Finite Group Databasebeta

← #13025321

Subgroups — #13025321

Order 1280.

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

normal subgroups only

This group has 220 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#10604069C211yesmaximal, characteristic, complemented
2#10604062C211yesmaximal, characteristic
3#10600112C211yesmaximal, characteristic
4#10598643C211yesmaximal, characteristic, complemented
5#10598640C211yesmaximal, characteristic, complemented
6#10598608C211yesmaximal, characteristic, complemented
7#10598607C211yesmaximal, characteristic
8#65709—21no—
9#65702—21no—
10C2×#3932C411yescharacteristic
11#65162C2211yescharacteristic
12#65161C2211yescharacteristic
13#64886C2211yescharacteristic
14#64881C2211yescharacteristic
15#64881C2211yescharacteristic
16#64879C2211yescharacteristic
17#64872—21no—
18#64871—21no—
19C5×#366C411yescharacteristic
20#64722C2211yescharacteristic
21#64712C411yescharacteristic
22#64711C411yescharacteristic
23#12077—51nomaximal, Sylow
24C2×D5⋊C8—41no—
25C2×Dic20C2×C411yescharacteristic
26C2×D40C2×C411yescharacteristic
27#4039—21no—
28#4033—21no—
29#4003—41no—
30#4002—41no—
31C4⋊#170—21no—
32C4⋊#170—21no—
33C4⋊#170—41no—
34C4×#170D411yescharacteristic
35C4×#170D411yescharacteristic
36C2×#674—21no—
37C2×C5×C16C2×C411yescharacteristic
38C5×#107C2×C411yescharacteristic
39C5×#107C2×C411yescharacteristic
40C8×Dic5C2311yescharacteristic
41C2×#672C2×C411yescharacteristic
42#3942—21no—
43#3941—21no—
44#3932—22no—
45#2175—51no—
46#1593—51no—
47#1580—51no—
48#1368—51no—
49#1334—51no—
50#1333—51no—
51#1313—51no—
52C2×D20—21no—
53C2×C4×D5—41no—
54C2×Dic10—21no—
55C2×#170—21no—
56C2×#170—21no—
57C2×#170—41no—
58C2×#170—41no—
59D5⋊C8—82no—
60C2×C5×C8C22×C411yescharacteristic
61C5×C4⋊C4—21no—
62C5×C4⋊C4—21no—
63#685—41no—
64#683—41no—
65C4×Dic5—41no—
66C4×Dic5C2×D411yescharacteristic
67C2×#168#4111yescharacteristic
68Dic20—21no—
69Dic20—21no—
70D40—21no—
71D40M1612yes—
72#674—22no—
73C5×C16—21no—
74#672—21no—
75C2×SD32—51no—
76#446—101no—
77C4×Q16—51no—
78C4×D8—51no—
79C8×D4—101no—
80#366AGL(1,𝔽5)11yescharacteristic
81#358—51no—
82#357—51no—
83#346—51no—
84#346—51no—
85#334—51no—
86#334—51no—
87Q8⋊C8—101no—
88D4⋊C8—101no—
89#322—51no—
90C22×D5—41no—
91C2×C4×C5—41no—
92C2×C4×C5—41no—
93C2×C4×C5C4×D411yescharacteristic
94C2×Dic5—41no—
95C2×Dic5AGL(1,ℤ/8)11yescharacteristic
96C2×Dic5AGL(1,ℤ/8)11yescharacteristic
97D20—22no—
98D20—41no—
99C4×D5—81no—
100C4×D5—81no—
101Dic10—41no—
102Dic10—41no—
103#170—41no—
104#170—41no—
105#170—81no—
106#170—81no—
107C5×C8C2×M1611yescharacteristic
108C5×C8#13111yescharacteristic
109#168—21no—
110C2×Q16—51no—
111C2×D8—51no—
112C22×C8—201no—
113C4×Q8—101no—
114C4×D4—101no—
115SD32—102no—
116C2×C16—51no—
117C2×C16—101no—
118C2×C16C2×AGL(1,𝔽5)11yescharacteristic
119#107C2×AGL(1,𝔽5)11yescharacteristic
120#107C2×AGL(1,𝔽5)11yescharacteristic
121C4⋊C8—101no—
122C4⋊C8—101no—
123C4⋊C8—201no—
124#103—101no—
125#102—101no—
126C22⋊C8—201no—
127#97—201no—
128C4×C8—51no—
129C4×C8—51no—
130C4×C8—51no—
131C22×C5#44211yescharacteristic
132C2×D5—42no—
133C2×D5—81no—
134C2×D5—81no—
135C4×C5—81no—
136C4×C5—81no—
137C4×C5#43511yescharacteristic
138C4×C5#44311yescharacteristic
139Dic5—21no—
140Dic5—21no—
141Dic5—81no—
142C2×Q8—101no—
143C2×D4—101no—
144C22×C4—201no—
145Q16—101no—
146Q16—101no—
147D8—52no—
148D8—101no—
149C2×C8—51no—
150C2×C8—101no—
151C2×C8—101no—
152C2×C8—201no—
153C2×C8—201no—
154C2×C8—402no—
155C2×C8C22×AGL(1,𝔽5)11yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—201no—
159C22⋊C4—201no—
160C42—51no—
161C42—201no—
162C16—21no—
163C16—102no—
164C16—101no—
165C2×C5#158611yescharacteristic
166C2×C5#218011yescharacteristic
167C2×C5AGL(1,ℤ/16)11yescharacteristic
168D5—82no—
169C23—201no—
170Q8—201no—
171Q8—201no—
172D4—102no—
173D4—201no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—51no—
177C2×C4—51no—
178C2×C4—201no—
179C2×C4—401no—
180C2×C4—401no—
181C2×C4D4×AGL(1,𝔽5)11yescharacteristic
182C8—101no—
183C8—201no—
184C8—201no—
185C8—401no—
186C8—401no—
187C8D5⋊M1611yescharacteristic
188C8#413311yescharacteristic
189C5#1207711yescharacteristic, complemented, Sylow
190C22—202no—
191C22—401no—
192C22—401no—
193C22#6573111yescharacteristic
194C4—81no—
195C4—81no—
196C4—101no—
197C4—101no—
198C4—401no—
199C4#6570411yescharacteristic
200C4#6574011yescharacteristic
201C2—402no—
202C2#1060406511yescharacteristic
203C2#1060412511yescharacteristic
204C2#1060413811yescharacteristic
subgroupG/H
centerC22#65731
commutatorC2×C5×C8C22×C4
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#366C4
socleC22×C5#442
prime radicalC2×D40C2×C4
cosocleC8×Dic5C23
hypercenter#366AGL(1,𝔽5)
hypocenterC5#12077
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. #10604069C2semidirect
4. #10598643C2semidirect
5. #10598640C2semidirect
6. #10598608C2semidirect
189. C5#12077semidirect

Maximal subgroups

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

subgroupindex
#106040692
#106040622
#106001122
#105986432
#105986402
#105986082
#105986072
#120775