Finite Group Databasebeta

← #13014507

Subgroups — #13014507

Order 1280.

274 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 46 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#10604142C212yesmaximal
2#10600233C211yesmaximal, characteristic
3#65811C2211yescharacteristic
4#65745—22no—
5C5×#376C411yescharacteristic, complemented
6C2×#3937—22no—
7#65213C411yescharacteristic, complemented
8#64854C414yescomplemented
9#64853—22no—
10#7506—51nomaximal, Sylow
11C2×#709D412yes—
12#4130—42no—
13C2×C42×C5—21no—
14C2×C42×C5C2×C411yescharacteristic
15#4076—41no—
16C2×#681—21no—
17#4021C2×C412yes—
18#4020D411yescharacteristic
19C4×D20—41no—
20#4015Q811yescharacteristic
21#4011—42no—
22#3999—24no—
23C5×#95—41no—
24#3937—44no—
25C4⋊#168—41no—
26#2126—52no—
27#1963—51no—
28C22×C4×C5—21no—
29C22×C4×C5—41no—
30C22×C4×C5C22⋊C411yescharacteristic
31C2×C22⋊D5—22no—
32#709—42no—
33#709—42no—
34C2×D20—41no—
35C2×D20C22⋊C412yes—
36C2×C4×D5—22no—
37C2×Dic10C4⋊C412yes—
38C22⋊AGL(1,𝔽5)—44no—
39C4⋊AGL(1,𝔽5)—82no—
40C4×AGL(1,𝔽5)—82no—
41C42×C5—21no—
42C42×C5—22no—
43C42×C5—41no—
44C42×C5C4211yescharacteristic
45C42×C5C4⋊C411yescharacteristic
46#685—42no—
47C4⋊Dic5—41no—
48#681—42no—
49C2×#168—41no—
50#532—51no—
51#423—51no—
52C2×#104—102no—
53#410—102no—
54#376AGL(1,𝔽5)11yescharacteristic, complemented
55#354—54no—
56#353—102no—
57C23×C5#9911yescharacteristic
58C22×D5—22no—
59C2×AGL(1,𝔽5)—84no—
60C2×C4×C5—21no—
61C2×C4×C5—21no—
62C2×C4×C5—21no—
63C2×C4×C5—21no—
64C2×C4×C5—42no—
65C2×C4×C5—81no—
66C2×C4×C5—82no—
67C2×C4×C5#9511yescharacteristic
68C2×C4×C5#9911yescharacteristic
69C22⋊D5—82no—
70C2×Dic5—22no—
71D20—42no—
72D20—82no—
73C4×D5—42no—
74C4×D5—42no—
75Dic10—42no—
76#168—81no—
77C2×#41—52no—
78C2×M16—101no—
79C4⋊Q8—51no—
80#127—51no—
81#124—52no—
82#121—201no—
83C4×D4—201no—
84#117—202no—
85C2×C42—21no—
86C2×C42C2×AGL(1,𝔽5)11yescharacteristic
87C4⋊C8—201no—
88#104—204no—
89#99—104no—
90#99—202no—
91#95—41no—
92C22×C5—21no—
93C22×C5—41no—
94C22×C5#34211yescharacteristic
95C2×D5—42no—
96C2×D5—82no—
97AGL(1,𝔽5)—164no—
98C4×C5—21no—
99C4×C5—41no—
100C4×C5—41no—
101C4×C5—82no—
102C4×C5#35311yescharacteristic
103C4×C5#35411yescharacteristic
104Dic5—42no—
105#41—202no—
106#41—202no—
107C2×Q8—52no—
108C2×D4—52no—
109C2×D4—102no—
110C2×D4—201no—
111C22×C4—21no—
112C22×C4—41no—
113C22×C4—102no—
114C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
115M16—202no—
116C2×C8—201no—
117C4⋊C4—201no—
118C4⋊C4—402no—
119C22⋊C4—202no—
120C22⋊C4—204no—
121C42—21no—
122C42—22no—
123C42—41no—
124C42—402no—
125C42C4×AGL(1,𝔽5)11yescharacteristic
126C42C4⋊AGL(1,𝔽5)11yescharacteristic
127C2×C5—21no—
128C2×C5—41no—
129C2×C5#139311yescharacteristic
130D5—82no—
131C23—102no—
132C23#401111yescharacteristic
133Q8—202no—
134D4—202no—
135D4—402no—
136D4—402no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—81no—
143C2×C4—82no—
144C2×C4—102no—
145C2×C4—202no—
146C2×C4—202no—
147C2×C4—404no—
148C2×C4#399911yescharacteristic
149C2×C4(C2×AGL(1,𝔽5))⋊C411yescharacteristic
150C8—401no—
151C5#750611yescharacteristic, complemented, Sylow
152C22—21no—
153C22—41no—
154C22—202no—
155C22—402no—
156C22#6491711yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—82no—
161C4—202no—
162C4—804no—
163C4#6485311yescharacteristic
164C4#6485411yescharacteristic
165C2—21no—
166C2—41no—
167C2—402no—
168C2#1059869311yescharacteristic
subgroupG/H
centerC4#64853
commutatorC42×C5C42
FrattiniC2×C42C2×AGL(1,𝔽5)
FittingC5×#376C4
socleC2×C5#1393
prime radical, cosocle#65811C22
hypercenter#376AGL(1,𝔽5)
hypocenterC5#7506
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
5. C5×#376C4semidirect
7. #65213C4semidirect
8. #64854C4semidirect
54. #376AGL(1,𝔽5)semidirect
151. C5#7506semidirect

Maximal subgroups

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

subgroupindex
#106041422
#106002332
#75065