Finite Group Databasebeta

← #12008737

Subgroups — #12008737

Order 1280.

280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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#10610380C211yesmaximal, characteristic
2#10599907C212yesmaximal, complemented
3C5×#1321C211yesmaximal, characteristic
4#10598181C211yesmaximal, characteristic
5#10598024C212yesmaximal, complemented
6#41×Dic5C411yescharacteristic
7C5×#408C2211yescharacteristic
8#65523C411yescharacteristic
9#65408C2211yescharacteristic
10M16×Dic5C2211yescharacteristic
11#65391C411yescharacteristic
12C2×#3947C411yescharacteristic
13#65009—22no—
14#65008—22no—
15C5×#349C2212yes—
16#64773C2212yes—
17#64732—22no—
18#64731—22no—
19#11523—51nomaximal, Sylow
20C2×C5×#41C2×C411yescharacteristic
21C2×C5×M16C2311yescharacteristic
22C22×C5×C8C2×C411yescharacteristic
23Q8×Dic5—21no—
24D4×Dic5—21no—
25D4×Dic5—22no—
26#4072—21no—
27#4072C2×C411yescharacteristic
28C2×C4×Dic5—21no—
29C2×C4×Dic5C2×C411yescharacteristic
30C2×#681C2×C411yescharacteristic
31C22×#168C2×C411yescharacteristic
32C5×M32—22no—
33C5×C22⋊C8—22no—
34C22⋊#168—22no—
35#3947—21no—
36#3947—21no—
37#3947D412yes—
38#3946—22no—
39#3946—22no—
40C8×Dic5D412yes—
41#3944—22no—
42#2923—51no—
43#2165—52no—
44#1328—52no—
45#1321—51no—
46#1321D511yescharacteristic
47C5×#41—41no—
48C5×#41—41no—
49C2×C5×Q8M1611yescharacteristic
50C2×C5×D4—21no—
51C2×C5×D4M1611yescharacteristic
52C22×C4×C5—21no—
53C22×C4×C5C22×C411yescharacteristic
54C22×Dic5—22no—
55C22×Dic5—21no—
56C5×M16—41no—
57C2×C5×C8—21no—
58C2×C5×C8—41no—
59C2×C5×C8C2×D412yes—
60C22⋊Dic5—22no—
61C22⋊Dic5M1612yes—
62C4⋊Dic5—22no—
63C4⋊Dic5—21no—
64C4×Dic5—22no—
65C4×Dic5—21no—
66C4×Dic5—21no—
67C4×Dic5C22⋊C411yescharacteristic
68C4×Dic5C22⋊C411yescharacteristic
69#681—41no—
70C2×#168—21no—
71C2×#168—41no—
72C2×#168C22⋊C412yes—
73C5×C16—42no—
74#672—42no—
75C4×#41—51no—
76#433—102no—
77#432—102no—
78#424—51no—
79#424—51no—
80#408—51no—
81#408C2×D511yescharacteristic
82C4×M16—51no—
83C2×#97—51no—
84#364—102no—
85#349—52no—
86#349C2×D512yes—
87#347—102no—
88C23×C5—21no—
89C23×C5C2×M1611yescharacteristic
90C5×Q8—41no—
91C5×D4—41no—
92C5×D4—42no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—41no—
97C2×C4×C5—41no—
98C2×C4×C5C2×C22⋊C411yescharacteristic
99C2×C4×C5C2×M1611yescharacteristic
100C2×Dic5—21no—
101C2×Dic5—22no—
102C2×Dic5—21no—
103C2×Dic5—81no—
104C2×Dic5—82no—
105C5×C8—22no—
106C5×C8—41no—
107#168—22no—
108#168—41no—
109C2×#41C4×D511yescharacteristic
110C2×M16—51no—
111C2×M16C22×D511yescharacteristic
112C22×C8—51no—
113C22×C8C4×D511yescharacteristic
114C4×Q8—101no—
115C4×D4—102no—
116C4×D4—101no—
117#117—51no—
118#117—101no—
119C2×C42—51no—
120C2×C42—101no—
121M32—22no—
122M32—102no—
123C4⋊C8—102no—
124C4⋊C8—102no—
125C22⋊C8—22no—
126C22⋊C8—102no—
127#97—52no—
128#97—101no—
129#97—101no—
130C4×C8—52no—
131C22×C5—21no—
132C22×C5—41no—
133C22×C5—42no—
134C22×C5—41no—
135C22×C5#40711yescharacteristic
136C4×C5—21no—
137C4×C5—41no—
138C4×C5#41011yescharacteristic
139C4×C5#41311yescharacteristic
140Dic5—42no—
141Dic5—41no—
142Dic5—41no—
143#41—41no—
144#41—41no—
145C2×Q8#67611yescharacteristic
146C2×D4—21no—
147C2×D4#67611yescharacteristic
148C22×C4—21no—
149C22×C4—102no—
150C22×C4—101no—
151C22×C4C2×C4×D511yescharacteristic
152M16—41no—
153M16—201no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—52no—
157C2×C8—101no—
158C2×C8—201no—
159C2×C8D4×D512yes—
160C4⋊C4—102no—
161C4⋊C4—101no—
162C22⋊C4—52no—
163C22⋊C4—102no—
164C42—51no—
165C42—51no—
166C42—102no—
167C42—101no—
168C42—101no—
169C16—42no—
170C16—202no—
171C2×C5—21no—
172C2×C5—41no—
173C2×C5—81no—
174C2×C5#146411yescharacteristic
175C23—21no—
176C23D5×M1611yescharacteristic
177Q8—41no—
178D4—41no—
179D4—42no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—101no—
186C2×C4—101no—
187C2×C4—102no—
188C2×C4—401no—
189C2×C4—402no—
190C2×C4D5×C22⋊C411yescharacteristic
191C2×C4C2×#67611yescharacteristic
192C8—22no—
193C8—41no—
194C8—102no—
195C8—201no—
196C5#1152311yescharacteristic, complemented, Sylow
197C22—21no—
198C22—41no—
199C22—42no—
200C22—41no—
201C22#6501511yescharacteristic
202C4—21no—
203C4—41no—
204C4—201no—
205C4—201no—
206C4—202no—
207C4#6502911yescharacteristic
208C4#6503411yescharacteristic
209C2—21no—
210C2—41no—
211C2—81no—
212C2#1059889511yescharacteristic
subgroupG/H
centerC4#65029
commutatorC22×C4×C5C22×C4
FrattiniC2×M16C22×D5
FittingC5×#1321C2
socleC2×C5#1464
prime radicalC2×C5×#41C2×C4
cosocleC2×C5×M16C23
hypercenter#1321D5
hypocenterC5#11523
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #10599907C2semidirect
5. #10598024C2semidirect
196. C5#11523semidirect

Maximal subgroups

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

subgroupindex
#106103802
#105999072
C5×#13212
#105981812
#105980242
#115235