Finite Group Databasebeta

← C2×#6790 #92048

Subgroups — C2×#6790 #92048

Order 480.

472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C23×D15C211yesmaximal, characteristic, complemented
2C22×D3×D5C211yesmaximal, characteristic, complemented
3C2×C5×#67C211yesmaximal, characteristic, complemented
4C2×C3×C22⋊D5C211yesmaximal, characteristic, complemented
5#6790C218yesmaximal, direct product factor
6C2×#1203C211yesmaximal, characteristic, complemented
7C2×#1202C211yesmaximal, characteristic, complemented
8C2×#1200C211yesmaximal, characteristic, complemented
9C2×D4×D5—31nomaximal, Hall
10C23×C3×C5C2211yescharacteristic, complemented
11C22×D15—24no—
12C22×D15C2211yescharacteristic
13C22×D15C2214yescomplemented
14C22×D15C2211yescharacteristic, complemented
15C22×C5×D3C2211yescharacteristic, complemented
16C22×C3×D5C2211yescharacteristic, complemented
17C2×D3×D5—24no—
18C2×D3×D5C2214yescomplemented
19C5×#67C2214yescomplemented
20C2×C5×Dic3C2211yescharacteristic, complemented
21C3×C22⋊D5C2214yescomplemented
22C2×C3×Dic5C2211yescharacteristic, complemented
23#1203C2214yescomplemented
24#1202C2214yescomplemented
25#1200C2214yescomplemented
26C2×D3×D4—51nomaximal, Hall
27C23×D5—31no—
28C23×D5—31no—
29C2×C5×D4—31no—
30C2×C22⋊D5—31no—
31C2×C22⋊D5D311yescharacteristic, complemented
32D4×D5—38no—
33C2×D20—31no—
34C2×C4×D5—31no—
35C22×C3×C5—22no—
36C22×C3×C5C2311yescharacteristic
37C22×C3×C5C2312yescomplemented
38C2×D15—22no—
39C2×D15—28no—
40C2×D15D414yescomplemented
41C2×D15C2312yes—
42C2×D15C2312yescomplemented
43C2×C5×D3—22no—
44C2×C5×D3C2312yescomplemented
45C2×C3×D5—22no—
46C2×C3×D5C2312yescomplemented
47D3×D5—28no—
48C3×Dic5C2312yescomplemented
49C5×Dic3C2312yescomplemented
50C23×D3—51no—
51C23×D3—51no—
52C2×C3×D4—51no—
53C2×#67—51no—
54C2×#67D511yescharacteristic, complemented
55D3×D4—58no—
56C2×D12—51no—
57C2×C4×D3—51no—
58C23×C5—31no—
59C23×C5C2×D311yescharacteristic, complemented
60C22×D5—31no—
61C22×D5—31no—
62C22×D5—34no—
63C22×D5—34no—
64C22×D5—64no—
65C22×D5—64no—
66C22×D5C2×D311yescharacteristic, complemented
67C5×D4—34no—
68C2×C4×C5—31no—
69C22⋊D5—34no—
70C22⋊D5C2×D314yescomplemented
71C2×Dic5C2×D311yescharacteristic, complemented
72D20—34no—
73C4×D5—34no—
74C22×D4—151noSylow
75C2×C3×C5—22no—
76C2×C3×C5C2×D412yescomplemented
77C2×C3×C5C2411yescharacteristic
78D15—22no—
79D15C2×D414yescomplemented
80C3×D5—22no—
81C5×D3—22no—
82C23×C3—51no—
83C23×C3C2×D511yescharacteristic, complemented
84C22×D3—51no—
85C22×D3—51no—
86C22×D3—54no—
87C22×D3—54no—
88C22×D3—104no—
89C22×D3—104no—
90C22×D3C2×D511yescharacteristic, complemented
91C3×D4—54no—
92C2×C3×C4—51no—
93#67—54no—
94#67C2×D514yescomplemented
95C2×Dic3C2×D511yescharacteristic, complemented
96D12—54no—
97C4×D3—54no—
98C22×C5—22no—
99C22×C5—32no—
100C22×C5—62no—
101C22×C5C22×D311yescharacteristic
102C22×C5C22×D312yescomplemented
103C2×D5—22no—
104C2×D5—34no—
105C2×D5—32no—
106C2×D5—32no—
107C2×D5—68no—
108C2×D5—68no—
109C2×D5—62no—
110C2×D5C22×D312yescomplemented
111C4×C5—32no—
112Dic5C22×D312yescomplemented
113C24—151no—
114C24—151no—
115C2×D4—31no—
116C2×D4—51no—
117C2×D4—151no—
118C2×D4—151no—
