Finite Group Databasebeta

← #13014130

Subgroups — #13014130

Order 1280.

202 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 36 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#10600233C211yesmaximal, characteristic
2#10598691C212yesmaximal, complemented
3#65811C411yescharacteristic
4C5×#376C411yescharacteristic
5C2×#3937—22no—
6#65213C2211yescharacteristic
7#64912—22no—
8#7356—51nomaximal, Sylow
9C2×#709—21no—
10C2×C42×C5—21no—
11C2×C42×C5C2×C411yescharacteristic
12#4076—41no—
13C2×#681D412yes—
14#4021—21no—
15#4020C811yescharacteristic
16C4×D20—41no—
17#4015C811yescharacteristic
18#3998—42no—
19C5×#95—41no—
20#3937—44no—
21C4⋊#168—41no—
22#1963—51no—
23#1327—52no—
24C22×C4×C5—21no—
25C22×C4×C5—41no—
26C22×C4×C5C22⋊C411yescharacteristic
27C2×C22⋊D5—41no—
28#709—42no—
29#709—42no—
30C2×D20—21no—
31C2×D20—41no—
32C2×C4×D5—41no—
33C2×Dic10—21no—
34C42×C5—21no—
35C42×C5—22no—
36C42×C5—41no—
37C42×C5C2×C811yescharacteristic
38C42×C5M1611yescharacteristic
39#685—42no—
40C4⋊Dic5—41no—
41#681—42no—
42C2×#168—22no—
43#674—82no—
44#532—51no—
45#423—51no—
46C2×#104—102no—
47#376AGL(1,𝔽5)11yescharacteristic
48#349—102no—
49C23×C5#10011yescharacteristic
50C22×D5—41no—
51C2×C4×C5—21no—
52C2×C4×C5—21no—
53C2×C4×C5—21no—
54C2×C4×C5—21no—
55C2×C4×C5—42no—
56C2×C4×C5—81no—
57C2×C4×C5—82no—
58C2×C4×C5C22⋊C811yescharacteristic
59C2×C4×C5#9911yescharacteristic
60C22⋊D5—82no—
61C2×Dic5—41no—
62D20—42no—
63D20—82no—
64C4×D5—81no—
65C4×D5—81no—
66Dic10—42no—
67#168—42no—
68C2×#41—101no—
69C2×M16—52no—
70C4⋊Q8—51no—
71#127—51no—
72#124—101no—
73#121—201no—
74C4×D4—201no—
75C2×C42—21no—
76C2×C42C2×AGL(1,𝔽5)11yescharacteristic
77M32—202no—
78C4⋊C8—201no—
79#104—204no—
80#95—41no—
81C22×C5—21no—
82C22×C5—41no—
83C22×C5#32311yescharacteristic
84C2×D5—82no—
85C2×D5—81no—
86C4×C5—21no—
87C4×C5—41no—
88C4×C5—41no—
89C4×C5—82no—
90C4×C5#35311yescharacteristic
91C4×C5#35511yescharacteristic
92Dic5—81no—
93#41—202no—
94#41—202no—
95C2×Q8—101no—
96C2×D4—101no—
97C2×D4—201no—
98C2×D4—201no—
99C22×C4—21no—
100C22×C4—41no—
101C22×C4—201no—
102C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
103M16—202no—
104C2×C8—102no—
105C4⋊C4—201no—
106C22⋊C4—202no—
107C42—21no—
108C42—22no—
109C42—41no—
110C42D5⋊C811yescharacteristic
111C42#70011yescharacteristic
112C16—402no—
113C2×C5—21no—
114C2×C5—41no—
115C2×C5#131811yescharacteristic
116D5—161no—
117C23—201no—
118C23#401311yescharacteristic
119Q8—202no—
120D4—202no—
121D4—402no—
122D4—402no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—42no—
128C2×C4—81no—
129C2×C4—82no—
130C2×C4—201no—
131C2×C4—401no—
132C2×C4—401no—
133C2×C4#399911yescharacteristic
134C2×C4#400311yescharacteristic
135C8—202no—
136C5#735611yescharacteristic, complemented, Sylow
137C22—21no—
138C22—41no—
139C22—402no—
140C22—401no—
141C22#6491511yescharacteristic
142C4—21no—
143C4—41no—
144C4—41no—
145C4—82no—
146C4—401no—
147C4#6485311yescharacteristic
148C4#6485611yescharacteristic
149C2—21no—
150C2—41no—
151C2—801no—
152C2#1059868611yescharacteristic
subgroupG/H
centerC4#64853
commutatorC42×C5C2×C8
FrattiniC2×C42C2×AGL(1,𝔽5)
FittingC5×#376C4
socleC2×C5#1318
prime radical#65811C4
cosocle#65213C22
hypercenter#376AGL(1,𝔽5)
hypocenterC5#7356
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
2. #10598691C2semidirect
136. C5#7356semidirect

Maximal subgroups

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

subgroupindex
#106002332
#105986912
#73565