Finite Group Databasebeta

← #92027

Subgroups — #92027

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
1D4×D15C211yesmaximal, characteristic, complemented
2C5×D3×D4C211yesmaximal, characteristic, complemented
3C3×#711C211yesmaximal, characteristic, complemented
4#6790C212yesmaximal, complemented
5D3×C22⋊D5C212yesmaximal, complemented
6C2×#1203C212yesmaximal, complemented
7#6782C212yesmaximal, complemented
8D5×D12C211yesmaximal, characteristic, complemented
9#6771C211yesmaximal, characteristic, complemented
10#6769C211yesmaximal, characteristic, complemented
11#6768C211yesmaximal, characteristic, complemented
12#4144—31nomaximal, Hall
13C22×D15C2212yescomplemented
14C22×C5×D3C2212yescomplemented
15C2×D3×D5C2212yescomplemented
16C3×C5×D4C2211yescharacteristic, complemented
17#1220C2212yescomplemented
18D60C2211yescharacteristic, complemented
19C4×D15C2211yescharacteristic, complemented
20C5×#67C2212yescomplemented
21C5×D12C2211yescharacteristic, complemented
22C4×C5×D3C2211yescharacteristic, complemented
23C3×C22⋊D5C2212yescomplemented
24C2×C3×Dic5C2212yescomplemented
25C3×C4×D5C2211yescharacteristic, complemented
26C3×Dic10C2211yescharacteristic, complemented
27#1204C2211yescharacteristic, complemented
28#1203C2212yescomplemented
29#1203C2212yescomplemented
30#1203C2211yescharacteristic, complemented
31#1203C2212yescomplemented
32#1202C2211yescharacteristic, complemented
33#1201C2211yescharacteristic, complemented
34#1200C2212yescomplemented
35D3×Dic5C2212yescomplemented
36#1009—51nomaximal, Hall
37C2×C5×D4—31no—
38C2×C22⋊D5—32no—
39C2×C22⋊D5—32no—
40#711—32no—
41#711—31no—
42#711D311yescharacteristic, complemented
43D4×D5—31no—
44D4×D5—32no—
45D4×D5—31no—
46#709—31no—
47#709—31no—
48C22×C3×C5C2312yes—
49C2×D15—42no—
50C2×D15C2312yes—
51C2×D15C2311yescharacteristic
52C2×C5×D3—42no—
53C2×C5×D3C2312yes—
54C2×C5×D3C2311yescharacteristic
55C2×C3×D5C2311yescharacteristic
56D3×D5—42no—
57C3×C4×C5C2311yescharacteristic
58Dic15C2311yescharacteristic
59C3×Dic5C2312yes—
60C3×Dic5C2311yescharacteristic
61C5×Dic3C2311yescharacteristic
62C3×#41—51no—
63#239—51no—
64#239—51no—
65D3×D4—52no—
66D3×D4—51no—
67D3×D4—52no—
68D3×D4D511yescharacteristic, complemented
69#235—52no—
70#235—51no—
71C2×D12—52no—
72C2×D12—51no—
73C23×C5—32no—
74C22×D5—32no—
75C22×D5—32no—
76C5×D4—32no—
77C5×D4—31no—
78C5×D4C2×D311yescharacteristic, complemented
79C2×C4×C5—31no—
80C22⋊D5—32no—
81C22⋊D5—31no—
82C22⋊D5—31no—
83C22⋊D5—32no—
84C22⋊D5—32no—
85C22⋊D5—32no—
86C22⋊D5C2×D312yescomplemented
87C2×Dic5—32no—
88C2×Dic5C2×D312yescomplemented
89D20—31no—
90D20—31no—
91C4×D5—31no—
92C4×D5—32no—
93C4×D5C2×D311yescharacteristic, complemented
94Dic10—31no—
95Dic10C2×D311yescharacteristic, complemented
96H(5,𝔽2)—151noSylow
97C2×C3×C5—22no—
98C2×C3×C5C2411yescharacteristic
99D15—22no—
100D15—21no—
101C3×D5—21no—
102C5×D3—22no—
103C5×D3—21no—
104C22×D3—52no—
105C22×D3—52no—
106C22×D3C2×D512yescomplemented
107C3×Q8—51no—
108C3×D4—52no—
109C3×D4C2×D511yescharacteristic, complemented
110C2×C3×C4—52no—
111C2×C3×C4—51no—
112#67—52no—
113#67—51no—
114#67—51no—
115#67C2×D512yescomplemented
116D12—52no—
117D12—51no—
118D12—52no—
119D12—52no—
120D12—51no—
121D12C2×D511yescharacteristic, complemented
122C4×D3—52no—
123C4×D3—51no—
124C4×D3—52no—
125C4×D3C2×D511yescharacteristic, complemented
126Dic6—51no—
127C22×C5—32no—
128C22×C5—31no—
