Finite Group Databasebeta

← #92024

Subgroups — #92024

Order 480.

328 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 110 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×#237C211yesmaximal, characteristic, complemented
3C3×#711C211yesmaximal, characteristic, complemented
4#6790C212yesmaximal, complemented
5C2×#1200C212yesmaximal, complemented
6#6782C212yesmaximal, complemented
7#6779C212yesmaximal, complemented
8C4×D3×D5C211yesmaximal, characteristic, complemented
9#6773C211yesmaximal, characteristic, complemented
10D15⋊Q8C211yesmaximal, characteristic, complemented
11#6769C211yesmaximal, characteristic, complemented
12D5×#41—31nomaximal, Hall
13C22×D15C2212yes—
14C2×D3×D5C2211yescharacteristic
15C3×C5×D4C2211yescharacteristic, complemented
16#1220C2212yescomplemented
17D60C2211yescharacteristic, complemented
18C4×D15C2211yescharacteristic
19C5×#67C2212yescomplemented
20C2×C5×Dic3C2212yescomplemented
21C4×C5×D3C2211yescharacteristic, complemented
22C5×Dic6C2211yescharacteristic, complemented
23C3×C22⋊D5C2212yescomplemented
24C2×C3×Dic5C2212yescomplemented
25C3×C4×D5C2211yescharacteristic, complemented
26C3×Dic10C2211yescharacteristic, complemented
27#1204C2212yescomplemented
28#1203C2212yescomplemented
29#1202C2212yescomplemented
30#1200C2212yes—
31#1200C2211yescharacteristic
32#1200C2212yescomplemented
33#1200C2212yescomplemented
34D3×Dic5C2211yescharacteristic, complemented
35D5×Dic3C2211yescharacteristic, complemented
36D3×#41—51nomaximal, Hall
37C5×#41—31no—
38#713—31no—
39Q8×D5—31no—
40#711—32no—
41#711D311yescharacteristic, complemented
42D4×D5—31no—
43D4×D5—32no—
44#709—32no—
45#709—31no—
46C2×C4×D5—32no—
47C2×C4×D5—31no—
48C22×C3×C5C2312yes—
49C2×D15—24no—
50C2×D15C2312yes—
51C2×D15C2311yescharacteristic
52C2×C5×D3C2311yescharacteristic
53C2×C3×D5C2311yescharacteristic
54D3×D5—22no—
55C3×C4×C5C2311yescharacteristic
56Dic15C2311yescharacteristic
57C3×Dic5C2311yescharacteristic
58C3×Dic5C2312yes—
59C5×Dic3C2311yescharacteristic
60C5×Dic3C2312yes—
61C3×#41—51no—
62#239—51no—
63D3×Q8—51no—
64#237—52no—
65#237D511yescharacteristic, complemented
66D3×D4—51no—
67D3×D4—52no—
68#235—52no—
69#235—51no—
70C2×C4×D3—52no—
71C2×C4×D3—51no—
72C22×D5—32no—
73C22×D5—31no—
74C5×Q8—31no—
75C5×D4—32no—
76C5×D4C2×D311yescharacteristic, complemented
77C2×C4×C5—32no—
78C2×C4×C5—31no—
79C22⋊D5—32no—
80C22⋊D5—32no—
81C22⋊D5C2×D312yescomplemented
82C2×Dic5—31no—
83C2×Dic5C2×D312yescomplemented
84D20—32no—
85D20—31no—
86C4×D5—31no—
87C4×D5—31no—
88C4×D5—31no—
89C4×D5—32no—
90C4×D5—32no—
91C4×D5—32no—
92C4×D5C2×D311yescharacteristic, complemented
93Dic10—32no—
94Dic10C2×D311yescharacteristic, complemented
95C2×#41—151noSylow
96C2×C3×C5—22no—
97C2×C3×C5C2411yescharacteristic
98D15—22no—
99D15#4112yescomplemented
100C3×D5—21no—
101C5×D3—21no—
102C22×D3—52no—
103C22×D3—51no—
104C3×Q8—51no—
105C3×D4—52no—
106C3×D4C2×D511yescharacteristic, complemented
107C2×C3×C4—52no—
108C2×C3×C4—51no—
109#67—52no—
110#67—52no—
111#67C2×D512yescomplemented
112C2×Dic3—51no—
113C2×Dic3C2×D512yescomplemented
114D12—52no—
115D12—51no—
116C4×D3—51no—
117C4×D3—51no—
118C4×D3—51no—
119C4×D3—52no—
120C4×D3—52no—
121C4×D3—52no—
122C4×D3C2×D511yescharacteristic, complemented
123Dic6—52no—
