Finite Group Databasebeta

← #12008733

Subgroups — #12008733

Order 1280.

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

normal subgroups only

This group has 284 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#10610351C211yesmaximal, characteristic
2#10599907C212yesmaximal, complemented
3C5×#1320C211yesmaximal, characteristic
4#10598172C211yesmaximal, characteristic
5#10598023C212yesmaximal, complemented
6C2×#4072C411yescharacteristic
7C5×#407C2211yescharacteristic
8#65496C411yescharacteristic
9#65407C411yescharacteristic
10#65407C2211yescharacteristic
11M16×Dic5C411yescharacteristic
12M16×Dic5C2211yescharacteristic
13#65009—22no—
14#65009—22no—
15C5×#349C2212yes—
16#64773C2212yes—
17#64732—22no—
18#64731—22no—
19#11522—51nomaximal, Sylow
20C23×C4×C5C2×C411yescharacteristic
21C2×C5×M16C2×C411yescharacteristic
22C2×C5×M16C2311yescharacteristic
23C2×C22⋊Dic5—21no—
24#4072—21no—
25#4072—21no—
26#4072—22no—
27C2×C4⋊Dic5—21no—
28C2×C4×Dic5C2×C411yescharacteristic
29C2×C4×Dic5C2×C411yescharacteristic
30C2×#681C2×C411yescharacteristic
31C2×#681C2×C411yescharacteristic
32C5×M32—22no—
33C5×C22⋊C8—22no—
34C22⋊#168—22no—
35#3947—21no—
36#3947D412yes—
37#3946—22no—
38#3946—22no—
39C8×Dic5—21no—
40C8×Dic5D412yes—
41#3944—22no—
42#2921—51no—
43#2165—52no—
44#1327—52no—
45#1320—51no—
46#1320D511yescharacteristic
47C24×C5M1611yescharacteristic
48C22×C4×C5—21no—
49C22×C4×C5—21no—
50C22×C4×C5—41no—
51C22×C4×C5—41no—
52C22×C4×C5M1611yescharacteristic
53C22×C4×C5C22×C411yescharacteristic
54C22×Dic5—21no—
55C22×Dic5—21no—
56C5×M16—41no—
57C5×M16—41no—
58C2×C5×C8—21no—
59C2×C5×C8C2×D412yes—
60C22⋊Dic5—22no—
61C22⋊Dic5—22no—
62C4⋊Dic5—22no—
63C4⋊Dic5—22no—
64C4×Dic5—21no—
65C4×Dic5—21no—
66C4×Dic5C22⋊C411yescharacteristic
67C4×Dic5C22⋊C411yescharacteristic
68C4×Dic5M1612yes—
69#681—41no—
70#681—41no—
71C2×#168—21no—
72C2×#168C22⋊C412yes—
73C5×C16—42no—
74#672—42no—
75C2×#117—51no—
76#433—102no—
77#433—102no—
78#423—51no—
79#423—51no—
80#407—51no—
81#407C2×D511yescharacteristic
82C4×M16—51no—
83C4×M16—51no—
84#364—102no—
85#349—52no—
86#349C2×D512yes—
87#347—102no—
88C23×C5—21no—
89C23×C5—41no—
90C23×C5—81no—
91C23×C5C2×M1611yescharacteristic
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—42no—
96C2×C4×C5—41no—
97C2×C4×C5—41no—
98C2×C4×C5—41no—
99C2×C4×C5C2×C22⋊C411yescharacteristic
100C2×C4×C5C2×M1611yescharacteristic
101C2×Dic5—21no—
102C2×Dic5—21no—
103C2×Dic5—22no—
104C2×Dic5—81no—
105C2×Dic5—81no—
106C5×C8—22no—
107C5×C8—41no—
108#168—22no—
109#168—41no—
110C23×C4C4×D511yescharacteristic
111C2×M16—51no—
112C2×M16—51no—
113C2×M16C4×D511yescharacteristic
114C2×M16C22×D511yescharacteristic
115#117—101no—
116#117—101no—
117#117—102no—
118C2×C4⋊C4—101no—
119C2×C22⋊C4—101no—
120C2×C42—51no—
121C2×C42—51no—
122M32—22no—
123M32—102no—
124C4⋊C8—102no—
125C4⋊C8—102no—
126C22⋊C8—22no—
127C22⋊C8—102no—
128#97—52no—
129#97—101no—
130C4×C8—52no—
131C4×C8—101no—
132C22×C5—21no—
133C22×C5—41no—
134C22×C5—42no—
135C22×C5—41no—
136C22×C5—82no—
137C22×C5#40711yescharacteristic
138C4×C5—21no—
139C4×C5—41no—
140C4×C5#41011yescharacteristic
141C4×C5#41311yescharacteristic
142Dic5—41no—
143Dic5—41no—
144Dic5—42no—
145C24#67611yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—101no—
151C22×C4—101no—
152C22×C4#67611yescharacteristic
153C22×C4C2×C4×D511yescharacteristic
154M16—41no—
155M16—41no—
156M16—201no—
157M16—201no—
158C2×C8—21no—
159C2×C8—52no—
160C2×C8—101no—
161C2×C8D4×D512yes—
162C4⋊C4—102no—
163C4⋊C4—102no—
164C22⋊C4—102no—
165C22⋊C4—102no—
166C42—51no—
167C42—51no—
168C42—52no—
169C42—101no—
170C42—101no—
171C16—42no—
172C16—202no—
173C2×C5—21no—
174C2×C5—41no—
175C2×C5—81no—
176C2×C5#146411yescharacteristic
177C23—21no—
178C23—41no—
179C23—81no—
180C23C2×#67611yescharacteristic
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—101no—
189C2×C4—101no—
190C2×C4—102no—
191C2×C4—401no—
192C2×C4—401no—
193C2×C4D5×C22⋊C411yescharacteristic
194C2×C4D5×M1611yescharacteristic
195C8—22no—
196C8—41no—
197C8—102no—
198C8—201no—
199C5#1152211yescharacteristic, complemented, Sylow
200C22—21no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22—82no—
205C22#6501511yescharacteristic
206C4—21no—
207C4—41no—
208C4—201no—
209C4—201no—
210C4—202no—
211C4#6502911yescharacteristic
212C4#6503411yescharacteristic
213C2—21no—
214C2—41no—
215C2—81no—
216C2#1059889511yescharacteristic
subgroupG/H
centerC4#65029
commutatorC22×C4×C5C22×C4
FrattiniC2×M16C22×D5
FittingC5×#1320C2
socleC2×C5#1464
prime radicalC24×C5M16
cosocleC2×C5×M16C23
hypercenter#1320D5
hypocenterC5#11522
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #10599907C2semidirect
5. #10598023C2semidirect
199. C5#11522semidirect

Maximal subgroups

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

subgroupindex
#106103512
#105999072
C5×#13202
#105981722
#105980232
#115225