Finite Group Databasebeta

← #65879

Subgroups — #65879

Order 320.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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
2C4×C5×D4C211yesmaximal, characteristic, complemented
3D4×Dic5C211yesmaximal, characteristic, complemented
4C4×C22⋊D5C212yesmaximal, complemented
5C2×#685C212yesmaximal, complemented
6#4039C211yesmaximal, characteristic, complemented
7#4038C211yesmaximal, characteristic, complemented
8#4027C212yesmaximal, complemented
9D5×C22⋊C4C212yesmaximal, complemented
10C4×D20C211yesmaximal, characteristic, complemented
11#4018C211yesmaximal, characteristic, complemented
12C23×D5C2212yes—
13C2×C5×D4C2211yescharacteristic
14C22×C4×C5C2212yescomplemented
15C2×C22⋊D5C2212yes—
16C22×Dic5C2212yescomplemented
17D4×D5C418yescomplemented
18C2×D20C2211yescharacteristic
19C2×C4×D5C2211yescharacteristic
20C2×C4×D5C2212yescomplemented
21C2×C4×D5C2212yescomplemented
22C5×C4⋊C4C2211yescharacteristic, complemented
23C5×C22⋊C4C2212yescomplemented
24C42×C5C2211yescharacteristic, complemented
25C22⋊Dic5C2212yescomplemented
26#685C2211yescharacteristic
27#685C2211yescharacteristic
28#685C2212yes—
29#685C2212yescomplemented
30#685C2212yescomplemented
31C4⋊Dic5C2211yescharacteristic, complemented
32#683C2211yescharacteristic, complemented
33#683C2211yescharacteristic, complemented
34C4×Dic5C2211yescharacteristic, complemented
35C4×Dic5C2212yescomplemented
36#518—51nomaximal, Sylow
37C23×C5C2312yes—
38C22×D5—42no—
39C22×D5—42no—
40C22×D5C2×C418yescomplemented
41C22×D5C2311yescharacteristic
42C22×D5C2312yes—
43C5×D4C2×C414yescomplemented
44C2×C4×C5—42no—
45C2×C4×C5C2312yes—
46C2×C4×C5C2311yescharacteristic
47C2×C4×C5C2311yescharacteristic
48C2×C4×C5C2311yescharacteristic
49C22⋊D5C2×C418yescomplemented
50C2×Dic5—42no—
51C2×Dic5C2311yescharacteristic
52C2×Dic5C2311yescharacteristic
53C2×Dic5C2312yes—
54C2×Dic5C2311yescharacteristic
55D20C2×C414yescomplemented
56C4×D5—42no—
57C4×D5—42no—
58C4×D5C2×C414yescomplemented
59C22×D4—51no—
60C4×D4—51no—
61C4×D4—52no—
62C4×D4—51no—
63C4×D4—52no—
64C4×D4—51no—
65C4×D4D511yescharacteristic, complemented
66#117—51no—
67#117—51no—
68C2×C22⋊C4—52no—
69C2×C22⋊C4—52no—
70C22×C5—22no—
71C22×C5—22no—
72C22×C5C22×C414yes—
73C22×C5C2411yescharacteristic
74C2×D5—22no—
75C2×D5—22no—
76C2×D5—21no—
77C2×D5—21no—
78C2×D5—48no—
79C2×D5C22×C412yes—
80C2×D5C22×C414yes—
81C4×C5—21no—
82C4×C5—22no—
83C4×C5—21no—
84C4×C5C22×C412yes—
85Dic5—21no—
86Dic5—22no—
87Dic5—21no—
88Dic5C22×C412yes—
89C24—52no—
90C2×D4—52no—
91C2×D4—58no—
92C2×D4—51no—
93C2×D4C2×D511yescharacteristic
94C22×C4—51no—
95C22×C4—52no—
96C22×C4—52no—
97C22×C4—52no—
98C22×C4C2×D512yescomplemented
99C4⋊C4—51no—
100C4⋊C4—51no—
101C4⋊C4—51no—
102C4⋊C4C2×D511yescharacteristic, complemented
103C22⋊C4—52no—
104C22⋊C4—52no—
105C22⋊C4—51no—
106C22⋊C4—51no—
107C22⋊C4—52no—
108C22⋊C4—52no—
109C22⋊C4C2×D512yescomplemented
110C42—52no—
111C42—51no—
112C42C2×D511yescharacteristic, complemented
113C2×C5—24no—
114C2×C5C23×C411yescharacteristic
115C2×C5H(5,𝔽2)11yescharacteristic
116C2×C5H(5,𝔽2)11yescharacteristic
117D5—22no—
118D5—24no—
119C23—51no—
120C23—52no—
121C23—58no—
122C23—202no—
123C23—202no—
124C23C22×D512yes—
125D4—58no—
126D4—54no—
127D4C4×D514yescomplemented
128C2×C4—42no—
129C2×C4—51no—
130C2×C4—54no—
131C2×C4—51no—
132C2×C4—52no—
133C2×C4—51no—
134C2×C4—202no—
135C2×C4—202no—
136C2×C4—202no—
137C2×C4C22×D512yes—
138C2×C4C22×D511yescharacteristic
139C2×C4C22×D511yescharacteristic
140C2×C4C22×D511yescharacteristic
141C5#51811yescharacteristic, complemented, Sylow
142C22—22no—
143C22—22no—
144C22—52no—
145C22—54no—
146C22—102no—
147C22—101no—
148C22—102no—
149C22—101no—
150C22—208no—
151C22C2×C4×D514yes—
152C22C23×D511yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—52no—
157C4—101no—
158C4—102no—
159C4—101no—
160C4C2×C4×D512yes—
161C2—24no—
162C2—102no—
163C2—104no—
164C2C22×C4×D511yescharacteristic
165C2#414411yescharacteristic
166C2#414911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D5
commutatorC2×C5C23×C4
FittingC4×C5×D4C2
socle, cosocleC22×C5C24
prime radicalC2×D4×D5C2
hypercenterC4×D4D5
hypocenterC5#518
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×C5×D4C2semidirect
3. D4×Dic5C2semidirect
4. C4×C22⋊D5C2semidirect
5. C2×#685C2semidirect
6. #4039C2semidirect
7. #4038C2semidirect
8. #4027C2semidirect
9. D5×C22⋊C4C2semidirect
10. C4×D20C2semidirect
11. #4018C2semidirect
14. C22×C4×C5C22semidirect
16. C22×Dic5C22semidirect
17. D4×D5C4semidirect
20. C2×C4×D5C22semidirect
21. C2×C4×D5C22semidirect
22. C5×C4⋊C4C22semidirect
23. C5×C22⋊C4C22semidirect
24. C42×C5C22semidirect
25. C22⋊Dic5C22semidirect
29. #685C22semidirect
30. #685C22semidirect
31. C4⋊Dic5C22semidirect
32. #683C22semidirect
33. #683C22semidirect
34. C4×Dic5C22semidirect
35. C4×Dic5C22semidirect
40. C22×D5C2×C4semidirect
43. C5×D4C2×C4semidirect
49. C22⋊D5C2×C4semidirect
55. D20C2×C4semidirect
58. C4×D5C2×C4semidirect
65. C4×D4D5semidirect
98. C22×C4C2×D5semidirect
102. C4⋊C4C2×D5semidirect
109. C22⋊C4C2×D5semidirect
112. C42C2×D5semidirect
127. D4C4×D5semidirect
141. C5#518semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D52
C4×C5×D42
D4×Dic52
C4×C22⋊D52
C2×#6852
#40392
#40382
#40272
D5×C22⋊C42
C4×D202
#40182
#5185