Finite Group Databasebeta

← #65946

Subgroups — #65946

Order 320.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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#4084C212yesmaximal, complemented
5#4083C212yesmaximal, complemented
6#4082C211yesmaximal, characteristic, complemented
7C4×C22⋊D5C211yesmaximal, characteristic, complemented
8#4043C211yesmaximal, characteristic, complemented
9#4039C211yesmaximal, characteristic, complemented
10#4029C212yesmaximal, complemented
11D5×C22⋊C4C212yesmaximal, complemented
12C23×D5C2212yes—
13C2×C5×D4C2211yescharacteristic
14C2×C5×D4C2212yescomplemented
15C22×C4×C5C2211yescharacteristic, complemented
16C2×C22⋊D5C2212yes—
17C2×C22⋊D5C2211yescharacteristic
18C2×C22⋊D5C2212yescomplemented
19D4×D5—24no—
20#709—24no—
21C2×D20C2211yescharacteristic
22C2×C4×D5C2211yescharacteristic
23C2×C4×D5C2212yescomplemented
24C2×C4×D5C2212yescomplemented
25C2×Dic10C2211yescharacteristic, complemented
26C5×C4⋊C4C2211yescharacteristic, complemented
27C5×C22⋊C4C2212yescomplemented
28C22⋊Dic5C2212yescomplemented
29C22⋊Dic5C2212yescomplemented
30C22⋊Dic5C2211yescharacteristic, complemented
31#685C2211yescharacteristic
32#685C2212yes—
33#685C2212yescomplemented
34C4⋊Dic5C2212yescomplemented
35#683C2211yescharacteristic, complemented
36C4×Dic5C2211yescharacteristic, complemented
37#546—51nomaximal, Sylow
38C23×C5C2312yes—
39C23×C5C2311yescharacteristic
40C22×D5—24no—
41C22×D5—24no—
42C22×D5—42no—
43C22×D5C2312yes—
44C22×D5C2311yescharacteristic
45C5×D4—22no—
46C5×D4—42no—
47C2×C4×C5—22no—
48C2×C4×C5C2311yescharacteristic
49C2×C4×C5C2312yes—
50C2×C4×C5C2311yescharacteristic
51C22⋊D5—24no—
52C22⋊D5—24no—
53C22⋊D5—22no—
54C2×Dic5C2311yescharacteristic
55C2×Dic5C2311yescharacteristic
56C2×Dic5C2311yescharacteristic
57C2×Dic5C2312yes—
58D20D414yescomplemented
59C4×D5—24no—
60C4×D5—22no—
61C4×D5—42no—
62Dic10—22no—
63C2×#41—51no—
64C22×D4—51no—
65#124—51no—
66#123—52no—
67C22⋊Q8—51no—
68#121—52no—
69#121D511yescharacteristic, complemented
70#120—52no—
71C4×D4—51no—
72C4×D4—51no—
73C2×C22⋊C4—52no—
74C22×C5—21no—
75C22×C5—22no—
76C22×C5—21no—
77C22×C5—22no—
78C22×C5—21no—
79C22×C5—22no—
80C22×C5C2411yescharacteristic
81C2×D5—21no—
82C2×D5—22no—
83C2×D5—22no—
84C2×D5—21no—
85C2×D5—48no—
86C2×D5C2×D414yes—
87C2×D5#4112yescomplemented
88C4×C5—21no—
89C4×C5—22no—
90C4×C5C2×D412yes—
91Dic5—22no—
92Dic5—21no—
93Dic5—21no—
94Dic5—21no—
95C24—52no—
96#41—104no—
97C2×Q8—51no—
98C2×D4—51no—
99C2×D4—52no—
100C2×D4—52no—
101C2×D4—51no—
102C2×D4—104no—
103C2×D4C2×D511yescharacteristic
104C2×D4C2×D512yescomplemented
105C22×C4—52no—
106C22×C4—51no—
107C22×C4—52no—
108C22×C4C2×D511yescharacteristic, complemented
109C4⋊C4—51no—
110C4⋊C4—52no—
111C4⋊C4C2×D511yescharacteristic, complemented
112C22⋊C4—52no—
113C22⋊C4—51no—
114C22⋊C4—52no—
115C22⋊C4—51no—
116C22⋊C4—52no—
117C22⋊C4—52no—
118C22⋊C4C2×D512yescomplemented
119C42—51no—
120C2×C5—42no—
121C2×C5—41no—
122C2×C5C22×D411yescharacteristic
123C2×C5C2×#4111yescharacteristic
124C2×C5H(5,𝔽2)11yescharacteristic
125D5—22no—
126D5—24no—
127C23—51no—
128C23—52no—
129C23—104no—
130C23—104no—
131C23—202no—
132C23C22×D512yes—
133C23C22×D511yescharacteristic
134Q8—102no—
135D4—22no—
136D4—42no—
137D4—54no—
138D4—104no—
139D4—104no—
140D4—102no—
141C2×C4—22no—
142C2×C4—51no—
143C2×C4—51no—
144C2×C4—52no—
145C2×C4—51no—
146C2×C4—104no—
147C2×C4—102no—
148C2×C4—202no—
149C2×C4C22×D512yes—
150C2×C4C22×D511yescharacteristic
151C2×C4C22×D511yescharacteristic
152C5#54611yescharacteristic, complemented, Sylow
153C22—21no—
154C22—22no—
155C22—21no—
156C22—22no—
157C22—21no—
158C22—22no—
159C22—54no—
160C22—52no—
161C22—101no—
162C22—102no—
163C22—101no—
164C22—102no—
165C22—208no—
166C22C23×D511yescharacteristic
167C4—21no—
168C4—22no—
169C4—101no—
170C4—102no—
171C4—101no—
172C4—101no—
173C4D4×D512yes—
174C2—42no—
175C2—41no—
176C2—102no—
177C2—104no—
178C2C2×D4×D511yescharacteristic
179C2#414411yescharacteristic
180C2D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D5
commutator, socle, cosocleC22×C5C24
FittingC5×#121C2
hypercenter#121D5
hypocenterC5#546
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. #4084C2semidirect
5. #4083C2semidirect
6. #4082C2semidirect
7. C4×C22⋊D5C2semidirect
8. #4043C2semidirect
9. #4039C2semidirect
10. #4029C2semidirect
11. D5×C22⋊C4C2semidirect
14. C2×C5×D4C22semidirect
15. C22×C4×C5C22semidirect
18. C2×C22⋊D5C22semidirect
23. C2×C4×D5C22semidirect
24. C2×C4×D5C22semidirect
25. C2×Dic10C22semidirect
26. C5×C4⋊C4C22semidirect
27. C5×C22⋊C4C22semidirect
28. C22⋊Dic5C22semidirect
29. C22⋊Dic5C22semidirect
30. C22⋊Dic5C22semidirect
33. #685C22semidirect
34. C4⋊Dic5C22semidirect
35. #683C22semidirect
36. C4×Dic5C22semidirect
58. D20D4semidirect
69. #121D5semidirect
87. C2×D5#41semidirect
104. C2×D4C2×D5semidirect
108. C22×C4C2×D5semidirect
111. C4⋊C4C2×D5semidirect
118. C22⋊C4C2×D5semidirect
152. C5#546semidirect

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
#40842
#40832
#40822
C4×C22⋊D52
#40432
#40392
#40292
D5×C22⋊C42
#5465