Finite Group Databasebeta

← #65941

Subgroups — #65941

Order 320.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×D4×D5C211yesmaximal, characteristic, complemented
2C2×#709C211yesmaximal, characteristic, complemented
3C5×#121C211yesmaximal, characteristic, complemented
4#4086C212yesmaximal, complemented
5#4084C211yesmaximal, characteristic, complemented
6#4083C212yesmaximal, complemented
7#4076C211yesmaximal, characteristic, complemented
8#4041C211yesmaximal, characteristic, complemented
9#4038C211yesmaximal, characteristic, complemented
10#4031C212yesmaximal, complemented
11#4028C212yesmaximal, complemented
12C23×D5C2212yes—
13C2×C5×D4C2211yescharacteristic
14C2×C5×D4C2212yescomplemented
15C22×C4×C5C2211yescharacteristic, complemented
16C2×C22⋊D5C2211yescharacteristic
17C2×C22⋊D5C2212yes—
18C2×C22⋊D5C2211yescharacteristic, complemented
19C2×C22⋊D5C2212yescomplemented
20C2×C22⋊D5C2212yescomplemented
21D4×D5—24no—
22#709—24no—
23C2×D20C2211yescharacteristic
24C2×D20C2211yescharacteristic
25C2×D20C2212yescomplemented
26C2×C4×D5C2211yescharacteristic
27C2×C4×D5C2211yescharacteristic, complemented
28C2×Dic10C2211yescharacteristic, complemented
29C5×C4⋊C4C2211yescharacteristic, complemented
30C5×C22⋊C4C2212yescomplemented
31C22⋊Dic5C2212yescomplemented
32#685C2212yes—
33#685C2212yescomplemented
34#685C2212yescomplemented
35C4⋊Dic5C2211yescharacteristic, complemented
36C4×Dic5C2212yescomplemented
37#535—51nomaximal, Sylow
38C23×C5C2312yes—
39C23×C5C2311yescharacteristic
40C22×D5—24no—
41C22×D5—42no—
42C22×D5—42no—
43C22×D5C2312yes—
44C22×D5C2311yescharacteristic
45C22×D5C2311yescharacteristic
46C5×D4—22no—
47C5×D4—42no—
48C2×C4×C5—22no—
49C2×C4×C5C2312yes—
50C2×C4×C5C2311yescharacteristic
51C2×C4×C5C2311yescharacteristic
52C22⋊D5—22no—
53C22⋊D5—22no—
54C22⋊D5—24no—
55C22⋊D5—42no—
56C22⋊D5—42no—
57C2×Dic5C2312yes—
58C2×Dic5C2311yescharacteristic
59C2×Dic5C2311yescharacteristic
60D20—22no—
61D20—22no—
62D20—42no—
63C4×D5—22no—
64C4×D5D414yescomplemented
65Dic10—22no—
66C2×#41—51no—
67C22×D4—51no—
68#127—52no—
69#124—52no—
70#121—51no—
71#121—51no—
72#121—51no—
73#121D511yescharacteristic, complemented
74#120—52no—
75#120—52no—
76#117—51no—
77C22×C5—21no—
78C22×C5—22no—
79C22×C5—21no—
80C22×C5—22no—
81C22×C5—21no—
82C22×C5—22no—
83C22×C5C2411yescharacteristic
84C2×D5—21no—
85C2×D5—21no—
86C2×D5—21no—
87C2×D5—22no—
88C2×D5—21no—
89C2×D5—22no—
90C2×D5—21no—
91C2×D5—22no—
92C2×D5—48no—
93C2×D5C2×D412yes—
94C4×C5—21no—
95C4×C5—22no—
96C4×C5C2×D412yes—
97Dic5—21no—
98Dic5—22no—
99Dic5C2×D412yes—
100C24—52no—
101#41—104no—
102C2×Q8—51no—
103C2×D4—51no—
104C2×D4—52no—
105C2×D4—51no—
106C2×D4—52no—
107C2×D4—52no—
108C2×D4—51no—
109C2×D4—51no—
110C2×D4—52no—
111C2×D4—104no—
112C2×D4C2×D511yescharacteristic
113C2×D4C2×D512yescomplemented
114C22×C4—51no—
115C22×C4—51no—
116C22×C4C2×D511yescharacteristic, complemented
117C4⋊C4—51no—
118C4⋊C4C2×D511yescharacteristic, complemented
119C22⋊C4—52no—
120C22⋊C4—52no—
121C22⋊C4—52no—
122C22⋊C4—52no—
123C22⋊C4C2×D512yescomplemented
124C42—52no—
125C2×C5—42no—
126C2×C5—41no—
127C2×C5C22×D411yescharacteristic
128C2×C5H(5,𝔽2)11yescharacteristic
129C2×C5H(5,𝔽2)11yescharacteristic
130D5—22no—
131D5—41no—
132D5—42no—
133C23—51no—
134C23—52no—
135C23—51no—
136C23—104no—
137C23—202no—
138C23—202no—
139C23C22×D512yes—
140C23C22×D511yescharacteristic
141Q8—102no—
142D4—22no—
143D4—42no—
144D4—102no—
145D4—104no—
146D4—102no—
147D4—102no—
148D4—102no—
149D4—202no—
150D4—202no—
151D4—202no—
152C2×C4—22no—
153C2×C4—51no—
154C2×C4—54no—
155C2×C4—52no—
156C2×C4—51no—
157C2×C4—102no—
158C2×C4C22×D512yes—
159C2×C4C22×D511yescharacteristic
160C2×C4C22×D511yescharacteristic
161C5#53511yescharacteristic, complemented, Sylow
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—52no—
169C22—101no—
170C22—101no—
171C22—101no—
172C22—102no—
173C22—101no—
174C22—102no—
175C22—101no—
176C22—102no—
177C22—208no—
178C22C23×D511yescharacteristic
179C4—21no—
180C4—22no—
181C4—52no—
182C4—101no—
183C4—102no—
184C4D4×D512yes—
185C2—42no—
186C2—41no—
187C2—102no—
188C2—202no—
189C2—201no—
190C2C2×D4×D511yescharacteristic
191C2#414411yescharacteristic
192C2#414911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D5
commutator, socle, cosocleC22×C5C24
FittingC5×#121C2
hypercenter#121D5
hypocenterC5#535
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D5C2semidirect
2. C2×#709C2semidirect
3. C5×#121C2semidirect
4. #4086C2semidirect
5. #4084C2semidirect
6. #4083C2semidirect
7. #4076C2semidirect
8. #4041C2semidirect
9. #4038C2semidirect
10. #4031C2semidirect
11. #4028C2semidirect
14. C2×C5×D4C22semidirect
15. C22×C4×C5C22semidirect
18. C2×C22⋊D5C22semidirect
19. C2×C22⋊D5C22semidirect
20. C2×C22⋊D5C22semidirect
25. C2×D20C22semidirect
27. C2×C4×D5C22semidirect
28. C2×Dic10C22semidirect
29. C5×C4⋊C4C22semidirect
30. C5×C22⋊C4C22semidirect
31. C22⋊Dic5C22semidirect
33. #685C22semidirect
34. #685C22semidirect
35. C4⋊Dic5C22semidirect
36. C4×Dic5C22semidirect
64. C4×D5D4semidirect
73. #121D5semidirect
113. C2×D4C2×D5semidirect
116. C22×C4C2×D5semidirect
118. C4⋊C4C2×D5semidirect
123. C22⋊C4C2×D5semidirect
161. C5#535semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D52
C2×#7092
C5×#1212
#40862
#40842
#40832
#40762
#40412
#40382
#40312
#40282
#5355