Finite Group Databasebeta

← #13013746

Subgroups — #13013746

Order 1280.

206 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 60 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#10603846C211yesmaximal, characteristic
2#10603817C211yesmaximal, characteristic
3#10599866C211yesmaximal, characteristic
4#65689—21no—
5#65681—21no—
6C4×C8×D5C2211yescharacteristic
7#64893—21no—
8#64893C412yes—
9#64883—21no—
10#64883C412yescomplemented
11C5×#346C411yescharacteristic, complemented
12#64727—21no—
13#64721—21no—
14#64681C411yescharacteristic, complemented
15#7221—51nomaximal, Sylow
16C2×C4⋊AGL(1,𝔽5)—22no—
17C2×#700—41no—
18C2×C8×D5C2×C411yescharacteristic
19C2×C8×D5D411yescharacteristic
20C42×D5D411yescharacteristic
21(C2×AGL(1,𝔽5))⋊C4—41no—
22(C2×AGL(1,𝔽5))⋊C4—41no—
23C4⋊#170—22no—
24C4⋊#170—41no—
25C2×C5×C16—21no—
26C4×C5×C8C2×C411yescharacteristic
27C8×Dic5C2×C411yescharacteristic
28C8×Dic5D411yescharacteristic
29C2×#672—21no—
30C4×#168Q811yescharacteristic
31#2163—51no—
32#1835—51no—
33#1566—51no—
34C22×AGL(1,𝔽5)—42no—
35C2×C4×D5C22⋊C411yescharacteristic
36C2×C4×D5D811yescharacteristic
37C2×C4×D5SD1611yescharacteristic
38C2×#170—42no—
39C4⋊AGL(1,𝔽5)—42no—
40C4⋊AGL(1,𝔽5)—42no—
41#700—82no—
42C2×C5×C8C4211yescharacteristic
43C2×C5×C8C22⋊C411yescharacteristic
44C42×C5C4⋊C411yescharacteristic
45C4×Dic5C22⋊C411yescharacteristic
46C4×Dic5SD1611yescharacteristic
47C4×Dic5Q1611yescharacteristic
48C2×#168C4⋊C411yescharacteristic
49C2×#168C4⋊C411yescharacteristic
50C8×D5—41no—
51C8×D5—41no—
52C5×C16—41no—
53#672—41no—
54#423—101no—
55C2×C4×C8—51no—
56#382—101no—
57C4⋊C16—101no—
58C22⋊C16—101no—
59#346—51no—
60#346AGL(1,𝔽5)11yescharacteristic, complemented
61#340—52no—
62#340—101no—
63#334—52no—
64#334—101no—
65C22×D5#10211yescharacteristic
66C2×AGL(1,𝔽5)—82no—
67C2×AGL(1,𝔽5)—82no—
68C2×AGL(1,𝔽5)—82no—
69C2×C4×C5#9511yescharacteristic
70C2×C4×C5#10611yescharacteristic
71C2×C4×C5#10711yescharacteristic
72C2×Dic5#10211yescharacteristic
73C2×Dic5#10311yescharacteristic
74C2×Dic5#10311yescharacteristic
75C4×D5—22no—
76C4×D5—21no—
77C4×D5—21no—
78C4×D5—41no—
79#170—82no—
80C5×C8—21no—
81C5×C8—21no—
82#168—21no—
83#168—21no—
84C2×M16—201no—
85C22×C8—51no—
86C22×C8—51no—
87C2×C4⋊C4—102no—
88C2×C42—51no—
89C2×C16—21no—
90C2×C16—101no—
91C4⋊C8—102no—
92C4⋊C8—201no—
93C4×C8—51no—
94C4×C8—51no—
95C4×C8—51no—
96C4×C8C2×AGL(1,𝔽5)11yescharacteristic
97#95—201no—
98#95—201no—
99C22×C5#34011yescharacteristic
100C2×D5—21no—
101C2×D5—21no—
102C2×D5#36012yes—
103AGL(1,𝔽5)—162no—
104C4×C5—21no—
105C4×C5—21no—
106C4×C5H(3,ℤ/4)11yescharacteristic
107C4×C5#34411yescharacteristic
108Dic5—21no—
109Dic5—21no—
110Dic5—21no—
111C22×C4—51no—
112C22×C4—51no—
113C22×C4—51no—
114C22×C4—202no—
115M16—402no—
116C2×C8—51no—
117C2×C8—51no—
118C2×C8—201no—
119C2×C8—201no—
120C2×C8—202no—
121C2×C8C4×AGL(1,𝔽5)11yescharacteristic
122C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
123C4⋊C4—202no—
124C4⋊C4—202no—
125C42—51no—
126C42—51no—
127C42—51no—
128C42C4⋊AGL(1,𝔽5)11yescharacteristic
129C16—41no—
130C16—201no—
131C2×C5#128611yescharacteristic
132C2×C5#138611yescharacteristic
133C2×C5#138911yescharacteristic
134D5—22no—
135C23—51no—
136C2×C4—51no—
137C2×C4—51no—
138C2×C4—51no—
139C2×C4—102no—
140C2×C4—101no—
141C2×C4—101no—
142C2×C4—201no—
143C2×C4—402no—
144C2×C4—402no—
145C2×C4—402no—
146C2×C4#399311yescharacteristic
147C2×C4#399411yescharacteristic
148C2×C4(C2×AGL(1,𝔽5))⋊C411yescharacteristic
149C8—21no—
150C8—21no—
151C8—101no—
152C8—101no—
153C8—402no—
154C5#722111yescharacteristic, complemented, Sylow
155C22—52no—
156C22—101no—
157C22—101no—
158C22#6489311yescharacteristic
159C4—21no—
160C4—21no—
161C4—101no—
162C4—101no—
163C4—101no—
164C4—802no—
165C4#6486311yescharacteristic
166C4#6489411yescharacteristic
167C2—102no—
168C2#1059852711yescharacteristic
169C2#1059867511yescharacteristic
170C2#1059867711yescharacteristic
subgroupG/H
centerC22#64893
commutatorC2×C5×C8C42
FrattiniC4×C8C2×AGL(1,𝔽5)
FittingC5×#346C4
socleC22×C5#340
prime radicalC22×D5#102
cosocleC4×C8×D5C22
hypercenter#346AGL(1,𝔽5)
hypocenterC5#7221
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #346

Complements

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

NH ≅ G/Ntype
10. #64883C4semidirect
11. C5×#346C4semidirect
14. #64681C4semidirect
60. #346AGL(1,𝔽5)semidirect
154. C5#7221semidirect

Maximal subgroups

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

subgroupindex
#106038462
#106038172
#105998662
#72215