119C2×D4—158no—
120C22×C4—151no—
121C3×C5C22×D411yescharacteristic, complemented, Hall
122C22×C3—22no—
123C22×C3—52no—
124C22×C3—102no—
125C22×C3C22×D511yescharacteristic
126C22×C3C22×D512yescomplemented
127C2×D3—22no—
128C2×D3—54no—
129C2×D3—52no—
130C2×D3—52no—
131C2×D3—108no—
132C2×D3—108no—
133C2×D3—102no—
134C2×D3C22×D512yescomplemented
135C3×C4—52no—
136Dic3C22×D512yescomplemented
137C2×C5—22no—
138C2×C5—62no—
139C2×C5D3×D412yescomplemented
140C2×C5C23×D311yescharacteristic
141D5—22no—
142D5—34no—
143D5—62no—
144C23—31no—
145C23—51no—
146C23—154no—
147C23—151no—
148C23—151no—
149C23—154no—
150C23—304no—
151C23—304no—
152C23D3×D511yescharacteristic, complemented
153D4—34no—
154D4—54no—
155D4—154no—
156D4—154no—
157C2×C4—31no—
158C2×C4—51no—
159C2×C4—154no—
160C2×C3—22no—
161C2×C3—102no—
162C2×C3D4×D512yescomplemented
163C2×C3C23×D511yescharacteristic
164D3—22no—
165D3—54no—
166D3—102no—
167C5C2×D3×D411yescharacteristic, complemented, Sylow
168C22—22no—
169C22—32no—
170C22—52no—
171C22—62no—
172C22—102no—
173C22—154no—
174C22—152no—
175C22—152no—
176C22—308no—
177C22—308no—
178C22—302no—
179C22C2×D3×D511yescharacteristic
180C22C2×D3×D512yescomplemented
181C4—32no—
182C4—52no—
183C3C2×D4×D511yescharacteristic, complemented, Sylow
184C2—22no—
185C2—62no—
186C2—102no—
187C2—154no—
188C2—302no—
189C2#679012yesdirect product factor
190C2C22×D3×D511yescharacteristic
subgroupG/H
centerC22C2×D3×D5
commutator, cosocleC2×C3×C5C24
FrattiniC2C22×D3×D5
FittingC23×C3×C5C22
socleC22×C3×C5C23
hypercenterC23D3×D5
hypocenterC3×C5C22×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×D15C2semidirect
2. C22×D3×D5C2semidirect
3. C2×C5×#67C2semidirect
4. C2×C3×C22⋊D5C2semidirect
5. #6790C2direct (N × H)
6. C2×#1203C2semidirect
7. C2×#1202C2semidirect
8. C2×#1200C2semidirect
10. C23×C3×C5C22semidirect
13. C22×D15C22semidirect
14. C22×D15C22semidirect
15. C22×C5×D3C22semidirect
16. C22×C3×D5C22semidirect
18. C2×D3×D5C22semidirect
19. C5×#67C22semidirect
20. C2×C5×Dic3C22semidirect
21. C3×C22⋊D5C22semidirect
22. C2×C3×Dic5C22semidirect
23. #1203C22semidirect
24. #1202C22semidirect
25. #1200C22semidirect
31. C2×C22⋊D5D3semidirect
37. C22×C3×C5C23semidirect
40. C2×D15D4semidirect
42. C2×D15C23semidirect
44. C2×C5×D3C23semidirect
46. C2×C3×D5C23semidirect
48. C3×Dic5C23semidirect
49. C5×Dic3C23semidirect
54. C2×#67D5semidirect
59. C23×C5C2×D3semidirect
66. C22×D5C2×D3semidirect
70. C22⋊D5C2×D3semidirect
71. C2×Dic5C2×D3semidirect
76. C2×C3×C5C2×D4semidirect
79. D15C2×D4semidirect
83. C23×C3C2×D5semidirect
90. C22×D3C2×D5semidirect
94. #67C2×D5semidirect
95. C2×Dic3C2×D5semidirect
102. C22×C5C22×D3semidirect
110. C2×D5C22×D3semidirect
112. Dic5C22×D3semidirect
121. C3×C5C22×D4semidirect
126. C22×C3C22×D5semidirect
134. C2×D3C22×D5semidirect
136. Dic3C22×D5semidirect
139. C2×C5D3×D4semidirect
152. C23D3×D5semidirect
162. C2×C3D4×D5semidirect
167. C5C2×D3×D4semidirect
180. C22C2×D3×D5semidirect
183. C3C2×D4×D5semidirect
189. C2#6790direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D152
C22×D3×D52
C2×C5×#672
C2×C3×C22⋊D52
#67902
C2×#12032
C2×#12022
C2×#12002
C2×D4×D53
C2×D3×D45