Finite Group Databasebeta

← #13014126

Subgroups — #13014126

Order 1280.

268 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 40 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
1#10600565C211yesmaximal, characteristic
2#10598689C212yesmaximal, complemented
3C2×#4020C411yescharacteristic
4C2×C4×C5×C8C411yescharacteristic
5C2×#3953—22no—
6#65224C2211yescharacteristic
7#64913—22no—
8#7354—51nomaximal, Sylow
9C22×D20—21no—
10C22×D20—41no—
11C22×C5×C8—21no—
12C2×C42×C5C2×C411yescharacteristic
13C2×C4⋊Dic5—41no—
14C2×C4⋊Dic5D412yes—
15#4020—21no—
16#4020—41no—
17#4020C812yescomplemented
18C22⋊#170—42no—
19C4×C5×C8—41no—
20#3953—44no—
21#1957—51no—
22#1325—52no—
23C23×D5—41no—
24C22×C4×C5—21no—
25C22×C4×C5C22⋊C411yescharacteristic
26C22×Dic5—22no—
27C2×D20—22no—
28C2×D20—42no—
29C2×D20—42no—
30C2×D20—42no—
31C2×D20—42no—
32C2×D20—41no—
33C2×D20—82no—
34C2×D20—82no—
35C2×#170—82no—
36C2×C5×C8—22no—
37C2×C5×C8—41no—
38C2×C5×C8—41no—
39C42×C5—21no—
40C42×C5C2×C811yescharacteristic
41C42×C5M1611yescharacteristic
42C4⋊Dic5—42no—
43C4⋊Dic5—82no—
44C2×#127—51no—
45C2×#102—102no—
46C2×C4×C8AGL(1,𝔽5)11yescharacteristic
47#384—51no—
48#324—102no—
49C23×C5#9911yescharacteristic
50C22×D5—42no—
51C22×D5—82no—
52C22×D5—82no—
53C22×D5—81no—
54C22×D5—81no—
55C2×C4×C5—22no—
56C2×C4×C5—22no—
57C2×C4×C5—21no—
58C2×C4×C5—21no—
59C2×C4×C5—21no—
60C2×C4×C5—21no—
61C2×C4×C5C22⋊C811yescharacteristic
62C2×C4×C5#10011yescharacteristic
63C2×Dic5—42no—
64C2×Dic5—82no—
65D20—44no—
66D20—82no—
67D20—84no—
68D20—84no—
69#170—162no—
70C5×C8—42no—
71C22×D4—101no—
72C22×D4—201no—
73C22×C8—21no—
74#127—52no—
75#127—101no—
76#127—201no—
77C2×C4⋊C4—52no—
78C2×C4⋊C4—201no—
79C2×C42C2×AGL(1,𝔽5)11yescharacteristic
80#102—204no—
81C22⋊C8—202no—
82C4×C8—41no—
83C22×C5—21no—
84C22×C5—21no—
85C22×C5#32311yescharacteristic
86C22×C5#35311yescharacteristic
87C22×C5#35511yescharacteristic
88C2×D5—84no—
89C2×D5—82no—
90C2×D5—162no—
91C2×D5—161no—
92C2×D5—161no—
93C4×C5—22no—
94C4×C5—22no—
95C4×C5—21no—
96C4×C5—21no—
97Dic5—82no—
98C24—201no—
99C2×D4—102no—
100C2×D4—202no—
101C2×D4—202no—
102C2×D4—202no—
103C2×D4—202no—
104C2×D4—201no—
105C2×D4—402no—
106C2×D4—402no—
107C22×C4—21no—
108C22×C4—102no—
109C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
110C2×C8—22no—
111C2×C8—41no—
112C2×C8—41no—
113C2×C8—402no—
114C4⋊C4—202no—
115C4⋊C4—402no—
116C42—21no—
117C42D5⋊C811yescharacteristic
118C42#70011yescharacteristic
119C2×C5—21no—
120C2×C5—21no—
121C2×C5#131811yescharacteristic
122C2×C5#140811yescharacteristic
123C2×C5#141011yescharacteristic
124D5—162no—
125C23—202no—
126C23—402no—
127C23—402no—
128C23—401no—
129C23—401no—
130C23#399911yescharacteristic
131D4—204no—
132D4—402no—
133D4—404no—
134D4—404no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—202no—
142C2×C4—402no—
143C2×C4#400311yescharacteristic
144C2×C4#401311yescharacteristic
145C8—42no—
146C8—802no—
147C5#735411yescharacteristic, complemented, Sylow
148C22—21no—
149C22—21no—
150C22—404no—
151C22—402no—
152C22—802no—
153C22—801no—
154C22—801no—
155C22#6485311yescharacteristic
156C22#6485611yescharacteristic
157C22#6491511yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—21no—
162C4—402no—
163C2—21no—
164C2—21no—
165C2—802no—
166C2#1059851611yescharacteristic
167C2#1059852011yescharacteristic
168C2#1059868611yescharacteristic
subgroupG/H
centerC22#64853
commutatorC42×C5C2×C8
FrattiniC2×C42C2×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC22×C5#353
prime radicalC2×#4020C4
cosocle#65224C22
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5#7354
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #10598689C2semidirect
17. #4020C8semidirect
147. C5#7354semidirect

Maximal subgroups

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

subgroupindex
#106005652
#105986892
#73545