Finite Group Databasebeta

← #10602057

Subgroups — #10602057

Order 640.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#66064C211yesmaximal, characteristic, complemented
2C5×#492C211yesmaximal, characteristic, complemented
3#65364C211yesmaximal, characteristic, complemented
4#65361C211yesmaximal, characteristic
5#64766C211yesmaximal, characteristic, complemented
6#64679C211yesmaximal, characteristic, complemented
7#64676C211yesmaximal, characteristic, complemented
8C2×C5×SD16—22no—
9C5×C4⋊Q8C2211yescharacteristic
10C5×#127C2211yescharacteristic
11#4092—22no—
12C2×#687—21no—
13C2×#686—21no—
14#4043—21no—
15#4039—21no—
16D5×C4⋊C4—21no—
17#4036—21no—
18C4×D20C2211yescharacteristic
19C4×Dic10C2211yescharacteristic
20C4×C5×C8C2211yescharacteristic
21#3964—21no—
22#3964—21no—
23C4⋊#168C2211yescharacteristic
24C4⋊#168C2211yescharacteristic
25#1622—51nomaximal, Sylow
26C2×C5×Q8D412yes—
27C2×C5×D4—21no—
28C2×C5×D4—21no—
29C2×C5×D4—21no—
30C2×D20D411yescharacteristic
31C2×C4×D5—21no—
32C2×C4×D5—22no—
33C2×Dic10D411yescharacteristic
34C5×SD16—44no—
35C2×C5×C8—21no—
36C5×C4⋊C4—21no—
37C5×C4⋊C4—21no—
38C42×C5C2311yescharacteristic
39#687—42no—
40#686—42no—
41#685—22no—
42#685—21no—
43C4⋊Dic5—22no—
44C4⋊Dic5D411yescharacteristic
45C4⋊Dic5D411yescharacteristic
46#683—22no—
47#683—21no—
48C4×Dic5—21no—
49C2×#168—21no—
50C2×#168—21no—
51#554—51no—
52#492D511yescharacteristic, complemented
53#460—51no—
54#459—51no—
55#333—51no—
56Q8⋊C8—51no—
57D4⋊C8—51no—
58C23×C5—41no—
59C22×D5—21no—
60C5×Q8—42no—
61C5×D4—42no—
62C5×D4—41no—
63C5×D4—41no—
64C5×D4—41no—
65C5×D4—41no—
66C2×C4×C5—22no—
67C2×C4×C5C2×D411yescharacteristic
68C2×C4×C5C2×D411yescharacteristic
69C2×C4×C5C2×D411yescharacteristic
70C2×Dic5—21no—
71C2×Dic5—21no—
72C2×Dic5—21no—
73D20—21no—
74D20SD1612yescomplemented
75C4×D5—41no—
76C4×D5—41no—
77C4×D5—82no—
78Dic10—21no—
79Dic10—21no—
80C5×C8—22no—
81#168—41no—
82#168—41no—
83C2×SD16—22no—
84C2×SD16—101no—
85C2×D8—101no—
86C4⋊Q8C2×D511yescharacteristic
87#127C2×D511yescharacteristic
88#125—101no—
89C22⋊Q8—101no—
90C22⋊Q8—102no—
91C4×Q8—51no—
92C4×D4—51no—
93C4×D4—101no—
94C2×C4⋊C4—101no—
95C4⋊C8—51no—
96C4⋊C8—51no—
97#102—101no—
98#102—101no—
99C4×C8C2×D511yescharacteristic
100C22×C5—81no—
101C22×C5—81no—
102C22×C5—81no—
103C22×C5#12011yescharacteristic
104C2×D5—22no—
105C2×D5—41no—
106C2×D5—41no—
107C4×C5—21no—
108C4×C5—42no—
109C4×C5C2×SD1611yescharacteristic
110C4×C5#13511yescharacteristic
111C4×C5AGL(1,ℤ/8)11yescharacteristic
112C4×C5#13711yescharacteristic
113Dic5—41no—
114Dic5—41no—
115Dic5—41no—
116C2×Q8—51no—
117C2×Q8C22⋊D512yes—
118C2×D4—21no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4—51no—
122C22×C4—102no—
123C22×C4—101no—
124SD16—44no—
125SD16—202no—
126D8—202no—
127C2×C8—21no—
128C2×C8—101no—
129C2×C8—101no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—51no—
133C4⋊C4—51no—
134C4⋊C4—102no—
135C4⋊C4—102no—
136C4⋊C4—101no—
137C22⋊C4—102no—
138C22⋊C4—101no—
139C42—101no—
140C42C22×D511yescharacteristic
141C2×C5—161no—
142C2×C5#44811yescharacteristic
143C2×C5#44911yescharacteristic
144C2×C5#45311yescharacteristic
145D5—42no—
146C23—41no—
147C23—101no—
148Q8—42no—
149Q8—101no—
150Q8—101no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—52no—
157D4—101no—
158C2×C4—22no—
159C2×C4—101no—
160C2×C4—101no—
161C2×C4—101no—
162C2×C4—201no—
163C2×C4—201no—
164C2×C4—402no—
165C2×C4D4×D511yescharacteristic
166C2×C4D4×D511yescharacteristic
167C2×C4C2×C22⋊D511yescharacteristic
168C8—22no—
169C8—201no—
170C8—201no—
171C5#162211yescharacteristic, complemented, Sylow
172C22—81no—
173C22—81no—
174C22—81no—
175C22—102no—
176C22—201no—
177C22—201no—
178C22#408311yescharacteristic
179C4—21no—
180C4—42no—
181C4—201no—
182C4—201no—
183C4—201no—
184C4D5×SD1611yescharacteristic
185C4#406011yescharacteristic
186C4#406111yescharacteristic
187C4#406211yescharacteristic
188C2—161no—
189C2—202no—
190C2#6536611yescharacteristic
191C2#6545911yescharacteristic
192C2#6546111yescharacteristic
subgroupG/H
centerC22#4083
commutator, cosocleC42×C5C23
FrattiniC42C22×D5
FittingC5×#492C2
socleC22×C5#120
prime radical#65361C2
hypercenter#492D5
hypocenterC5#1622
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #66064C2semidirect
2. C5×#492C2semidirect
3. #65364C2semidirect
5. #64766C2semidirect
6. #64679C2semidirect
7. #64676C2semidirect
52. #492D5semidirect
74. D20SD16semidirect
171. C5#1622semidirect

Maximal subgroups

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

subgroupindex
#660642
C5×#4922
#653642
#653612
#647662
#646792
#646762
#16225