64#235—52no—
65C23×C5—31no—
66C23×C5C2×D311yescharacteristic, complemented
67C22×D5—31no—
68C22×D5—32no—
69C22×D5C2×D311yescharacteristic, complemented
70C5×D4—32no—
71C5×D4—32no—
72C2×C4×C5—31no—
73C22⋊D5—32no—
74C22⋊D5—32no—
75C22⋊D5—32no—
76C22⋊D5—32no—
77C22⋊D5C2×D312yescomplemented
78C22⋊D5C2×D312yescomplemented
79C2×Dic5—31no—
80C2×Dic5—32no—
81C2×Dic5C2×D311yescharacteristic, complemented
82D20—32no—
83C4×D5—32no—
84C4×D5—32no—
85Dic10—32no—
86H(5,𝔽2)—151noSylow
87C2×C3×C5—21no—
88C2×C3×C5—21no—
89C2×C3×C5—21no—
90C2×C3×C5C2411yescharacteristic
91D15—22no—
92C3×D5—22no—
93C5×D3—22no—
94C23×C3—51no—
95C23×C3C2×D511yescharacteristic, complemented
96C22×D3—51no—
97C22×D3—52no—
98C22×D3C2×D511yescharacteristic, complemented
99C3×D4—52no—
100C3×D4—52no—
101C2×C3×C4—51no—
102#67—52no—
103#67—52no—
104#67—52no—
105#67—52no—
106#67C2×D512yescomplemented
107#67C2×D512yescomplemented
108C2×Dic3—51no—
109C2×Dic3—52no—
110C2×Dic3C2×D511yescharacteristic, complemented
111D12—52no—
112C4×D3—52no—
113C4×D3—52no—
114Dic6—52no—
115C22×C5—32no—
116C22×C5—41no—
117C22×C5—121no—
118C22×C5C22×D311yescharacteristic
119C22×C5C22×D311yescharacteristic
120C22×C5C22×D311yescharacteristic
121C2×D5—32no—
122C2×D5—41no—
123C2×D5—122no—
124C2×D5—121no—
125C2×D5C22×D312yes—
126C4×C5—32no—
127Dic5—32no—
128Dic5C22×D312yes—
129#41—152no—
130#41—152no—
131#41—152no—
132C2×D4—31no—
133C2×D4—51no—
134C2×D4—152no—
135C2×D4—152no—
136C2×D4—152no—
137C2×D4—151no—
138C3×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
139C22×C3—41no—
140C22×C3—52no—
141C22×C3—201no—
142C22×C3C22×D511yescharacteristic
143C22×C3C22×D511yescharacteristic
144C22×C3C22×D511yescharacteristic
145C2×D3—41no—
146C2×D3—52no—
147C2×D3—202no—
148C2×D3—201no—
149C2×D3C22×D512yes—
150C3×C4—52no—
151Dic3—52no—
152Dic3C22×D512yes—
153C2×C5—21no—
154C2×C5—21no—
155C2×C5—21no—
156C2×C5—62no—
157C2×C5C23×D311yescharacteristic
158D5—22no—
159D5—62no—
160C23—31no—
161C23—51no—
162C23—152no—
163C23—151no—
164C23D3×D511yescharacteristic, complemented
165Q8—152no—
166D4—32no—
167D4—32no—
168D4—52no—
169D4—52no—
170D4—152no—
171D4—152no—
172D4—152no—
173D4—152no—
174D4—152no—
175C2×C4—31no—
176C2×C4—51no—
177C2×C4—152no—
178C2×C4—152no—
179C2×C4—152no—
180C2×C4—151no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—102no—
185C2×C3C23×D511yescharacteristic
186D3—22no—
187D3—102no—
188C5#100411yescharacteristic, complemented, Sylow
189C22—32no—
190C22—41no—
191C22—52no—
192C22—121no—
193C22—152no—
194C22—201no—
195C22—601no—
196C22—602no—
197C22C2×D3×D511yescharacteristic
198C22C2×D3×D511yescharacteristic
199C22C2×D3×D511yescharacteristic
200C4—32no—
201C4—52no—
202C4—152no—
203C3#414411yescharacteristic, complemented, Sylow
204C2—21no—
205C2—21no—
206C2—21no—
207C2—62no—
208C2—102no—
209C2—302no—
210C2C22×D3×D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D5
commutator, socle, cosocleC2×C3×C5C24
FittingC23×C3×C5C22
hypercenterC23D3×D5
hypocenterC3×C5H(5,𝔽2)
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#1220C2semidirect
2. C2×C5×#67C2semidirect
3. C2×C3×C22⋊D5C2semidirect
4. #6790C2semidirect
5. D3×C22⋊D5C2semidirect
6. D5×#67C2semidirect
7. #6782C2semidirect
8. #6780C2semidirect
9. #6779C2semidirect
11. C23×C3×C5C22semidirect
12. C22×D15C22semidirect
13. C22×C5×D3C22semidirect
14. C22×C3×D5C22semidirect
15. C2×D3×D5C22semidirect
16. #1220C22semidirect
17. #1220C22semidirect
18. C2×Dic15C22semidirect
19. C5×#67C22semidirect
20. C5×#67C22semidirect
21. C2×C5×Dic3C22semidirect
22. C3×C22⋊D5C22semidirect
23. C3×C22⋊D5C22semidirect
24. C2×C3×Dic5C22semidirect
25. #1204C22semidirect
26. #1203C22semidirect
27. #1202C22semidirect
28. #1201C22semidirect
29. #1200C22semidirect
30. D3×Dic5C22semidirect
31. D5×Dic3C22semidirect
36. C2×C22⋊D5D3semidirect
59. C2×#67D5semidirect
66. C23×C5C2×D3semidirect
69. C22×D5C2×D3semidirect
77. C22⋊D5C2×D3semidirect
78. C22⋊D5C2×D3semidirect
81. C2×Dic5C2×D3semidirect
95. C23×C3C2×D5semidirect
98. C22×D3C2×D5semidirect
106. #67C2×D5semidirect
107. #67C2×D5semidirect
110. C2×Dic3C2×D5semidirect
138. C3×C5H(5,𝔽2)semidirect
164. C23D3×D5semidirect
188. C5#1004semidirect
203. C3#4144semidirect

Maximal subgroups

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

subgroupindex
C2×#12202
C2×C5×#672
C2×C3×C22⋊D52
#67902
D3×C22⋊D52
D5×#672
#67822
#67802
#67792
#41443
#10045