129C22×C5—122no—
130C22×C5C22×D312yes—
131C2×D5—32no—
132C2×D5—31no—
133C2×D5—122no—
134C2×D5—122no—
135C2×D5C22×D311yescharacteristic
136C4×C5—31no—
137C4×C5C22×D311yescharacteristic
138Dic5—31no—
139Dic5C22×D311yescharacteristic
140Dic5C22×D312yes—
141#41—51no—
142#41—151no—
143#41—151no—
144#41—152no—
145#41—151no—
146C2×D4—31no—
147C2×D4—151no—
148C2×D4—152no—
149C2×D4—152no—
150C2×D4—152no—
151C2×D4—151no—
152C3×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
153C22×C3—51no—
154C22×C3C22×D512yes—
155C2×D3—42no—
156C2×D3—52no—
157C2×D3—51no—
158C2×D3—202no—
159C2×D3—202no—
160C2×D3C22×D512yes—
161C2×D3C22×D511yescharacteristic
162C3×C4—51no—
163C3×C4—52no—
164C3×C4C22×D511yescharacteristic
165Dic3—51no—
166Dic3C22×D511yescharacteristic
167C2×C5—22no—
168C2×C5—62no—
169C2×C5—61no—
170C2×C5C23×D311yescharacteristic
171D5—21no—
172D5—62no—
173D5—61no—
174C23—32no—
175C23—152no—
176C23—152no—
177Q8—51no—
178Q8—151no—
179D4—32no—
180D4—31no—
181D4—52no—
182D4—151no—
183D4—151no—
184D4—152no—
185D4—152no—
186D4—152no—
187D4—151no—
188D4—152no—
189D4—151no—
190D4D3×D511yescharacteristic, complemented
191C2×C4—31no—
192C2×C4—52no—
193C2×C4—51no—
194C2×C4—152no—
195C2×C4—152no—
196C2×C4—151no—
197C2×C3—22no—
198C2×C3—101no—
199C2×C3C23×D511yescharacteristic
200D3—21no—
201D3—22no—
202D3—102no—
203D3—101no—
204C5#100911yescharacteristic, complemented, Sylow
205C22—31no—
206C22—32no—
207C22—51no—
208C22—122no—
209C22—152no—
210C22—151no—
211C22—602no—
212C22—602no—
213C22C2×D3×D512yes—
214C4—31no—
215C4—51no—
216C4—52no—
217C4—151no—
218C4C2×D3×D511yescharacteristic
219C3#414411yescharacteristic, complemented, Sylow
220C2—22no—
221C2—61no—
222C2—62no—
223C2—101no—
224C2—301no—
225C2—302no—
226C2C22×D3×D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D5
commutator, socle, cosocleC2×C3×C5C24
FittingC3×C5×D4C22
hypercenterD4D3×D5
hypocenterC3×C5H(5,𝔽2)
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. D4×D15C2semidirect
2. C5×D3×D4C2semidirect
3. C3×#711C2semidirect
4. #6790C2semidirect
5. D3×C22⋊D5C2semidirect
6. C2×#1203C2semidirect
7. #6782C2semidirect
8. D5×D12C2semidirect
9. #6771C2semidirect
10. #6769C2semidirect
11. #6768C2semidirect
13. C22×D15C22semidirect
14. C22×C5×D3C22semidirect
15. C2×D3×D5C22semidirect
16. C3×C5×D4C22semidirect
17. #1220C22semidirect
18. D60C22semidirect
19. C4×D15C22semidirect
20. C5×#67C22semidirect
21. C5×D12C22semidirect
22. C4×C5×D3C22semidirect
23. C3×C22⋊D5C22semidirect
24. C2×C3×Dic5C22semidirect
25. C3×C4×D5C22semidirect
26. C3×Dic10C22semidirect
27. #1204C22semidirect
28. #1203C22semidirect
29. #1203C22semidirect
30. #1203C22semidirect
31. #1203C22semidirect
32. #1202C22semidirect
33. #1201C22semidirect
34. #1200C22semidirect
35. D3×Dic5C22semidirect
42. #711D3semidirect
68. D3×D4D5semidirect
78. C5×D4C2×D3semidirect
86. C22⋊D5C2×D3semidirect
88. C2×Dic5C2×D3semidirect
93. C4×D5C2×D3semidirect
95. Dic10C2×D3semidirect
106. C22×D3C2×D5semidirect
109. C3×D4C2×D5semidirect
115. #67C2×D5semidirect
121. D12C2×D5semidirect
125. C4×D3C2×D5semidirect
152. C3×C5H(5,𝔽2)semidirect
190. D4D3×D5semidirect
204. C5#1009semidirect
219. C3#4144semidirect

Maximal subgroups

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

subgroupindex
D4×D152
C5×D3×D42
C3×#7112
#67902
D3×C22⋊D52
C2×#12032
#67822
D5×D122
#67712
#67692
#67682
#41443
#10095