124Dic6C2×D511yescharacteristic, complemented
125C22×C5—31no—
126C22×C5C22×D312yes—
127C2×D5—31no—
128C2×D5—32no—
129C2×D5—62no—
130C2×D5—64no—
131C2×D5C22×D311yescharacteristic
132C4×C5—32no—
133C4×C5—31no—
134C4×C5C22×D311yescharacteristic
135Dic5—31no—
136Dic5C22×D312yes—
137Dic5C22×D311yescharacteristic
138#41—31no—
139#41—51no—
140#41—152no—
141#41—151no—
142#41—152no—
143#41—151no—
144C2×Q8—151no—
145C2×D4—152no—
146C2×D4—151no—
147C22×C4—152no—
148C22×C4—151no—
149C3×C5C2×#4111yescharacteristic, complemented, Hall
150C22×C3—51no—
151C22×C3C22×D512yes—
152C2×D3—51no—
153C2×D3—52no—
154C2×D3—102no—
155C2×D3—104no—
156C2×D3C22×D511yescharacteristic
157C3×C4—52no—
158C3×C4—51no—
159C3×C4C22×D511yescharacteristic
160Dic3—51no—
161Dic3C22×D512yes—
162Dic3C22×D511yescharacteristic
163C2×C5—22no—
164C2×C5—61no—
165C2×C5C23×D311yescharacteristic
166D5—21no—
167D5—32no—
168D5—62no—
169C23—151no—
170C23—152no—
171Q8—31no—
172Q8—51no—
173Q8—152no—
174D4—32no—
175D4—52no—
176D4—152no—
177D4—152no—
178D4—152no—
179D4—151no—
180D4D3×D511yescharacteristic, complemented
181C2×C4—32no—
182C2×C4—31no—
183C2×C4—52no—
184C2×C4—51no—
185C2×C4—151no—
186C2×C4—152no—
187C2×C4—152no—
188C2×C4—152no—
189C2×C4—151no—
190C2×C4—151no—
191C2×C4—151no—
192C2×C3—22no—
193C2×C3—101no—
194C2×C3C23×D511yescharacteristic
195D3—21no—
196D3—52no—
197D3—102no—
198C5D3×#4111yescharacteristic, complemented, Sylow
199C22—31no—
200C22—51no—
201C22—151no—
202C22—152no—
203C22—304no—
204C22—302no—
205C22C2×D3×D512yes—
206C4—31no—
207C4—32no—
208C4—51no—
209C4—52no—
210C4—151no—
211C4C2×D3×D511yescharacteristic
212C3D5×#4111yescharacteristic, complemented, Sylow
213C2—22no—
214C2—61no—
215C2—101no—
216C2—152no—
217C2—302no—
218C2C22×D3×D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D5
commutator, socle, cosocleC2×C3×C5C24
FittingC3×C5×D4C22
hypercenterD4D3×D5
hypocenterC3×C5C2×#41
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×#237C2semidirect
3. C3×#711C2semidirect
4. #6790C2semidirect
5. C2×#1200C2semidirect
6. #6782C2semidirect
7. #6779C2semidirect
8. C4×D3×D5C2semidirect
9. #6773C2semidirect
10. D15⋊Q8C2semidirect
11. #6769C2semidirect
15. C3×C5×D4C22semidirect
16. #1220C22semidirect
17. D60C22semidirect
19. C5×#67C22semidirect
20. C2×C5×Dic3C22semidirect
21. C4×C5×D3C22semidirect
22. C5×Dic6C22semidirect
23. C3×C22⋊D5C22semidirect
24. C2×C3×Dic5C22semidirect
25. C3×C4×D5C22semidirect
26. C3×Dic10C22semidirect
27. #1204C22semidirect
28. #1203C22semidirect
29. #1202C22semidirect
32. #1200C22semidirect
33. #1200C22semidirect
34. D3×Dic5C22semidirect
35. D5×Dic3C22semidirect
41. #711D3semidirect
65. #237D5semidirect
76. C5×D4C2×D3semidirect
81. C22⋊D5C2×D3semidirect
83. C2×Dic5C2×D3semidirect
92. C4×D5C2×D3semidirect
94. Dic10C2×D3semidirect
99. D15#41semidirect
106. C3×D4C2×D5semidirect
111. #67C2×D5semidirect
113. C2×Dic3C2×D5semidirect
122. C4×D3C2×D5semidirect
124. Dic6C2×D5semidirect
149. C3×C5C2×#41semidirect
180. D4D3×D5semidirect
198. C5D3×#41semidirect
212. C3D5×#41semidirect

Maximal subgroups

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

subgroupindex
D4×D152
C5×#2372
C3×#7112
#67902
C2×#12002
#67822
#67792
C4×D3×D52
#67732
D15⋊Q82
#67692
D5×#413
D3×#415