Finite Group Databasebeta

← #66010

Subgroups — #66010

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×#713C211yesmaximal, characteristic, complemented
2C2×D4×D5C211yesmaximal, characteristic, complemented
3C5×#124C211yesmaximal, characteristic, complemented
4#4092C211yesmaximal, characteristic, complemented
5#4084C211yesmaximal, characteristic, complemented
6#4030C212yesmaximal, complemented
7#4029C212yesmaximal, complemented
8#4028C212yesmaximal, complemented
9D5×C22⋊C4C212yesmaximal, complemented
10C4×D20C211yesmaximal, characteristic, complemented
11C4×D20C211yesmaximal, characteristic, complemented
12C23×D5C2212yes—
13C2×C5×Q8C2211yescharacteristic, complemented
14C2×C5×D4C2211yescharacteristic
15C2×C22⋊D5C2212yes—
16C2×C22⋊D5C2212yescomplemented
17#713—24no—
18D4×D5—24no—
19C2×D20C2211yescharacteristic
20C2×D20C2211yescharacteristic
21C2×D20C2212yescomplemented
22C2×C4×D5C2211yescharacteristic
23C2×C4×D5C2211yescharacteristic, complemented
24C2×C4×D5C2212yescomplemented
25C2×C4×D5C2212yescomplemented
26C5×C22⋊C4C2212yescomplemented
27C5×C22⋊C4C2212yescomplemented
28C42×C5C2211yescharacteristic, complemented
29C22⋊Dic5C2212yescomplemented
30#685C2211yescharacteristic
31#685C2212yes—
32#685C2212yescomplemented
33#685C2211yescharacteristic, complemented
34C4⋊Dic5C2211yescharacteristic, complemented
35C4⋊Dic5C2211yescharacteristic, complemented
36#683C2212yescomplemented
37#546—51nomaximal, Sylow
38C23×C5C2312yes—
39C22×D5—24no—
40C22×D5—24no—
41C22×D5—42no—
42C22×D5C2311yescharacteristic
43C22×D5C2312yes—
44C22×D5C2311yescharacteristic
45C5×Q8—22no—
46C5×D4—22no—
47C2×C4×C5C2312yes—
48C2×C4×C5C2311yescharacteristic
49C2×C4×C5C2311yescharacteristic
50C2×C4×C5C2311yescharacteristic
51C22⋊D5—24no—
52C22⋊D5—42no—
53C2×Dic5C2311yescharacteristic
54C2×Dic5C2312yes—
55C2×Dic5C2311yescharacteristic
56D20—24no—
57D20—22no—
58D20D414yescomplemented
59C4×D5—24no—
60C4×D5—22no—
61C4×D5—22no—
62C4×D5—42no—
63C2×#41—51no—
64C22×D4—51no—
65#124D511yescharacteristic, complemented
66#123—52no—
67C22⋊Q8—51no—
68#121—51no—
69#121—52no—
70#120—52no—
71C4×D4—51no—
72C4×D4—51no—
73C2×C22⋊C4—52no—
74C22×C5—22no—
75C22×C5—22no—
76C22×C5—22no—
77C22×C5C2411yescharacteristic
78C2×D5—21no—
79C2×D5—22no—
80C2×D5—22no—
81C2×D5—21no—
82C2×D5—21no—
83C2×D5—21no—
84C2×D5—21no—
85C2×D5—48no—
86C2×D5C2×D414yes—
87C2×D5#4112yescomplemented
88C4×C5—22no—
89C4×C5—21no—
90C4×C5—21no—
91C4×C5C2×D412yes—
92Dic5—21no—
93Dic5—21no—
94Dic5—22no—
95C24—52no—
96#41—104no—
97C2×Q8C2×D511yescharacteristic, complemented
98C2×D4—52no—
99C2×D4—52no—
100C2×D4—51no—
101C2×D4—51no—
102C2×D4—52no—
103C2×D4—104no—
104C2×D4C2×D511yescharacteristic
105C22×C4—52no—
106C22×C4—51no—
107C22×C4—51no—
108C22×C4—52no—
109C4⋊C4—51no—
110C4⋊C4—51no—
111C4⋊C4—52no—
112C22⋊C4—52no—
113C22⋊C4—51no—
114C22⋊C4—52no—
115C22⋊C4—52no—
116C22⋊C4—51no—
117C22⋊C4C2×D512yescomplemented
118C22⋊C4C2×D512yescomplemented
119C42C2×D511yescharacteristic, complemented
120C2×C5—42no—
121C2×C5C22×D411yescharacteristic
122C2×C5C2×#4111yescharacteristic
123C2×C5H(5,𝔽2)11yescharacteristic
124D5—22no—
125D5—24no—
126D5—41no—
127C23—51no—
128C23—52no—
129C23—51no—
130C23—104no—
131C23—104no—
132C23—202no—
133C23C22×D512yes—
134Q8—22no—
135D4—22no—
136D4—54no—
137D4—104no—
138D4—102no—
139D4—104no—
140D4—202no—
141C2×C4—52no—
142C2×C4—51no—
143C2×C4—51no—
144C2×C4—104no—
145C2×C4—102no—
146C2×C4—102no—
147C2×C4—202no—
148C2×C4C22×D511yescharacteristic
149C2×C4C22×D511yescharacteristic
150C2×C4C22×D512yes—
151C2×C4C22×D511yescharacteristic
152C5#54611yescharacteristic, complemented, Sylow
153C22—22no—
154C22—22no—
155C22—22no—
156C22—54no—
157C22—52no—
158C22—101no—
159C22—102no—
160C22—102no—
161C22—101no—
162C22—101no—
163C22—101no—
164C22—101no—
165C22—208no—
166C22C23×D511yescharacteristic
167C4—22no—
168C4—21no—
169C4—21no—
170C4—101no—
171C4—101no—
172C4—102no—
173C4D4×D512yes—
174C2—42no—
175C2—102no—
176C2—104no—
177C2—201no—
178C2C2×D4×D511yescharacteristic
179C2D5×#4111yescharacteristic
180C2#414911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D5
commutator, socle, cosocleC22×C5C24
FittingC5×#124C2
hypercenter#124D5
hypocenterC5#546
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#713C2semidirect
2. C2×D4×D5C2semidirect
3. C5×#124C2semidirect
4. #4092C2semidirect
5. #4084C2semidirect
6. #4030C2semidirect
7. #4029C2semidirect
8. #4028C2semidirect
9. D5×C22⋊C4C2semidirect
10. C4×D20C2semidirect
11. C4×D20C2semidirect
13. C2×C5×Q8C22semidirect
16. C2×C22⋊D5C22semidirect
21. C2×D20C22semidirect
23. C2×C4×D5C22semidirect
24. C2×C4×D5C22semidirect
25. C2×C4×D5C22semidirect
26. C5×C22⋊C4C22semidirect
27. C5×C22⋊C4C22semidirect
28. C42×C5C22semidirect
29. C22⋊Dic5C22semidirect
32. #685C22semidirect
33. #685C22semidirect
34. C4⋊Dic5C22semidirect
35. C4⋊Dic5C22semidirect
36. #683C22semidirect
58. D20D4semidirect
65. #124D5semidirect
87. C2×D5#41semidirect
97. C2×Q8C2×D5semidirect
117. C22⋊C4C2×D5semidirect
118. C22⋊C4C2×D5semidirect
119. C42C2×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×#7132
C2×D4×D52
C5×#1242
#40922
#40842
#40302
#40292
#40282
D5×C22⋊C42
C4×D202
#5465